Finite Group Databasebeta

← #33950828

Subgroups — #33950828

Order 18688.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623261C211yesmaximal, characteristic
2#22619008C212yesmaximal, complemented
3#22619003C212yesmaximal, complemented
4#22618999C212yesmaximal, complemented
5#22618996C212yesmaximal, complemented
6#22618989C211yesmaximal, characteristic, complemented
7#22618987C211yesmaximal, characteristic, complemented
8#22618983C211yesmaximal, characteristic, complemented
9#22618981C212yesmaximal, complemented
10#22618977C212yesmaximal, complemented
11#22618660C212yesmaximal, complemented
12#22618657C212yesmaximal, complemented
13#22618631C212yesmaximal, complemented
14#22618622C212yesmaximal, complemented
15#22618587C212yesmaximal, complemented
16#22618381C212yesmaximal, complemented
17#22618373C211yesmaximal, characteristic, complemented
18#408×D73C211yesmaximal, characteristic, complemented
19C73×#2978C211yesmaximal, characteristic, complemented
20C22×#11924028C2211yescharacteristic
21C2×#41×D73C2211yescharacteristic
22C2×#14556599C2212yes—
23C2×#14556599C2212yes—
24C22×#11924011C2211yescharacteristic, complemented
25C2×M16×D73C2211yescharacteristic, complemented
26C2×M16×D73C2211yescharacteristic, complemented
27C22×C8×D73C2211yescharacteristic, complemented
28#17989167C412yes—
29#17989166C412yes—
30#17989160C412yes—
31#17989159C411yescharacteristic
32#17989159C411yescharacteristic
33#17989153C412yes—
34#17989152C411yescharacteristic
35#17989152C411yescharacteristic
36#17989148C411yescharacteristic
37#17989148C411yescharacteristic
38#17989147C411yescharacteristic
39#17989147C411yescharacteristic
40#17989134C2212yes—
41#17989134C2212yes—
42#17989099C2211yescharacteristic
43#17989098C2211yescharacteristic
44#17989096C2212yes—
45#17989096C2212yes—
46#17989094C2211yescharacteristic
47#117×D73C2211yescharacteristic
48#17988666C2212yescomplemented
49#17988664C2212yescomplemented
50#17988663C2212yescomplemented
51#17988663C2212yescomplemented
52#17988663C2212yescomplemented
53#17988662C2212yescomplemented
54#17988661C2212yescomplemented
55#17988660C2212yescomplemented
56#17988660C2212yescomplemented
57#17988659C2212yescomplemented
58#17988659C2212yescomplemented
59#17988658C2212yescomplemented
60#17988657C2212yescomplemented
61#17988657C2212yescomplemented
62#17988656C2212yescomplemented
63#17988656C2212yescomplemented
64#17988656C2212yescomplemented
65#17988655C2212yescomplemented
66#17988655C2212yescomplemented
67#17988655C2212yescomplemented
68C8×D292C2212yescomplemented
69D4×#10596831C2212yescomplemented
70D4×#10596831C2212yescomplemented
71#17988652C2212yescomplemented
72C8×C22⋊D73C2212yescomplemented
73#17988650C2212yescomplemented
74#17988650C2212yescomplemented
75#17988650C2212yescomplemented
76#17988648C2212yescomplemented
77#17988645C2212yescomplemented
78#17988645C2212yescomplemented
79#17988643C2212yescomplemented
80#17988642C2212yescomplemented
81#17988639C2212yescomplemented
82#17988638C2212yescomplemented
83#17988612C2212yescomplemented
84#17988612C2212yescomplemented
85#17988555C2211yescharacteristic, complemented
86#17988555C2211yescharacteristic, complemented
87#17988555C2212yescomplemented
88#17988555C2212yescomplemented
89#17988554C2211yescharacteristic
90#17988554C2211yescharacteristic
91#17988553C2211yescharacteristic, complemented
92#17988553C2211yescharacteristic, complemented
93#17988552C2212yes—
94#17988552C2212yes—
95#17988552C2212yes—
96#17988552C2212yes—
97#17988552C2212yescomplemented
98#17988552C2212yescomplemented
99#17988552C2212yescomplemented
100#17988552C2212yescomplemented
101#17988549C2212yes—
102#17988549C2212yescomplemented
103#17988549C2212yescomplemented
104C2×C22⋊#10596831C2212yescomplemented
105C22⋊C8×D73C2212yes—
106C22⋊C8×D73C2212yescomplemented
