Finite Group Databasebeta

← #33246163

Subgroups — #33246163

Order 18688.

2470 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11924028C211yesmaximal, characteristic
2#22612883C212yesmaximal, complemented
3#22612857C212yesmaximal, complemented
4#22612856C212yesmaximal, complemented
5C4⋊C4×C22⋊D73C212yesmaximal, complemented
6#22612811C212yesmaximal, complemented
7#22612787C212yesmaximal, complemented
8#22612784C212yesmaximal, complemented
9#22612758C212yesmaximal
10#22612579C212yesmaximal, complemented
11#22612567C212yesmaximal, complemented
12#22612565C212yesmaximal, complemented
13#22612337C211yesmaximal, characteristic, complemented
14#22612329C211yesmaximal, characteristic, complemented
15#22612324C211yesmaximal, characteristic, complemented
16#22612324C211yesmaximal, characteristic, complemented
17#382×D73C211yesmaximal, characteristic, complemented
18#22612289C212yesmaximal, complemented
19C2×#382×C73C211yesmaximal, characteristic, complemented
20C22×#11924028C2211yescharacteristic
21C4×#11924028C4116yescomplemented
22C2×C4×Dic146C2211yescharacteristic
23C2×C4×Dic146C2211yescharacteristic
24C2×C4×D292C2211yescharacteristic
25C2×C4×D292C2211yescharacteristic
26C2×C4×C22⋊D73C2214yes—
27C2×C4×C22⋊D73C2211yescharacteristic
28C2×C4×C22⋊D73C2211yescharacteristic
29C2×C4×C22⋊D73C2211yescharacteristic
30C2×C4×C22⋊D73C2211yescharacteristic
31C2×#14556550C2211yescharacteristic
32C2×#14556549C2212yes—
33C2×#14556548C2211yescharacteristic
34C2×#14556548C2211yescharacteristic
35C2×C4⋊C4×D73C2212yes—
36C2×C42×D73C2211yescharacteristic
37C2×C42×D73C2211yescharacteristic
38#17988491C2214yes—
39#17988482C2214yes—
40#17988477C2214yes—
41#17988476C2214yes—
42#17988472C2214yes—
43#17988470C2214yes—
44#17988469C2214yes—
45#17988468C2214yes—
46#17988466C2214yes—
47#17988465C2214yes—
48#17988460C2214yes—
49#17988458C2214yes—
50#17988456C2212yes—
51#17988455C2212yes—
52#17988454C2212yes—
53#17988454C2212yes—
54#17988453C2211yescharacteristic
55#17988453C2211yescharacteristic
56#17988452C2212yes—
57#17988451C2212yes—
58#17988451C2212yes—
59#17988450C2212yes—
60#17988449C2212yes—
61#17988449C2212yes—
62#17988447C2212yes—
63#17988446C2212yes—
64#17988446C2212yes—
65#17988444C2212yes—
66#17988444C2212yes—
67C4⋊C4×Dic73C2212yes—
68C4⋊C4×Dic73C2212yes—
69C4×C4⋊Dic73C2212yes—
70#17988438C2212yes—
71#17988438C2214yes—
72#17988438C2212yes—
73C4×C22⋊Dic73C2214yes—
74C4×C22⋊Dic73C2212yes—
75#17988434C2212yes—
76#17988434C2214yes—
77#17988434C2212yes—
78#17988433C2212yes—
79#17988432C2212yes—
80#17988432C2212yes—
81#95×D73C2212yes—
82#95×D73C2212yes—
83C22×C4⋊C4×C73C2212yes—
84C22×C42×C73C2211yescharacteristic
85#382×C73C2212yes—
86#382×C73C2212yes—
87#382×C73C2211yescharacteristic
