Finite Group Databasebeta

← #33053598

Subgroups — #33053598

Order 18688.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623666C211yesmaximal, characteristic
2#22612791C211yesmaximal, characteristic, complemented
3#22608509C211yesmaximal, characteristic, complemented
4#22608492C211yesmaximal, characteristic, complemented
5#22608488C211yesmaximal, characteristic, complemented
6#22608479C211yesmaximal, characteristic, complemented
7#22608470C211yesmaximal, characteristic, complemented
8#22608461C211yesmaximal, characteristic, complemented
9#22608457C211yesmaximal, characteristic, complemented
10#22608440C211yesmaximal, characteristic, complemented
11#22608436C211yesmaximal, characteristic, complemented
12#22608427C211yesmaximal, characteristic, complemented
13#22608418C211yesmaximal, characteristic, complemented
14C2×#17988322C211yesmaximal, characteristic, complemented
15C73×#2924C211yesmaximal, characteristic, complemented
16#17989300—21no—
17#17989285—21no—
18#17989281—21no—
19#17989261—21no—
20#17989261—21no—
21#17989238—21no—
22#17989227—21no—
23#17989227—21no—
24#17989215C411yescharacteristic, complemented
25#17989208C411yescharacteristic, complemented
26#17989208C411yescharacteristic, complemented
27#17989192C411yescharacteristic, complemented
28#17989192C411yescharacteristic, complemented
29#17989156C411yescharacteristic, complemented
30#17989137C2211yescharacteristic
31#17989137C2211yescharacteristic
32#17989121C2211yescharacteristic
33#17989121C2211yescharacteristic
34#17989098C2211yescharacteristic
35C2×#14556565C2211yescharacteristic
36#17989067C411yescharacteristic, complemented
37#17989061C411yescharacteristic, complemented
38#17988473—21no—
39#17988473—21no—
40#17988462—21no—
41#17988455C2211yescharacteristic, complemented
42#17988453C2211yescharacteristic, complemented
43#17988450C2211yescharacteristic
44C4×C4⋊Dic73C2211yescharacteristic, complemented
45C22⋊C4×Dic73—21no—
46#17988433C2211yescharacteristic, complemented
47C2×#14556498C2211yescharacteristic
48#17988325C2211yescharacteristic, complemented
49#17988325C2211yescharacteristic, complemented
50#17988325C2211yescharacteristic, complemented
51#17988325C2211yescharacteristic, complemented
52#17988322C2211yescharacteristic
53#17988322C2211yescharacteristic
54#17988322C2211yescharacteristic
55#17988322C2211yescharacteristic
56#17988322C2211yescharacteristic
57#17988322C2211yescharacteristic
58#17988322C2211yescharacteristic
59#17988322C2211yescharacteristic
60#17988322C2211yescharacteristic, complemented
61#17988322C2211yescharacteristic, complemented
62#17988322C2211yescharacteristic, complemented
63#17988322C2211yescharacteristic, complemented
64C2×#117×C73C2211yescharacteristic
65#433×C73—21no—
66#433×C73—21no—
67#432×C73C2211yescharacteristic, complemented
68#432×C73C2211yescharacteristic, complemented
69#431×C73C2211yescharacteristic, complemented
70#431×C73C2211yescharacteristic, complemented