107C22⋊C8×D73C2212yescomplemented
108#17988544C2212yescomplemented
109#17988541C2212yescomplemented
110#525×C73C2211yescharacteristic
111#436×C73C2212yescomplemented
112#436×C73C2212yescomplemented
113#435×C73C2212yescomplemented
114#435×C73C2212yescomplemented
115#433×C73C2212yescomplemented
116#408×C73C2211yescharacteristic
117#408×C73C2211yescharacteristic
118#407×C73C2212yescomplemented
119C2×#11924029C2×C411yescharacteristic
120C2×#11924028—42no—
121C2×#11924028—42no—
122C2×#11924028C2×C412yes—
123C2×#11924028C2×C412yes—
124C2×#11924028C2312yes—
125C2×#11924028C2311yescharacteristic
126C2×#11924028C2311yescharacteristic
127C2×#11924028C2312yes—
128C2×#11924028C2311yescharacteristic
129C2×#11924027C2×C411yescharacteristic
130C2×#11924027C2×C411yescharacteristic
131C2×#11924027C2×C411yescharacteristic
132#41×D73—42no—
133#41×D73—42no—
134C22×Dic146C2×C411yescharacteristic
135C2×Q8×D73C2×C411yescharacteristic
136C22×D292C2×C411yescharacteristic
137C22×C22⋊D73C2×C411yescharacteristic
138C22×C22⋊D73C2×C411yescharacteristic
139C2×D4×D73C2×C411yescharacteristic
140C2×D4×D73C2×C411yescharacteristic
141C2×D4×D73C2×C411yescharacteristic
142C22×C4×D73C2311yescharacteristic
143C22×C4×D73C2311yescharacteristic
144C22×C4×D73C2311yescharacteristic
145C22×C4×D73C2311yescharacteristic
146#14556599—44no—
147#14556599—44no—
148C2×#11924012C2311yescharacteristic
149C2×#11924012C2311yescharacteristic
150C2×#11924011—42no—
151C2×#11924011C2312yes—
152C2×#11924011C2312yes—
153C2×#11924011C2312yes—
154C2×#11924011C2312yes—
155C2×#11924011C2312yes—
156C2×#11924011C2312yes—
157M16×D73—42no—
158M16×D73—42no—
159C22×#10596831C2311yescharacteristic
160C22×#10596831C2312yes—
161C22×#10596831C2311yescharacteristic
162C22×#10596831C2312yes—
163C2×C8×D73—42no—
164C2×C8×D73C2312yes—
165C2×C8×D73C2312yes—
166C2×C8×D73C2312yes—
167C2×C8×D73C2312yes—
168C2×C8×D73C2312yes—
169C2×C8×D73C2312yes—
170#14556590C2×C412yes—
171#14556590C2×C412yes—
172#14556587C2×C412yes—
173#14556587C2×C412yes—
174#14556577C2×C412yes—
175#14556577C2×C412yes—
176#14556577C2×C412yes—
177#14556577C2×C412yes—
178#14556576C2×C412yes—
179#14556576C2×C412yes—
180#14556575C2×C411yescharacteristic
181#14556575C2×C411yescharacteristic
182#14556574C2×C411yescharacteristic
183#14556574C2×C411yescharacteristic
184#14556573C2×C412yes—
185#14556573C2×C412yes—
186#14556572C2×C411yescharacteristic
187#14556572C2×C411yescharacteristic
188#14556571C2×C412yes—
189#14556570C2×C412yes—
190#14556569C2×C412yes—
191#14556569C2×C412yes—
192#14556568C2×C412yes—
193#14556568C2×C412yes—
194#14556567C2×C412yes—
195#14556566C2×C412yes—
196#14556566C2×C412yes—
197#14556566C2×C412yes—
198#14556565C2×C412yes—
199#14556564C2×C412yes—
200#14556564C2×C412yes—
201#14556564C2×C412yes—
202#14556564C2×C412yes—
203#14556564C2×C412yes—
204#14556564C2×C412yes—
205#14556563C2×C412yes—
206#14556563C2×C412yes—
207#14556562C2×C412yes—
208#14556562C2×C412yes—
209#14556562C2×C412yes—
210#14556561C2×C411yescharacteristic
211#14556561C2×C411yescharacteristic
212#14556561C2×C412yes—
213#14556561C2×C412yes—
214#14556560C2×C411yescharacteristic
215#14556560C2×C411yescharacteristic
216#14556559C2×C412yes—
217#14556559C2×C412yes—
218#14556559C2×C411yescharacteristic
219#14556559C2×C411yescharacteristic
220C4×D292C2312yes—
221C4×D292C2312yes—
222C4×C22⋊D73C2312yes—
223C4×C22⋊D73C2312yes—
224C4×C22⋊D73C2312yes—
225C4×C22⋊D73C2312yes—
226#14556550C2311yescharacteristic
227#14556549C2×C412yes—
228#14556548C2312yes—
229#14556547C2×C411yescharacteristic
230#14556547C2×C411yescharacteristic
231C4⋊C4×D73C2×C412yes—
232C22⋊C4×D73C2×C411yescharacteristic
233C22⋊C4×D73C2×C411yescharacteristic
234C42×D73C2312yes—
235C4⋊#10596831C2312yes—
236C4⋊#10596831C2312yes—
237#14556520C2312yes—
238#14556520C2312yes—