88#382×C73C2211yescharacteristic
89#382×C73C2212yes—
90C2×#95×C73C2212yes—
91C2×#95×C73C2212yes—
92C2×#11924028—28no—
93C2×#11924028C2×C418yes—
94C22×Dic146C2311yescharacteristic
95C22×D292C2311yescharacteristic
96C22×C22⋊D73C2311yescharacteristic
97C22×C22⋊D73C2311yescharacteristic
98C22×C4×D73C2311yescharacteristic
99C22×C4×D73C2311yescharacteristic
100C22×C4×D73C2311yescharacteristic
101C22×C4×D73C2311yescharacteristic
102C22×C4×D73C2314yes—
103C22×C4×D73C2311yescharacteristic
104C22×C4×D73C2311yescharacteristic
105C4×Dic146C2×C418yescomplemented
106C4×Dic146C2×C418yescomplemented
107C4×D292C2×C418yescomplemented
108C4×D292C2×C418yescomplemented
109C4×C22⋊D73—216no—
110C4×C22⋊D73C2×C418yes—
111C4×C22⋊D73C2×C418yes—
112C4×C22⋊D73C2×C418yescomplemented
113C4×C22⋊D73C2×C418yescomplemented
114#14556550C2×C418yescomplemented
115#14556549—44no—
116#14556548C2×C418yescomplemented
117#14556548C2×C418yescomplemented
118C2×C4⋊Dic73C2312yes—
119C2×C4⋊Dic73C2312yes—
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×#11924007C2314yes—
123C2×#11924007C2314yes—
124C2×#11924007C2314yes—
125C2×#11924007C2311yescharacteristic
126C2×#11924007C2311yescharacteristic
127C2×#11924007C2311yescharacteristic
128C2×#11924007C2311yescharacteristic
129C4⋊C4×D73—44no—
130C2×C22⋊Dic73C2314yes—
131C2×C22⋊Dic73C2311yescharacteristic
132C2×C22⋊Dic73C2311yescharacteristic
133C2×#11924005C2314yes—
134C2×#11924005C2314yes—
135C2×#11924005C2314yes—
136C2×#11924005C2311yescharacteristic
137C2×#11924005C2311yescharacteristic
138C2×#11924005C2311yescharacteristic
139C2×#11924005C2311yescharacteristic
140C2×C4×Dic73C2314yes—
141C2×C4×Dic73C2314yes—
142C2×C4×Dic73C2314yes—
143C2×C4×Dic73C2314yes—
144C2×C4×Dic73C2311yescharacteristic
145C2×C4×Dic73C2311yescharacteristic
146C2×C4×Dic73C2311yescharacteristic
147C2×C4×Dic73C2311yescharacteristic
148C2×C4×Dic73C2311yescharacteristic
149C2×C4×Dic73C2311yescharacteristic
150C42×D73C2×C418yescomplemented
151C42×D73C2×C418yescomplemented
152#14556498C2312yes—
153#14556498C2312yes—
154#14556498C2314yes—
155#14556498C2314yes—
156#14556498C2312yes—
157#14556498C2314yes—
158#14556498C2312yes—
159#14556498C2314yes—
160#14556498C2314yes—
161#14556498C2314yes—
162#14556498C2314yes—
163#14556498C2314yes—
164C23×C4×C73C2311yescharacteristic
165C23×C4×C73C2311yescharacteristic
166C23×C4×C73C2314yes—
167C23×C4×C73C2311yescharacteristic
168C2×C4⋊C4×C73—44no—
169C2×C4⋊C4×C73C2312yes—
170C2×C4⋊C4×C73C2312yes—
171C2×C4⋊C4×C73C2314yes—
172C2×C42×C73C2×C418yescomplemented
173C2×C42×C73C2311yescharacteristic
174C2×C42×C73C2311yescharacteristic
175C2×C42×C73C2311yescharacteristic
176C2×C42×C73C2311yescharacteristic
177#95×C73C2312yes—
178#95×C73C2312yes—
179#95×C73C2312yes—