71#424×C73—21no—
72#407×C73C2211yescharacteristic
73C2×C22⋊C8×C73C2211yescharacteristic
74#405×C73—21no—
75C2×#11924028—21no—
76C2×#11924028—21no—
77C2×#11924028C2×C411yescharacteristic
78C22×D292C2×C411yescharacteristic
79C22×C22⋊D73—21no—
80C23×Dic73—21no—
81#14556591C2×C411yescharacteristic, complemented
82#14556591C2×C411yescharacteristic, complemented
83#14556590—21no—
84#14556588C2×C411yescharacteristic, complemented
85#14556588C2×C411yescharacteristic, complemented
86#14556586—21no—
87#14556586—21no—
88#14556585—21no—
89#14556585—21no—
90#14556583C2×C411yescharacteristic, complemented
91#14556583C2×C411yescharacteristic, complemented
92#14556582—21no—
93#14556579—21no—
94#14556579—21no—
95#14556579C2×C411yescharacteristic, complemented
96#14556579C2×C411yescharacteristic, complemented
97#14556577—21no—
98#14556577—21no—
99#14556576—21no—
100#14556576—21no—
101#14556576—21no—
102#14556576—21no—
103#14556574—21no—
104#14556574—21no—
105#14556574—21no—
106#14556573—21no—
107#14556573—21no—
108#14556570C2×C411yescharacteristic
109#14556570C2311yescharacteristic
110#14556569—21no—
111#14556569—21no—
112#14556568—21no—
113#14556568—21no—
114#14556566—21no—
115#14556566—21no—
116#14556565—21no—
117#14556565—21no—
118#14556565—21no—
119#14556565—21no—
120#14556565C2×C411yescharacteristic
121#14556565C2×C411yescharacteristic
122#14556565C2×C411yescharacteristic
123#14556565C2311yescharacteristic
124#14556565C2311yescharacteristic
125#14556565C2311yescharacteristic
126#14556564—21no—
127#14556564—21no—
128#14556564—21no—
129#14556564—21no—
130#14556561—21no—
131#14556561—21no—
132#14556560—21no—
133C4×Dic146C2×C411yescharacteristic, complemented
134C4×Dic146C2×C411yescharacteristic, complemented
135C4×D292—21no—
136C4×D292—21no—
137C4×D292C2×C411yescharacteristic, complemented
138C4×D292C2×C411yescharacteristic, complemented
139C4×D292C2×C411yescharacteristic, complemented
140C4×D292C2×C411yescharacteristic, complemented
141C4×D292C2×C411yescharacteristic, complemented
142C4×D292C2×C411yescharacteristic, complemented
143#14556553—21no—
144#14556553—21no—
145C4×C22⋊D73—21no—
146C4×C22⋊D73—21no—
147C4×C22⋊D73—21no—
148C4×C22⋊D73—21no—
149#14556551—21no—
150#14556551—21no—
151#14556550C2×C411yescharacteristic
152#14556549—21no—
153#14556548—21no—
154#14556548—21no—
155C2×C4⋊Dic73—21no—
156C2×C4⋊Dic73—21no—
157C2×C4⋊Dic73C2×C411yescharacteristic
158C4⋊C4×D73—21no—
159C2×C22⋊Dic73—21no—
160C2×#11924005—21no—
161C22⋊C4×D73—21no—
162C22⋊C4×D73—21no—
163C2×C4×Dic73—21no—
164C2×C4×Dic73—21no—
165#14556498—21no—
166#14556498—21no—
167#14556498—21no—
168#14556498—21no—
169#14556498—21no—
170#14556498—21no—
171#14556498C2311yescharacteristic
172#14556498C2311yescharacteristic
173#14556498C2311yescharacteristic
174#14556498C2311yescharacteristic
175C23×C4×C73C2311yescharacteristic
176C2×M16×C73—21no—
177C22×C8×C73—21no—
178#117×C73C2×C411yescharacteristic
179#117×C73C2×C411yescharacteristic