239#14556520C2312yes—
240#14556520C2312yes—
241C22⋊#10596831C2312yes—
242C22⋊#10596831C2312yes—
243C22⋊#10596831C2312yes—
244C22⋊#10596831C2312yes—
245C22⋊#10596831C2312yes—
246C22⋊#10596831C2312yes—
247#14556503C2312yes—
248#14556503C2312yes—
249#14556503C2312yes—
250#14556503C2312yes—
251#14556503C2312yes—
252#14556503C2312yes—
253#14556503C2312yes—
254#14556503C2312yes—
255#14556503C2312yes—
256#14556503C2312yes—
257#14556503C2312yes—
258#14556503C2312yes—
259#14556502C2312yes—
260#14556501C2312yes—
261#14556501C2312yes—
262C4×#10596831C2312yes—
263C8×Dic73C2312yes—
264C8×Dic73C2312yes—
265C2×#41×C73C2311yescharacteristic
266C23×C4×C73C2311yescharacteristic
267C2×M16×C73C2312yes—
268C2×M16×C73C2312yes—
269C2×M16×C73C2311yescharacteristic
270C2×M16×C73C2311yescharacteristic
271C22×C8×C73C2311yescharacteristic
272C22×C8×C73C2311yescharacteristic
273#123×C73C2×C411yescharacteristic
274#123×C73C2×C411yescharacteristic
275C22⋊Q8×C73C2×C412yes—
276#121×C73C2×C412yes—
277#120×C73C2×C411yescharacteristic
278#120×C73C2×C411yescharacteristic
279C4×D4×C73C2312yes—
280C4×D4×C73C2312yes—
281#117×C73C2311yescharacteristic
282C4⋊C8×C73C2312yes—
283C4⋊C8×C73C2312yes—
284C22⋊C8×C73C2312yes—
285C22⋊C8×C73C2312yes—
286C22⋊C8×C73C2312yes—
287C22⋊C8×C73C2312yes—
288C22⋊C8×C73C2312yes—
289C22⋊C8×C73C2312yes—
290#97×C73C2312yes—
291C4×C8×C73C2312yes—
292C23×D73C22×C411yescharacteristic
293C23×D73C22×C411yescharacteristic
294C23×D73C22×C411yescharacteristic
295C23×D73C22×C411yescharacteristic
296#11924029—42no—
297#11924028—24no—
298#11924028—24no—
299#11924028—44no—
300#11924028—41no—
301#11924028—41no—
302#11924028—41no—
303#11924028—41no—
304#11924028—41no—
305#11924028—41no—
306#11924028—42no—
307#11924028—42no—
308#11924028—44no—
309#11924027—42no—
310#11924027—42no—
311#11924027—42no—
312C2×Dic146—42no—
313C2×Dic146C22×C412yes—
314C2×Dic146C22×C411yescharacteristic
315C2×Dic146C22×C411yescharacteristic
316C2×Dic146C22×C411yescharacteristic
317C2×Dic146C22×C412yes—
318Q8×D73—42no—
319C2×D292—42no—
320C2×D292C22×C412yes—
321C2×D292C22×C412yes—
322C2×D292C22×C412yes—
323C2×D292C22×C411yescharacteristic
324C2×D292C22×C411yescharacteristic
325C2×D292C22×C412yes—
326C2×D292C22×C411yescharacteristic
327C2×C22⋊D73—42no—
328C2×C22⋊D73—42no—
329C2×C22⋊D73C22×C412yes—
330C2×C22⋊D73C22×C412yes—
331C2×C22⋊D73C22×C412yes—
332C2×C22⋊D73C22×C412yes—
333C2×C22⋊D73C22×C412yes—
334C2×C22⋊D73C22×C412yes—
335C2×C22⋊D73C22×C411yescharacteristic
336C2×C22⋊D73C22×C411yescharacteristic
337C2×C22⋊D73C22×C411yescharacteristic
338C2×C22⋊D73C22×C411yescharacteristic
339C2×C22⋊D73C22×C412yes—
340C2×C22⋊D73C22×C411yescharacteristic
341C2×C22⋊D73C22×C411yescharacteristic
342C2×C22⋊D73C22×C412yes—
343D4×D73—42no—
344D4×D73—42no—
345D4×D73—42no—
346C22×Dic73C22×C411yescharacteristic
347C22×Dic73C22×C411yescharacteristic
348C22×Dic73C22×C411yescharacteristic
349C22×Dic73C22×C411yescharacteristic
350C2×C4×D73—22no—
351C2×C4×D73—22no—
352C2×C4×D73—22no—
353C2×C4×D73—22no—
354C2×C4×D73—22no—
355C2×C4×D73—22no—
356C2×C4×D73—41no—
357C2×C4×D73—41no—
358C2×C4×D73C22×C411yescharacteristic
359C2×C4×D73C22×C411yescharacteristic
360C2×C4×D73C22×C411yescharacteristic
361C2×C4×D73C22×C411yescharacteristic
362C2×C4×D73C22×C411yescharacteristic
363C2×C4×D73C22×C411yescharacteristic
364C2×C4×D73C22×C412yes—
365C2×C4×D73C22×C412yes—
366C2×C4×D73C22×C412yes—
367C2×C4×D73C2411yescharacteristic
368C2×C4×D73C2411yescharacteristic
369C2×C4×D73C2411yescharacteristic
370C2×C4×D73C2412yes—
371C2×C4×D73C2411yescharacteristic
372#11924012—41no—
373#11924012—41no—
374#11924011—24no—
375#11924011—24no—
376#11924011—42no—
377#11924011—42no—
378#11924011—42no—
379#11924011—42no—
380C2×#10596831—41no—
381C2×#10596831—41no—
382C2×#10596831—42no—
383C2×#10596831—42no—
384C2×#10596831C2412yes—