180#95×C73C2312yes—
181#95×C73C2314yes—
182#95×C73C2314yes—
183C23×D73C2411yescharacteristic
184C23×D73C2411yescharacteristic
185#11924028—232no—
186C2×Dic146—24no—
187C2×Dic146C22×C414yes—
188C2×D292—24no—
189C2×D292C22×C414yes—
190C2×C22⋊D73—24no—
191C2×C22⋊D73C22×C414yes—
192C2×C22⋊D73C22×C414yes—
193C2×C22⋊D73#4118yes—
194C22×Dic73C2414yes—
195C22×Dic73C2414yes—
196C22×Dic73C2411yescharacteristic
197C22×Dic73C2411yescharacteristic
198C22×Dic73C2411yescharacteristic
199C22×Dic73C2411yescharacteristic
200C22×Dic73C2411yescharacteristic
201C22×Dic73C2411yescharacteristic
202C2×C4×D73—24no—
203C2×C4×D73—22no—
204C2×C4×D73—22no—
205C2×C4×D73—22no—
206C2×C4×D73—22no—
207C2×C4×D73—24no—
208C2×C4×D73—28no—
209C2×C4×D73—42no—
210C2×C4×D73—42no—
211C2×C4×D73—44no—
212C2×C4×D73—44no—
213C2×C4×D73C22×C414yes—
214C2×C4×D73C22×C414yes—
215C2×C4×D73C22×C414yes—
216C2×C4×D73C22×C414yes—
217C2×C4×D73C22×C414yes—
218C2×C4×D73C22×C414yes—
219C4⋊Dic73—24no—
220C4⋊Dic73—24no—
221C4⋊Dic73C22×C414yes—
222C4⋊Dic73C22×C414yes—
223#11924007—28no—
224#11924007—44no—
225#11924007—44no—
226#11924007C22×C414yes—
227#11924007C22×C414yes—
228#11924007C22×C414yes—
229#11924007C22×C414yes—
230C22⋊Dic73—28no—
231C22⋊Dic73C22×C414yes—
232C22⋊Dic73C22×C414yes—
233#11924005—28no—
234#11924005—44no—
235#11924005—44no—
236#11924005C22×C414yes—
237#11924005C22×C414yes—
238#11924005C22×C414yes—
239#11924005C22×C414yes—
240C4×Dic73—28no—
241C4×Dic73—44no—
242C4×Dic73—44no—
243C4×Dic73—44no—
244C4×Dic73C22×C414yes—
245C4×Dic73C22×C414yes—
246C4×Dic73C22×C414yes—
247C4×Dic73C22×C414yes—
248C4×Dic73C22×C414yes—
249C4×Dic73C22×C414yes—
250C24×C73C2411yescharacteristic
251C22×C4×C73—24no—
252C22×C4×C73—22no—
253C22×C4×C73—22no—
254C22×C4×C73—28no—
255C22×C4×C73—42no—
256C22×C4×C73—44no—
257C22×C4×C73—44no—
258C22×C4×C73C22×C414yes—
259C22×C4×C73C22×C414yes—
260C22×C4×C73C22×C414yes—
261C22×C4×C73C2414yes—
262C22×C4×C73C2414yes—
263C22×C4×C73C2411yescharacteristic
264C22×C4×C73C2411yescharacteristic
265C22×C4×C73C2411yescharacteristic
266C22×C4×C73C2411yescharacteristic
267C22×C4×C73C2411yescharacteristic
268C22×C4×C73C2411yescharacteristic
269C4⋊C4×C73—24no—
270C4⋊C4×C73—24no—
271C4⋊C4×C73—44no—
272C42×C73C22×C414yes—
273C42×C73C22×C414yes—
274C42×C73C22×C414yes—
275C42×C73C22×C414yes—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—22no—
279C23×C73C23×C412yes—
280C23×C73C2×#4114yes—
281C23×C73C2511yescharacteristic
282C22×D73—21no—
283C22×D73—21no—
284C22×D73—22no—
285C22×D73—22no—
286C22×D73—21no—
287C22×D73—21no—
288C22×D73—22no—
289C22×D73C23×C412yes—
290C22×D73C23×C412yes—
291C22×D73C2×#4114yes—
292C2×C4×C73—28no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—28no—
300C2×C4×C73—24no—
301C2×C4×C73—24no—