180#117×C73C2×C411yescharacteristic
181#117×C73C2×C411yescharacteristic
182#117×C73D411yescharacteristic
183#117×C73D411yescharacteristic
184#117×C73D411yescharacteristic
185#117×C73D411yescharacteristic
186C2×C4⋊C4×C73D411yescharacteristic
187C2×C4⋊C4×C73D411yescharacteristic
188C2×C22⋊C4×C73D411yescharacteristic
189C2×C22⋊C4×C73D411yescharacteristic
190C2×C42×C73C2311yescharacteristic
191C2×C42×C73C2311yescharacteristic
192C4⋊C8×C73—21no—
193C4⋊C8×C73—21no—
194C4⋊C8×C73—21no—
195C4⋊C8×C73—21no—
196C22⋊C8×C73—21no—
197C22⋊C8×C73—21no—
198C22⋊C8×C73C2311yescharacteristic
199C22⋊C8×C73C2311yescharacteristic
200C22⋊C8×C73C2311yescharacteristic
201C22⋊C8×C73C2311yescharacteristic
202#97×C73—21no—
203#97×C73—21no—
204C4×C8×C73—21no—
205C4×C8×C73—21no—
206C23×D73—21no—
207#11924028—42no—
208#11924028—81no—
209#11924028—81no—
210#11924028—81no—
211#11924028—81no—
212C2×Dic146—21no—
213C2×Dic146—21no—
214C2×Dic146C22×C411yescharacteristic
215C2×D292—21no—
216C2×D292—21no—
217C2×D292—21no—
218C2×D292—21no—
219C2×D292—21no—
220C2×D292—42no—
221C2×D292C22×C411yescharacteristic
222C2×D292C22×C411yescharacteristic
223C2×D292C22×C411yescharacteristic
224C2×C22⋊D73—21no—
225C2×C22⋊D73—21no—
226C2×C22⋊D73—21no—
227C2×C22⋊D73—21no—
228C2×C22⋊D73—21no—
229C2×C22⋊D73—21no—
230C2×C22⋊D73—21no—
231C2×C22⋊D73—81no—
232C2×C22⋊D73—81no—
233C22×Dic73—21no—
234C22×Dic73—21no—
235C22×Dic73—21no—
236C22×Dic73—21no—
237C22×Dic73—21no—
238C22×Dic73—42no—
239C22×Dic73—42no—
240C22×Dic73—81no—
241C2×C4×D73—21no—
242C2×C4×D73—21no—
243C2×C4×D73—21no—
244C2×C4×D73—21no—
245C2×C4×D73—21no—
246C2×C4×D73—21no—
247C2×C4×D73—21no—
248C4⋊Dic73—21no—
249C4⋊Dic73—21no—
250C4⋊Dic73—21no—
251C4⋊Dic73—42no—
252C4⋊Dic73—81no—
253C4⋊Dic73C22×C411yescharacteristic
254C4⋊Dic73C22×C411yescharacteristic
255C4⋊Dic73C22×C411yescharacteristic
256C4⋊Dic73C22×C411yescharacteristic
257#11924007—21no—
258#11924007—21no—
259#11924007—21no—
260#11924007—21no—
261#11924007—21no—
262#11924007—21no—
263#11924007—21no—
264#11924007—21no—
265C22⋊Dic73—21no—
266C22⋊Dic73—21no—
267C22⋊Dic73—21no—
268C22⋊Dic73—42no—
269#11924005—21no—
270#11924005—21no—
271#11924005—21no—
272#11924005—21no—
273#11924005—21no—
274#11924005—21no—
275#11924005—21no—
276#11924005—21no—
277#11924005—21no—
278#11924005—21no—
279#11924005—21no—
280#11924005—21no—
281#11924005—21no—
282#11924005—21no—
283#11924005—21no—
284#11924005—21no—
285C4×Dic73—21no—
286C4×Dic73—21no—
287C4×Dic73—21no—
288C4×Dic73—42no—
289C4×Dic73—81no—
290C24×C73C2×D411yescharacteristic
291C22×C4×C73—42no—
292C22×C4×C73C22×C411yescharacteristic
293C22×C4×C73C22×C411yescharacteristic
294C22×C4×C73C2×D411yescharacteristic
295C22×C4×C73C2×D411yescharacteristic
296C22×C4×C73C2×D411yescharacteristic
297C22×C4×C73C2×D411yescharacteristic
298C22×C4×C73C2×D411yescharacteristic
299C22×C4×C73C2×D411yescharacteristic
300C22×C4×C73C2×D411yescharacteristic
301C22×C4×C73C2411yescharacteristic