385C2×#10596831C2412yes—
386C2×#10596831C2412yes—
387C2×#10596831C2412yes—
388C8×D73—24no—
389C8×D73—24no—
390C8×D73—42no—
391C8×D73—42no—
392C8×D73—42no—
393C8×D73—42no—
394C4⋊Dic73C22×C412yes—
395C4⋊Dic73C22×C412yes—
396C4⋊Dic73C22×C412yes—
397#11924007C22×C412yes—
398#11924007C22×C412yes—
399#11924007C22×C412yes—
400#11924007C22×C412yes—
401#11924007C22×C412yes—
402#11924007C22×C412yes—
403C22⋊Dic73C22×C411yescharacteristic
404C22⋊Dic73C22×C411yescharacteristic
405C22⋊Dic73C22×C412yes—
406C22⋊Dic73C22×C412yes—
407C22⋊Dic73C22×C412yes—
408C22⋊Dic73C22×C412yes—
409#11924005C22×C412yes—
410#11924005C22×C412yes—
411#11924005C22×C412yes—
412#11924005C22×C412yes—
413#11924005C22×C412yes—
414#11924005C22×C412yes—
415#11924005C22×C412yes—
416#11924005C22×C412yes—
417#11924005C22×C412yes—
418#11924005C22×C412yes—
419C4×Dic73C22×C412yes—
420C4×Dic73C22×C412yes—
421C4×Dic73C2412yes—
422C24×C73C22×C411yescharacteristic
423#41×C73—41no—
424#41×C73—41no—
425C2×Q8×C73C22×C411yescharacteristic
426C2×D4×C73C22×C412yes—
427C2×D4×C73C22×C412yes—
428C2×D4×C73C22×C411yescharacteristic
429C2×D4×C73C22×C411yescharacteristic
430C2×D4×C73C22×C411yescharacteristic
431C22×C4×C73—41no—
432C22×C4×C73—41no—
433C22×C4×C73C22×C412yes—
434C22×C4×C73C22×C411yescharacteristic
435C22×C4×C73C2411yescharacteristic
436C22×C4×C73C2411yescharacteristic
437C22×C4×C73C2411yescharacteristic
438C22×C4×C73C2412yes—
439M16×C73—41no—
440M16×C73—41no—
441M16×C73—42no—
442M16×C73—42no—
443C2×C8×C73—41no—
444C2×C8×C73—41no—
445C2×C8×C73C2412yes—
446C2×C8×C73C2412yes—
447C2×C8×C73C2412yes—
448C2×C8×C73C2412yes—
449C4⋊C4×C73C22×C412yes—
450C4⋊C4×C73C22×C412yes—
451C4⋊C4×C73C22×C412yes—
452C22⋊C4×C73C22×C411yescharacteristic
453C22⋊C4×C73C22×C411yescharacteristic
454C22⋊C4×C73C22×C412yes—
455C22⋊C4×C73C22×C412yes—
456C22⋊C4×C73C22×C412yes—
457C22⋊C4×C73C22×C412yes—
458C42×C73C2412yes—
459C23×C73—41no—
460C23×C73—42no—
461C23×C73C23×C411yescharacteristic
462C23×C73C23×C412yes—
463C23×C73C23×C411yescharacteristic
464C23×C73C23×C411yescharacteristic
465C22×D73—22no—
466C22×D73—22no—
467C22×D73—22no—
468C22×D73—42no—
469C22×D73—41no—
470C22×D73—42no—
471C22×D73—42no—
472C22×D73—42no—
473C22×D73C23×C411yescharacteristic
474C22×D73C23×C411yescharacteristic
475C22×D73C23×C412yes—
476C22×D73C23×C411yescharacteristic
477C22×D73C23×C411yescharacteristic
478Q8×C73—41no—
479D4×C73—42no—
480D4×C73—42no—
481D4×C73—41no—
482D4×C73—41no—
483D4×C73—41no—
484C2×C4×C73—21no—
485C2×C4×C73—21no—
486C2×C4×C73—22no—
487C2×C4×C73—22no—
488C2×C4×C73—21no—
489C2×C4×C73—21no—
490C2×C4×C73—21no—
491C2×C4×C73—21no—
492C2×C4×C73—41no—
493C2×C4×C73—42no—
494C2×C4×C73C23×C412yes—
495C2×C4×C73C23×C412yes—
496C2×C4×C73C23×C412yes—
497C2×C4×C73C23×C411yescharacteristic
498C2×C4×C73C23×C411yescharacteristic
499C2×C4×C73C23×C411yescharacteristic
500C2×C4×C73C2511yescharacteristic
501C22⋊D73—24no—
502C22⋊D73—24no—
503C22⋊D73—41no—
504C22⋊D73—41no—
505C22⋊D73—41no—
506C22⋊D73—41no—
507C22⋊D73—41no—
508C22⋊D73—41no—
509C22⋊D73—42no—
510C22⋊D73—42no—
511C22⋊D73—42no—
512C22⋊D73—42no—
513C22⋊D73—42no—
514C22⋊D73—42no—
515C2×Dic73—22no—
516C2×Dic73—22no—
517C2×Dic73—22no—
518C2×Dic73—41no—
519C2×Dic73C23×C411yescharacteristic
520C2×Dic73C23×C412yes—
521C2×Dic73C23×C412yes—
522C2×Dic73C23×C412yes—
523C2×Dic73C23×C411yescharacteristic
524C2×Dic73C23×C411yescharacteristic
525C2×Dic73C23×C411yescharacteristic
526D292—24no—
527D292—41no—
528D292—41no—
529D292—41no—
530D292—42no—
531D292—42no—
532D292—42no—
533C4×D73—22no—
534C4×D73—22no—
535C4×D73—22no—
536C4×D73—21no—
537C4×D73—21no—
538C4×D73—22no—
539C4×D73—22no—
540C4×D73—21no—
541C4×D73—21no—
542C4×D73—21no—
543C4×D73—21no—
544C4×D73—22no—
545C4×D73—22no—
546C4×D73—22no—
547C4×D73—42no—
548C4×D73—42no—
549C4×D73—42no—
550C4×D73H(5,𝔽2)12yes—
551C4×D73H(5,𝔽2)12yes—
552Dic146—24no—
553Dic146—41no—
554Dic146—41no—
555Dic146—41no—
556Dic146—42no—
557C8×C73—22no—
558C8×C73—22no—
559C8×C73—22no—
560C8×C73—22no—
561#10596831—22no—
562#10596831—22no—
563#10596831—22no—
564#10596831—22no—
565C22×C73—21no—
566C22×C73—21no—
567C22×C73—21no—
568C22×C73—22no—
569C22×C73—22no—
570C22×C73—22no—
571C22×C73—22no—
572C22×C73—22no—
573C22×C73—22no—
574C22×C73—82no—
575C22×C73C24×C411yescharacteristic
576C2×D73—22no—
577C2×D73—21no—
578C2×D73—21no—
579C2×D73—21no—
580C2×D73—22no—
581C2×D73—22no—
582C2×D73—22no—
583C2×D73—22no—
584C2×D73—22no—
585C2×D73—22no—
586C2×D73—44no—
587C2×D73—82no—
588C2×D73—82no—
589C2×D73—82no—
590C2×D73#51812yes—
591C4×C73—22no—
592C4×C73—21no—
593C4×C73—21no—
594C4×C73—21no—
595C4×C73—22no—
596C4×C73—22no—
597C4×C73C2×H(5,𝔽2)11yescharacteristic
598C4×C73C2×H(5,𝔽2)11yescharacteristic
599Dic73—22no—
600Dic73—21no—
601Dic73—21no—
602Dic73—21no—
603Dic73—22no—
604Dic73—22no—
605Dic73#51812yes—
606#60235—731nomaximal, Sylow
607C2×C73—41no—
608C2×C73—41no—
609C2×C73—41no—
610C2×C73—42no—
611C2×C73C2×#51811yescharacteristic
612C2×C73#357312yes—
613D73—22no—
614D73—41no—
615D73—41no—
616D73—41no—
617D73—42no—
618#3449—731no—
619#2981—732no—
620#2981—732no—
621#2980—732no—
622#2979—732no—
623#2978—731no—
624#2978D7311yescharacteristic, complemented
625#2977—731no—
626#2977—731no—
627#2976—732no—
628#2976—732no—
629#2933—732no—
630#2933—732no—
631#2930—732no—
632#2929—732no—
633#2924—732no—
634#2880—732no—
635#2879—731no—
636C2×#408—731no—
637C73#6023511yescharacteristic, complemented, Sylow
638C22×#41—731no—
639C22×#41—731no—
640C2×#131—732no—
641C2×#131—732no—
642C22×M16—731no—
643C22×M16—731no—
644C22×M16—731no—
645C23×C8—731no—
646#537—732no—
647#537—732no—
648#536—731no—
649#536—731no—
650#536—732no—
651#535—732no—
652#535—731no—
653#535—731no—
654#534—731no—
655#534—731no—
656#534—731no—
657#534—731no—
658#532—732no—
659#532—732no—
660#525—731no—
661#525—731no—
662#525—732no—
663#525—732no—
664#525—731no—
665#525C2×D7311yescharacteristic
666C2×#117—731no—
667#436—732no—
668#436—732no—
669#436—732no—
670#436—732no—
671#436—732no—
672#436—732no—
673#436C2×D7312yescomplemented
674#436C2×D7312yescomplemented
675#435—732no—
676#435—732no—
677#435—732no—
678#435—732no—
679#435—732no—
680#435—732no—
681#435—732no—
682#435—732no—
683#435—732no—
684#435—732no—
685#435—732no—
686#435—732no—
687#435—732no—
688#435—732no—
689#435C2×D7312yescomplemented
690#435C2×D7312yescomplemented
691C8×D4—732no—
692C8×D4—732no—
693C8×D4—732no—
694C8×D4—732no—
695C8×D4—732no—
696C8×D4—732no—
697C8×D4—732no—
698C8×D4—732no—
699#433—732no—
700#433—732no—
701#433—732no—
702#433C2×D7312yescomplemented
703#432—732no—
704#432—732no—
705#431—732no—
706#431—732no—
707#424—732no—
708#424—732no—
709#408—731no—
710#408—731no—
711#408—731no—
712#408—731no—
713#408—732no—
714#408—732no—
715#408—731no—
716#408—731no—
717#408—732no—
718#408—732no—
719#408—732no—
720#408—732no—
721#408—732no—
722#408—732no—
723#408—732no—
724#408—732no—
725#408C2×D7311yescharacteristic
726#408C2×D7311yescharacteristic
727#407—732no—
728#407—732no—
729#407—732no—
730#407C2×D7312yescomplemented
731C2×C22⋊C8—732no—
732C2×C22⋊C8—732no—
733C2×C22⋊C8—732no—
734C2×C22⋊C8—732no—
735#405—732no—
736#405—732no—
737C2×#41—2922no—
738C2×#41—2922no—
739C2×#41—2922no—
740C2×#41—2922no—
741C2×#41—731no—
742C2×#41—731no—
743C2×#41—731no—
744C2×#41—731no—
745C2×#41—732no—
746C2×#41—732no—
747C2×#41—731no—
748C2×#41—732no—
749C2×#41—731no—
750C2×#41—731no—
751C2×#41—732no—
752C2×#41C22×D7311yescharacteristic
753C22×Q8—731no—
754C22×Q8—731no—
755C22×D4—731no—
756C22×D4—731no—
757C22×D4—731no—
758C22×D4—731no—
759C22×D4—731no—
760C22×D4—731no—
761C23×C4—731no—
762C23×C4—731no—
763C23×C4—731no—