302M16×C73—42no—
303C2×C8×C73—21no—
304C2×C8×C73—21no—
305C2×C8×C73—21no—
306C2×C8×C73—21no—
307C2×C8×C73—42no—
308C4⋊C4×C73C22⋊C411yescharacteristic
309C4⋊C4×C73C22⋊C411yescharacteristic
310C4⋊C4×C73C22⋊C411yescharacteristic
311C4⋊C4×C73C22⋊C411yescharacteristic
312C4⋊C4×C73C22⋊C411yescharacteristic
313C4⋊C4×C73C22⋊C411yescharacteristic
314C4⋊C4×C73C22⋊C411yescharacteristic
315C4⋊C4×C73C22⋊C411yescharacteristic
316C22⋊C4×C73C22⋊C411yescharacteristic
317C22⋊C4×C73C22⋊C411yescharacteristic
318C22⋊C4×C73C22⋊C411yescharacteristic
319C22⋊C4×C73C22⋊C411yescharacteristic
320C22⋊C4×C73C22⋊C411yescharacteristic
321C22⋊C4×C73C22⋊C411yescharacteristic
322C22⋊C4×C73C22⋊C411yescharacteristic
323C22⋊C4×C73C22⋊C411yescharacteristic
324C42×C73C22×C411yescharacteristic
325C42×C73C22×C411yescharacteristic
326C42×C73C22×C411yescharacteristic
327C42×C73C22×C411yescharacteristic
328C42×C73C2×D411yescharacteristic
329C42×C73C2×D411yescharacteristic
330C42×C73C2×D411yescharacteristic
331C42×C73C2×D411yescharacteristic
332C23×C73—21no—
333C23×C73—21no—
334C23×C73—22no—
335C23×C73—41no—
336C23×C73C2×C22⋊C411yescharacteristic
337C23×C73C2×C22⋊C411yescharacteristic
338C23×C73C22×D411yescharacteristic
339C22×D73—21no—
340C22×D73—21no—
341C22×D73—21no—
342C22×D73—42no—
343C22×D73—81no—
344C22×D73—81no—
345C2×C4×C73—21no—
346C2×C4×C73—21no—
347C2×C4×C73—21no—
348C2×C4×C73—21no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73C2×C22⋊C411yescharacteristic
358C2×C4×C73C2×C22⋊C411yescharacteristic
359C2×C4×C73C2×C22⋊C411yescharacteristic
360C2×C4×C73C2×C22⋊C411yescharacteristic
361C2×C4×C73C2×C22⋊C411yescharacteristic
362C2×C4×C73C2×C22⋊C411yescharacteristic
363C2×C4×C73C2×C22⋊C411yescharacteristic
364C2×C4×C73C2×C22⋊C411yescharacteristic
365C2×C4×C73C2×C22⋊C411yescharacteristic
366C2×C4×C73C2×C22⋊C411yescharacteristic
367C2×C4×C73C23×C411yescharacteristic
368C2×C4×C73C22×D411yescharacteristic
369C22⋊D73—41no—
370C22⋊D73—41no—
371C22⋊D73—41no—
372C22⋊D73—41no—
373C22⋊D73—41no—
374C22⋊D73—41no—
375C22⋊D73—42no—
376C22⋊D73—81no—
377C22⋊D73—81no—
378C22⋊D73—81no—
379C2×Dic73—22no—
380C2×Dic73—21no—
381C2×Dic73—21no—
382C2×Dic73—21no—
383C2×Dic73—21no—
384C2×Dic73—21no—
385C2×Dic73—41no—
386C2×Dic73—41no—
387C2×Dic73—41no—
388C2×Dic73—41no—
389C2×Dic73—41no—
390C2×Dic73—41no—
391C2×Dic73—41no—
392C2×Dic73—41no—
393C2×Dic73—41no—
394C2×Dic73—41no—
395C2×Dic73—41no—
396C2×Dic73—81no—
397C2×Dic73—84no—
398D292—41no—
399D292—41no—
400D292—41no—
401D292—42no—
402D292—81no—
403D292—81no—
404D292—81no—
405D292—81no—
406C4×D73—42no—
407C4×D73—81no—
408C4×D73—81no—
409C4×D73—81no—
410C4×D73—81no—
411C4×D73—81no—
412C4×D73—81no—
413Dic146—41no—
414Dic146—81no—
415Dic146—81no—
416C8×C73—41no—
417C8×C73—41no—
418C8×C73—41no—
419C8×C73—41no—
420C22×C73—21no—
421C22×C73—21no—
422C22×C73—21no—
423C22×C73—21no—
424C22×C73—21no—
425C22×C73—21no—
426C22×C73—21no—
427C22×C73—42no—
428C22×C73—42no—
429C22×C73#41012yes—