764C23×C4—731no—
765C23×C4C22×D7311yescharacteristic
766#131—2924no—
767#131—2924no—
768C2×M16—2922no—
769C2×M16—2922no—
770C2×M16—2922no—
771C2×M16—731no—
772C2×M16—731no—
773C2×M16—732no—
774C2×M16—732no—
775C2×M16—732no—
776C2×M16—732no—
777C2×M16—732no—
778C2×M16—732no—
779C2×M16C22×D7311yescharacteristic
780C2×M16C22×D7311yescharacteristic
781C2×M16C22×D7312yes—
782C2×M16C22×D7312yes—
783C22×C8—2922no—
784C22×C8—731no—
785C22×C8—731no—
786C22×C8—732no—
787C22×C8—732no—
788C22×C8—732no—
789C22×C8—732no—
790C22×C8—732no—
791C22×C8—732no—
792C22×C8—732no—
793C22×C8—732no—
794C22×C8C22×D7311yescharacteristic
795C22×C8C22×D7311yescharacteristic
796C4⋊Q8—732no—
797C4⋊Q8—732no—
798#127—732no—
799#127—732no—
800#124—732no—
801#124—732no—
802#124—732no—
803#124—732no—
804#123—731no—
805#123—731no—
806#123—731no—
807#123—731no—
808#123—732no—
809#123—732no—
810#123—732no—
811#123—732no—
812#123—731no—
813#123—731no—
814#123C4×D7311yescharacteristic
815#123C4×D7311yescharacteristic
816C22⋊Q8—732no—
817C22⋊Q8—732no—
818C22⋊Q8—732no—
819C22⋊Q8—732no—
820C22⋊Q8—732no—
821C22⋊Q8—732no—
822C22⋊Q8—732no—
823C22⋊Q8C4×D7312yes—
824#121—732no—
825#121—732no—
826#121—732no—
827#121—732no—
828#121—732no—
829#121—732no—
830#121—732no—
831#121—732no—
832#121—732no—
833#121—732no—
834#121—732no—
835#121—732no—
836#121—732no—
837#121—732no—
838#121—732no—
839#121C4×D7312yes—
840#120—731no—
841#120—731no—
842#120—731no—
843#120—731no—
844#120—732no—
845#120—732no—
846#120—732no—
847#120—732no—
848#120—731no—
849#120—731no—
850#120C4×D7311yescharacteristic
851#120C4×D7311yescharacteristic
852C4×D4—732no—
853C4×D4—732no—
854C4×D4—732no—
855C4×D4—732no—
856C4×D4—732no—
857C4×D4—732no—
858C4×D4C22×D7312yes—
859C4×D4C22×D7312yes—
860#117—731no—
861#117—732no—
862#117—731no—
863#117—731no—
864#117—732no—
865#117C22×D7311yescharacteristic
866C2×C4⋊C4—732no—
867C2×C22⋊C4—731no—
868C2×C22⋊C4—731no—
869C2×C42—732no—
870C4⋊C8—732no—
871C4⋊C8—732no—
872C4⋊C8—732no—
873C4⋊C8—732no—
874C4⋊C8—732no—
875C4⋊C8—732no—
876C4⋊C8C22×D7312yes—
877C4⋊C8C22×D7312yes—
878C22⋊C8—732no—
879C22⋊C8—732no—
880C22⋊C8—732no—
881C22⋊C8—732no—
882C22⋊C8—732no—
883C22⋊C8—732no—
884C22⋊C8—732no—
885C22⋊C8—732no—
886C22⋊C8—732no—
887C22⋊C8—732no—
888C22⋊C8—732no—
889C22⋊C8—732no—
890C22⋊C8—732no—
891C22⋊C8—732no—
892C22⋊C8—732no—
893C22⋊C8—732no—
894C22⋊C8—732no—
895C22⋊C8—732no—
896C22⋊C8C22×D7312yes—
897C22⋊C8C22×D7312yes—
898C22⋊C8C22×D7312yes—
899C22⋊C8C22×D7312yes—
900C22⋊C8C22×D7312yes—
901C22⋊C8C22×D7312yes—
902#97—732no—
903#97—732no—
904#97—732no—
905#97C22×D7312yes—
906C4×C8—732no—
907C4×C8—732no—
908C4×C8—732no—
909C4×C8C22×D7312yes—
910C24—731no—
911C24—731no—
912C24—731no—
913C24—731no—
914C24C2×C4×D7311yescharacteristic
915#41—41no—
916#41—41no—
917#41—2921no—
918#41—2921no—
919#41—2922no—
920#41—2922no—
921#41—2921no—
922#41—2921no—
923#41—2921no—
924#41—2921no—
925#41—2924no—
926#41—2924no—
927#41—2922no—
928#41—2922no—
929#41—2922no—
930#41—2922no—
931#41—1464no—
932#41—1464no—
933C2×Q8—2922no—
934C2×Q8—2922no—
935C2×Q8—731no—
936C2×Q8—731no—
937C2×Q8—731no—
938C2×Q8—732no—
939C2×Q8—732no—
940C2×Q8C2×C4×D7311yescharacteristic
941C2×D4—2922no—
942C2×D4—2922no—
943C2×D4—2922no—
944C2×D4—2922no—
945C2×D4—2922no—
946C2×D4—2922no—
947C2×D4—732no—
948C2×D4—732no—
949C2×D4—732no—
950C2×D4—732no—
951C2×D4—731no—
952C2×D4—731no—
953C2×D4—731no—
954C2×D4—731no—
955C2×D4—732no—
956C2×D4—731no—
957C2×D4—731no—
958C2×D4—732no—
959C2×D4—732no—
960C2×D4—732no—
961C2×D4—732no—
962C2×D4—732no—
963C2×D4—731no—
964C2×D4—731no—
965C2×D4—732no—
966C2×D4—731no—
967C2×D4—732no—
968C2×D4C2×C4×D7312yes—
969C2×D4C2×C4×D7312yes—
970C2×D4C2×C4×D7311yescharacteristic
971C2×D4C2×C4×D7311yescharacteristic
972C2×D4C2×C4×D7311yescharacteristic
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—2921no—
976C22×C4—2921no—
977C22×C4—731no—
978C22×C4—732no—
979C22×C4—732no—
980C22×C4—732no—
981C22×C4—731no—
982C22×C4—731no—
983C22×C4—731no—
984C22×C4—731no—
985C22×C4—731no—
986C22×C4—731no—
987C22×C4—731no—
988C22×C4—731no—
989C22×C4—731no—
990C22×C4—731no—
991C22×C4—731no—
992C22×C4—731no—
993C22×C4—731no—
994C22×C4—732no—
995C22×C4—1462no—
996C22×C4—1462no—
997C22×C4—1462no—
998C22×C4—1462no—
999C22×C4—1462no—
1000C22×C4—1462no—
1001C22×C4C2×C4×D7312yes—
1002C22×C4C2×C4×D7311yescharacteristic
1003C22×C4C23×D7311yescharacteristic
1004C22×C4C23×D7312yes—
1005C22×C4C23×D7311yescharacteristic
1006C22×C4C23×D7311yescharacteristic
1007M16—41no—
1008M16—41no—
1009M16—42no—
1010M16—42no—
1011M16—2922no—
1012M16—2922no—
1013M16—2922no—
1014M16—2922no—
1015M16—2921no—
1016M16—2921no—
1017M16—1464no—
1018M16—1464no—
1019C2×C8—41no—
1020C2×C8—41no—
1021C2×C8—2922no—
1022C2×C8—2922no—
1023C2×C8—2922no—
1024C2×C8—2922no—
1025C2×C8—2921no—
1026C2×C8—2921no—
1027C2×C8—2922no—
1028C2×C8—2922no—
1029C2×C8—732no—
1030C2×C8—732no—
1031C2×C8—732no—
1032C2×C8—732no—
1033C2×C8—1464no—
1034C2×C8—1464no—
1035C2×C8C23×D7312yes—
1036C2×C8C23×D7312yes—
1037C2×C8C23×D7312yes—
1038C2×C8C23×D7312yes—
1039C4⋊C4—732no—
1040C4⋊C4—732no—
1041C4⋊C4—732no—
1042C4⋊C4—732no—
1043C4⋊C4—732no—
1044C4⋊C4—732no—
1045C4⋊C4—732no—
1046C4⋊C4—732no—
1047C4⋊C4—732no—
1048C4⋊C4C2×C4×D7312yes—
1049C4⋊C4C2×C4×D7312yes—
1050C4⋊C4C2×C4×D7312yes—
1051C22⋊C4—731no—
1052C22⋊C4—731no—
1053C22⋊C4—732no—
1054C22⋊C4—732no—
1055C22⋊C4—732no—
1056C22⋊C4—732no—
1057C22⋊C4—732no—
1058C22⋊C4—732no—
1059C22⋊C4—732no—
1060C22⋊C4—732no—
1061C22⋊C4—732no—
1062C22⋊C4—732no—
1063C22⋊C4—732no—
1064C22⋊C4—732no—
1065C22⋊C4—732no—
1066C22⋊C4—732no—
1067C22⋊C4C2×C4×D7311yescharacteristic
1068C22⋊C4C2×C4×D7311yescharacteristic
1069C22⋊C4C2×C4×D7312yes—
1070C22⋊C4C2×C4×D7312yes—
1071C22⋊C4C2×C4×D7312yes—
1072C22⋊C4C2×C4×D7312yes—
1073C42—732no—
1074C42—732no—
1075C42—732no—
1076C42C23×D7312yes—
1077C23—41no—
1078C23—42no—
1079C23—2922no—
1080C23—2921no—
1081C23—2922no—
1082C23—2922no—
1083C23—2922no—
1084C23—731no—
1085C23—732no—
1086C23—731no—
1087C23—731no—
1088C23—731no—
1089C23—1462no—
1090C23—1462no—
1091C23—1462no—
1092C23C22×C4×D7311yescharacteristic
1093C23C22×C4×D7311yescharacteristic
1094C23C22×C4×D7311yescharacteristic
1095C23C22×C4×D7312yes—
1096Q8—41no—
1097Q8—2921no—
1098Q8—2922no—
1099Q8—2921no—
1100Q8—2921no—
1101Q8—1464no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—42no—
1106D4—42no—
1107D4—2921no—
1108D4—2922no—
1109D4—2921no—
1110D4—2921no—
1111D4—2922no—
1112D4—2922no—
1113D4—2922no—
1114D4—2922no—
1115D4—2921no—
1116D4—2921no—
1117D4—2921no—
1118D4—2921no—
1119D4—2921no—
1120D4—2921no—
1121D4—2922no—
1122D4—2922no—
1123D4—2922no—
1124D4—2922no—
1125D4—1464no—
1126D4—1464no—
1127D4—1464no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—2922no—
1139C2×C4—2922no—
1140C2×C4—2922no—
1141C2×C4—2921no—
1142C2×C4—731no—
1143C2×C4—732no—
1144C2×C4—732no—
1145C2×C4—731no—
1146C2×C4—732no—
1147C2×C4—732no—
1148C2×C4—732no—
1149C2×C4—731no—
1150C2×C4—731no—
1151C2×C4—1462no—
1152C2×C4—1462no—
1153C2×C4—1462no—
1154C2×C4—1462no—
1155C2×C4—1462no—
1156C2×C4—1462no—
1157C2×C4—1462no—
1158C2×C4—1462no—
1159C2×C4—1462no—
1160C2×C4—1461no—
1161C2×C4—1461no—
1162C2×C4—1462no—
1163C2×C4—1462no—
1164C2×C4—1461no—
1165C2×C4—1461no—
1166C2×C4—1461no—
1167C2×C4—1461no—
1168C2×C4C22×C4×D7312yes—
1169C2×C4C22×C4×D7312yes—
1170C2×C4C22×C4×D7311yescharacteristic
1171C2×C4C22×C4×D7311yescharacteristic
1172C2×C4C22×C4×D7312yes—
1173C2×C4C22×C4×D7311yescharacteristic
1174C2×C4C24×D7311yescharacteristic
1175C8—22no—
1176C8—22no—
1177C8—22no—
1178C8—22no—
1179C8—1462no—
1180C8—1462no—
1181C8—1462no—
1182C8—1462no—