430C22×C73C22×C22⋊C411yescharacteristic
431C22×C73#57611yescharacteristic
432C22×C73#57711yescharacteristic
433C2×D73—41no—
434C2×D73—41no—
435C2×D73—41no—
436C2×D73—41no—
437C2×D73—41no—
438C2×D73—41no—
439C2×D73—41no—
440C2×D73—41no—
441C2×D73—41no—
442C2×D73—162no—
443C4×C73—21no—
444C4×C73—21no—
445C4×C73—21no—
446C4×C73—21no—
447C4×C73—21no—
448C4×C73—21no—
449C4×C73—21no—
450C4×C73—21no—
451C4×C73—21no—
452C4×C73—21no—
453C4×C73—21no—
454C4×C73—21no—
455Dic73—42no—
456Dic73—41no—
457Dic73—41no—
458Dic73—41no—
459Dic73—41no—
460Dic73—41no—
461Dic73—81no—
462Dic73—81no—
463Dic73—81no—
464#17604—731nomaximal, Sylow
465C2×C73—21no—
466C2×C73—21no—
467C2×C73—22no—
468C2×C73—41no—
469C2×C73C2×#41011yescharacteristic
470C2×C73#289711yescharacteristic
471C2×C73#290111yescharacteristic
472D73—81no—
473D73—81no—
474D73—81no—
475#3494—731no—
476#2924D7311yescharacteristic, complemented
477#2343—731no—
478#1521—731no—
479#1517—731no—
480#1516—731no—
481#1514—731no—
482#1512—731no—
483#1510—731no—
484#1509—731no—
485#1505—731no—
486#1504—731no—
487#1502—731no—
488#1500—731no—
489C2×#327—731no—
490C73#1760411yescharacteristic, complemented, Sylow
491#555—1461no—
492#553—1461no—
493#553—1461no—
494#551—1461no—
495#551—1461no—
496#547—1461no—
497#546—1461no—
498#546—1461no—
499#544—731no—
500#542—731no—
501#542—731no—
502#540—731no—
503#540—731no—
504#535—731no—
505#532—731no—
506#532—731no—
507#529—731no—
508#529—731no—
509#525—731no—
510C2×#121—731no—
511#520—731no—
512#518—731no—
513C2×#117C2×D7311yescharacteristic
514#433—21no—
515#433—21no—
516#432C2×D7311yescharacteristic, complemented
517#432C2×D7311yescharacteristic, complemented
518#431C2×D7311yescharacteristic, complemented
519#431C2×D7311yescharacteristic, complemented
520#424—21no—
521#407C2×D7311yescharacteristic
522C2×C22⋊C8C2×D7311yescharacteristic
523#405—21no—
524#387—1461no—
525#387—1461no—
526#385—1461no—
527#383—731no—
528#382—731no—
529#381—731no—
530C4×C4⋊C4—731no—
531C4×C22⋊C4—1461no—
532#376—731no—
533C2×#95—731no—
534#328—731no—
535#328—731no—
536#328—731no—
537#328—731no—
538#327—731no—
539#327—731no—
540#327—731no—
541#327—731no—
542#327—731no—
543#327—731no—
544#327—731no—
545#327—731no—
546#327—731no—
547#327—731no—
548#327—731no—
549#327—731no—
550C2×#41—731no—
551C2×#41—1461no—
552C2×#41—1461no—
553C22×D4—731no—
554C22×D4—1461no—
555C23×C4—1461no—
556C23×C4C22×D7311yescharacteristic
557C2×M16—21no—
558C22×C8—21no—
559C4⋊Q8—731no—
560C4⋊Q8—731no—
561C4⋊Q8—1461no—
562#127—731no—
563#127—731no—
564#126—1461no—
565#126—1461no—
566#126—1461no—
567#126—1461no—
568#125—731no—
569#125—731no—
570#125—1461no—
571#124—731no—
572#124—731no—
573#124—1461no—
574#124—1461no—
575#124—1461no—
576#124—1461no—
577#123—1461no—
578#123—1461no—
579#123—1461no—
580#123—1461no—
581#123—1461no—
582#123—1461no—
583#123—1461no—
584#123—1461no—
585#123—1461no—
586C22⋊Q8—731no—
587C22⋊Q8—731no—
588C22⋊Q8—1461no—
589C22⋊Q8—1461no—
590C22⋊Q8—1461no—
591C22⋊Q8—1461no—
592#121—731no—
593#121—731no—
594#121—731no—
595#121—731no—
596#121—731no—
597#121—731no—
598#121—1461no—
599#121—1461no—
600#121—1461no—
601#121—1461no—
602#121—1461no—
603#121—1461no—
604#121—1461no—
605#121—1461no—
606#121—1461no—
607#121—1461no—
608#120—1461no—
609#120—1461no—
610#120—1461no—
611C4×Q8—731no—
612C4×Q8—731no—
613C4×D4—731no—
614C4×D4—731no—
615C4×D4—731no—
616C4×D4—731no—
617C4×D4—731no—
618C4×D4—731no—
619C4×D4—1461no—
620C4×D4—1461no—
621C4×D4—1461no—
622C4×D4—1461no—
623C4×D4—1461no—
624C4×D4—1461no—
625C4×D4—1461no—
626C4×D4—1461no—
627C4×D4—1461no—
628C4×D4—1461no—
629#117—731no—
630#117—1461no—
631#117—1461no—
632#117—1461no—
633#117C4×D7311yescharacteristic
634#117C4×D7311yescharacteristic
635#117C4×D7311yescharacteristic
636#117C4×D7311yescharacteristic
637#117C22⋊D7311yescharacteristic
638#117C22⋊D7311yescharacteristic
639#117C22⋊D7311yescharacteristic
640#117C22⋊D7311yescharacteristic
641C2×C4⋊C4—731no—
642C2×C4⋊C4—1461no—
643C2×C4⋊C4—1461no—
644C2×C4⋊C4—1461no—
645C2×C4⋊C4D29211yescharacteristic
646C2×C4⋊C4D29211yescharacteristic
647C2×C22⋊C4—1461no—
648C2×C22⋊C4—1461no—
649C2×C22⋊C4—1461no—
650C2×C22⋊C4—1461no—
651C2×C22⋊C4D29211yescharacteristic
652C2×C22⋊C4D29211yescharacteristic
653C2×C42—1461no—
654C2×C42—1461no—
655C2×C42C22×D7311yescharacteristic
656C2×C42C22×D7311yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8C22×D7311yescharacteristic
664C22⋊C8C22×D7311yescharacteristic
665C22⋊C8C22×D7311yescharacteristic
666C22⋊C8C22×D7311yescharacteristic
667#97—21no—
668#97—21no—
669C4×C8—21no—
670C4×C8—21no—
671#95—731no—
672#95—731no—
673#95—731no—
674#95—731no—
675#95—1461no—
676#95—1461no—
677#95—1461no—
678#95—1461no—
679#95—1461no—
680#95—1461no—
681C24—1461no—
682C24C2×D29211yescharacteristic
683#41—2922no—
684#41—5841no—
685#41—5841no—
686#41—5841no—
687#41—5841no—
688C2×Q8—731no—
689C2×Q8—1461no—
690C2×Q8—1461no—
691C2×D4—2922no—
692C2×D4—5841no—
693C2×D4—5841no—
694C2×D4—731no—
695C2×D4—731no—
696C2×D4—731no—
697C2×D4—1461no—
698C2×D4—1461no—
699C2×D4—1461no—
700C2×D4—1461no—
701C2×D4—1461no—
702C2×D4—1461no—
703C2×D4—1461no—
704C2×D4—1461no—
705C2×D4—1461no—
706C2×D4—1461no—
707C2×D4—1461no—
708C2×D4—1461no—
709C22×C4—42no—
710C22×C4—2922no—
711C22×C4—2922no—
712C22×C4—5841no—
713C22×C4—1461no—
714C22×C4—1461no—
715C22×C4—1461no—
716C22×C4—1461no—
717C22×C4—1461no—
718C22×C4—1461no—
719C22×C4—1461no—
720C22×C4—1461no—
721C22×C4—1461no—
722C22×C4—1461no—
723C22×C4—1461no—
724C22×C4—1461no—
725C22×C4C2×C4×D7311yescharacteristic
726C22×C4C2×C4×D7311yescharacteristic
727C22×C4C2×C22⋊D7311yescharacteristic
728C22×C4C2×C22⋊D7311yescharacteristic
729C22×C4C2×D29211yescharacteristic
730C22×C4C2×D29211yescharacteristic
731C22×C4C2×D29211yescharacteristic
732C22×C4C2×D29211yescharacteristic
733C22×C4C2×D29211yescharacteristic
734C22×C4C23×D7311yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—2922no—