1183C22—22no—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—21no—
1189C22—22no—
1190C22—21no—
1191C22—21no—
1192C22—82no—
1193C22—2924no—
1194C22—5842no—
1195C22—5842no—
1196C22—5842no—
1197C22—732no—
1198C22—1462no—
1199C22—1462no—
1200C22—1462no—
1201C22—1462no—
1202C22—1462no—
1203C22—1462no—
1204C22—1461no—
1205C22—1461no—
1206C22—1461no—
1207C22—1462no—
1208C22C23×C4×D7311yescharacteristic
1209C4—22no—
1210C4—22no—
1211C4—21no—
1212C4—22no—
1213C4—21no—
1214C4—21no—
1215C4—732no—
1216C4—1462no—
1217C4—1462no—
1218C4—1462no—
1219C4—1461no—
1220C4—1461no—
1221C4—1461no—
1222C4H(5,𝔽2)×D7311yescharacteristic
1223C4H(5,𝔽2)×D7311yescharacteristic
1224C2—41no—
1225C2—42no—
1226C2—41no—
1227C2—41no—
1228C2—2921no—
1229C2—2922no—
1230C2—2921no—
1231C2—2921no—
1232C2—1462no—
1233C2#518×D7311yescharacteristic
1234C2#2262464412yes—
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2978C2
prime radical#22623261C2
cosocleC2×C4×C73C25
hypercenter#2978D73
hypocenterC73#60235
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2978

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22619008C2semidirect
3. #22619003C2semidirect
4. #22618999C2semidirect
5. #22618996C2semidirect
6. #22618989C2semidirect
7. #22618987C2semidirect
8. #22618983C2semidirect
9. #22618981C2semidirect
10. #22618977C2semidirect
11. #22618660C2semidirect
12. #22618657C2semidirect
13. #22618631C2semidirect
14. #22618622C2semidirect
15. #22618587C2semidirect
16. #22618381C2semidirect
17. #22618373C2semidirect
18. #408×D73C2semidirect
19. C73×#2978C2semidirect
24. C22×#11924011C22semidirect
25. C2×M16×D73C22semidirect
26. C2×M16×D73C22semidirect
27. C22×C8×D73C22semidirect
48. #17988666C22semidirect
49. #17988664C22semidirect
50. #17988663C22semidirect
51. #17988663C22semidirect
52. #17988663C22semidirect
53. #17988662C22semidirect
54. #17988661C22semidirect
55. #17988660C22semidirect
56. #17988660C22semidirect
57. #17988659C22semidirect
58. #17988659C22semidirect
59. #17988658C22semidirect
60. #17988657C22semidirect
61. #17988657C22semidirect
62. #17988656C22semidirect
63. #17988656C22semidirect
64. #17988656C22semidirect
65. #17988655C22semidirect
66. #17988655C22semidirect
67. #17988655C22semidirect
68. C8×D292C22semidirect
69. D4×#10596831C22semidirect
70. D4×#10596831C22semidirect
71. #17988652C22semidirect
72. C8×C22⋊D73C22semidirect
73. #17988650C22semidirect
74. #17988650C22semidirect
75. #17988650C22semidirect
76. #17988648C22semidirect
77. #17988645C22semidirect
78. #17988645C22semidirect
79. #17988643C22semidirect
80. #17988642C22semidirect
81. #17988639C22semidirect
82. #17988638C22semidirect
83. #17988612C22semidirect
84. #17988612C22semidirect
85. #17988555C22semidirect
86. #17988555C22semidirect
87. #17988555C22semidirect
88. #17988555C22semidirect
91. #17988553C22semidirect
92. #17988553C22semidirect
97. #17988552C22semidirect
98. #17988552C22semidirect
99. #17988552C22semidirect
100. #17988552C22semidirect
102. #17988549C22semidirect
103. #17988549C22semidirect
104. C2×C22⋊#10596831C22semidirect
106. C22⋊C8×D73C22semidirect
107. C22⋊C8×D73C22semidirect
108. #17988544C22semidirect
109. #17988541C22semidirect
111. #436×C73C22semidirect
112. #436×C73C22semidirect
113. #435×C73C22semidirect
114. #435×C73C22semidirect
115. #433×C73C22semidirect
118. #407×C73C22semidirect
624. #2978D73semidirect
637. C73#60235semidirect
673. #436C2×D73semidirect
674. #436C2×D73semidirect
689. #435C2×D73semidirect
690. #435C2×D73semidirect
702. #433C2×D73semidirect
730. #407C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226232612
#226190082
#226190032
#226189992
#226189962
#226189892
#226189872
#226189832
#226189812
#226189772
#226186602
#226186572
#226186312
#226186222
#226185872
#226183812
#226183732
#408×D732
C73×#29782
#6023573