742C4⋊C4—5841no—
743C4⋊C4—731no—
744C4⋊C4—731no—
745C4⋊C4—731no—
746C4⋊C4—731no—
747C4⋊C4—1461no—
748C4⋊C4—1461no—
749C4⋊C4—1461no—
750C4⋊C4—1461no—
751C4⋊C4—1461no—
752C4⋊C4—1461no—
753C4⋊C4—1461no—
754C4⋊C4—1461no—
755C4⋊C4—1461no—
756C4⋊C4—1461no—
757C4⋊C4—1461no—
758C4⋊C4#1192400511yescharacteristic
759C4⋊C4#1192400511yescharacteristic
760C4⋊C4#1192400511yescharacteristic
761C4⋊C4#1192400511yescharacteristic
762C4⋊C4#1192400511yescharacteristic
763C4⋊C4#1192400511yescharacteristic
764C4⋊C4#1192400511yescharacteristic
765C4⋊C4#1192400511yescharacteristic
766C22⋊C4—2922no—
767C22⋊C4—1461no—
768C22⋊C4—1461no—
769C22⋊C4—1461no—
770C22⋊C4—1461no—
771C22⋊C4—1461no—
772C22⋊C4—1461no—
773C22⋊C4—1461no—
774C22⋊C4—1461no—
775C22⋊C4—1461no—
776C22⋊C4—1461no—
777C22⋊C4—1461no—
778C22⋊C4—1461no—
779C22⋊C4—1461no—
780C22⋊C4—1461no—
781C22⋊C4—1461no—
782C22⋊C4—1461no—
783C22⋊C4—1461no—
784C22⋊C4—1461no—
785C22⋊C4—1461no—
786C22⋊C4#1192400511yescharacteristic
787C22⋊C4#1192400511yescharacteristic
788C22⋊C4#1192400511yescharacteristic
789C22⋊C4#1192400511yescharacteristic
790C22⋊C4#1192400511yescharacteristic
791C22⋊C4#1192400511yescharacteristic
792C22⋊C4#1192400511yescharacteristic
793C22⋊C4#1192400511yescharacteristic
794C42—2922no—
795C42—5841no—
796C42—1461no—
797C42—1461no—
798C42—1461no—
799C42C2×C4×D7311yescharacteristic
800C42C2×C4×D7311yescharacteristic
801C42C2×C4×D7311yescharacteristic
802C42C2×C4×D7311yescharacteristic
803C42C2×C22⋊D7311yescharacteristic
804C42C2×C22⋊D7311yescharacteristic
805C42C2×C22⋊D7311yescharacteristic
806C42C2×C22⋊D7311yescharacteristic
807C23—21no—
808C23—21no—
809C23—22no—
810C23—41no—
811C23—2922no—
812C23—5841no—
813C23—5841no—
814C23—1461no—
815C23—1461no—
816C23—1461no—
817C23C2×#1192400511yescharacteristic
818C23C2×#1192400511yescharacteristic
819C23C22×D29211yescharacteristic
820Q8—2921no—
821Q8—5841no—
822Q8—5841no—
823D4—2921no—
824D4—2921no—
825D4—2921no—
826D4—2922no—
827D4—2921no—
828D4—2921no—
829D4—2921no—
830D4—2921no—
831D4—2921no—
832D4—2921no—
833D4—2922no—
834D4—5841no—
835D4—5841no—
836D4—5841no—
837D4—5841no—
838D4—5841no—
839D4—5841no—
840D4—5841no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—2922no—
854C2×C4—2921no—
855C2×C4—2921no—
856C2×C4—2921no—
857C2×C4—2921no—
858C2×C4—2921no—
859C2×C4—2921no—
860C2×C4—2921no—
861C2×C4—2921no—
862C2×C4—2921no—
863C2×C4—2921no—
864C2×C4—2921no—
865C2×C4—5841no—
866C2×C4—5841no—
867C2×C4—5841no—
868C2×C4—5841no—
869C2×C4—5841no—
870C2×C4—5841no—
871C2×C4—5841no—
872C2×C4—5844no—
873C2×C4—1462no—
874C2×C4—1461no—
875C2×C4—1461no—
876C2×C4—1461no—
877C2×C4—1461no—
878C2×C4—1461no—
879C2×C4C2×#1192400511yescharacteristic
880C2×C4C2×#1192400511yescharacteristic
881C2×C4C2×#1192400511yescharacteristic
882C2×C4C2×#1192400511yescharacteristic
883C2×C4C2×#1192400511yescharacteristic
884C2×C4C2×#1192400511yescharacteristic
885C2×C4C2×#1192400511yescharacteristic
886C2×C4C2×#1192400511yescharacteristic
887C2×C4C2×#1192400511yescharacteristic
888C2×C4C2×#1192400511yescharacteristic
889C2×C4C22×C4×D7311yescharacteristic
890C2×C4C22×C22⋊D7311yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—2921no—
905C22—2921no—
906C22—2921no—
907C22—2921no—
908C22—2921no—
909C22—2921no—
910C22—2921no—
911C22—2921no—
912C22—2921no—
913C22—11682no—
914C22#1798856012yes—
915C22C22×#1192400511yescharacteristic
916C22#1798939211yescharacteristic
917C22#1798939911yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—2922no—
931C4—2921no—
932C4—2921no—
933C4—2921no—
934C4—2921no—
935C4—2921no—
936C4—5841no—
937C4—5841no—
938C4—5841no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—5841no—
944C2—5841no—
945C2—5841no—
946C2C2×#1798856011yescharacteristic
947C2#2261845811yescharacteristic
948C2#2261847611yescharacteristic
subgroupG/H
centerC22C22×#11924005
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2924C2
socleC22×C73C22×C22⋊C4
prime radical#22623666C2
cosocleC22×C4×C73C24
hypercenter#2924D73
hypocenterC73#17604
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #22612791C2semidirect
3. #22608509C2semidirect
4. #22608492C2semidirect
5. #22608488C2semidirect
6. #22608479C2semidirect
7. #22608470C2semidirect
8. #22608461C2semidirect
9. #22608457C2semidirect
10. #22608440C2semidirect
11. #22608436C2semidirect
12. #22608427C2semidirect
13. #22608418C2semidirect
14. C2×#17988322C2semidirect
15. C73×#2924C2semidirect
24. #17989215C4semidirect
25. #17989208C4semidirect
26. #17989208C4semidirect
27. #17989192C4semidirect
28. #17989192C4semidirect
29. #17989156C4semidirect
36. #17989067C4semidirect
37. #17989061C4semidirect
41. #17988455C22semidirect
42. #17988453C22semidirect
44. C4×C4⋊Dic73C22semidirect
46. #17988433C22semidirect
48. #17988325C22semidirect
49. #17988325C22semidirect
50. #17988325C22semidirect
51. #17988325C22semidirect
60. #17988322C22semidirect
61. #17988322C22semidirect
62. #17988322C22semidirect
63. #17988322C22semidirect
67. #432×C73C22semidirect
68. #432×C73C22semidirect
69. #431×C73C22semidirect
70. #431×C73C22semidirect
81. #14556591C2×C4semidirect
82. #14556591C2×C4semidirect
84. #14556588C2×C4semidirect
85. #14556588C2×C4semidirect
90. #14556583C2×C4semidirect
91. #14556583C2×C4semidirect
95. #14556579C2×C4semidirect
96. #14556579C2×C4semidirect
133. C4×Dic146C2×C4semidirect
134. C4×Dic146C2×C4semidirect
137. C4×D292C2×C4semidirect
138. C4×D292C2×C4semidirect
139. C4×D292C2×C4semidirect
140. C4×D292C2×C4semidirect
141. C4×D292C2×C4semidirect
142. C4×D292C2×C4semidirect
476. #2924D73semidirect
490. C73#17604semidirect
516. #432C2×D73semidirect
517. #432C2×D73semidirect
518. #431C2×D73semidirect
519. #431C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226236662
#226127912
#226085092
#226084922
#226084882
#226084792
#226084702
#226084612
#226084572
#226084402
#226084362
#226084272
#226084182
C2×#179883222
C73×#29242
#1760473