302C2×C4×C73—24no—
303C2×C4×C73—24no—
304C2×C4×C73—24no—
305C2×C4×C73—24no—
306C2×C4×C73—44no—
307C2×C4×C73—88no—
308C2×C4×C73C23×C412yes—
309C2×C4×C73C23×C412yes—
310C2×C4×C73C23×C412yes—
311C2×C4×C73C23×C412yes—
312C2×C4×C73C23×C412yes—
313C2×C4×C73C23×C412yes—
314C2×C4×C73H(5,𝔽2)12yes—
315C2×C4×C732−1+412yes—
316C22⋊D73—28no—
317C22⋊D73#117116yescomplemented
318C2×Dic73—22no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—24no—
326C2×Dic73—24no—
327C2×Dic73—24no—
328C2×Dic73—24no—
329C2×Dic73—24no—
330C2×Dic73—24no—
331C2×Dic73C23×C412yes—
332C2×Dic73C23×C412yes—
333C2×Dic73C23×C412yes—
334C2×Dic73C23×C412yes—
335C2×Dic73C23×C412yes—
336C2×Dic73C23×C412yes—
337C2×Dic73C2×#4114yes—
338D292—28no—
339C4×D73—28no—
340C4×D73—28no—
341C4×D73—28no—
342C4×D73—28no—
343C4×D73—44no—
344C4×D73—44no—
345C4×D73—88no—
346Dic146—28no—
347C22×C73—22no—
348C22×C73—22no—
349C22×C73—24no—
350C22×C73—24no—
351C22×C73C2×#11714yes—
352C22×C73C24×C411yescharacteristic
353C22×C73C22×#4112yes—
354C22×C73C2×H(5,𝔽2)11yescharacteristic
355C22×C73C2×2−1+411yescharacteristic
356C22×C73#58512yes—
357C2×D73—22no—
358C2×D73—22no—
359C2×D73—24no—
360C2×D73—24no—
361C2×D73—22no—
362C2×D73—22no—
363C2×D73—22no—
364C2×D73—42no—
365C2×D73—42no—
366C2×D73C2×#11714yes—
367C4×C73—22no—
368C4×C73—22no—
369C4×C73—22no—
370C4×C73—22no—
371C4×C73—22no—
372C4×C73—44no—
373C4×C73—44no—
374C4×C73#52014yes—
375Dic73—22no—
376Dic73—22no—
377Dic73—22no—
378Dic73—22no—
379Dic73—22no—
380Dic73—44no—
381Dic73—44no—
382Dic73C2×#11714yes—
383#34191—731nomaximal, Sylow
384C2×C73—24no—
385C2×C73C22×#11711yescharacteristic
386C2×C73C2×#52011yescharacteristic
387C2×C73#342811yescharacteristic
388C2×C73#351412yes—
389C2×C73#351512yes—
390D73—24no—
391D73—42no—
392C2×C4×#41—731no—
393#2355—732no—
394#2352—732no—
395#2352—732no—
396D4×C4⋊C4—732no—
397#2346—732no—
398#2343—732no—
399#2343—732no—
400#2339—732no—
401#2320—732no—
402#2318—732no—
403#2318—732no—
404#2285—731no—
405#2283—731no—
406#2283—731no—
407#2283—731no—
408C2×#382—731no—
409C2×#382D7311yescharacteristic, complemented
410#2275—732no—
411C73#3419111yescharacteristic, complemented, Sylow
412C22×#41—731no—
413C4×#41—7316no—
414C2×C4×Q8—731no—
415C2×C4×Q8—731no—
416C2×C4×D4—731no—
417C2×C4×D4—731no—
418C2×C4×D4—731no—
419C2×C4×D4—731no—
420C2×C4×D4—734no—
421C2×C4×D4—731no—
422C2×C4×D4—731no—
423C2×#117—731no—
424C2×#117—732no—
425C2×#117—731no—
426C2×#117—731no—
427C22×C4⋊C4—732no—
428C22×C4⋊C4C2×D7312yes—
429C22×C42—731no—
430C22×C42—731no—
431C22×C42C2×D7311yescharacteristic
432#391—734no—
433#389—734no—
434#388—734no—
435#388—734no—
436#387—734no—
437#387—734no—
438#387—734no—
439#387—734no—
440#386—734no—
441#386—734no—
442#385—734no—
443#385—734no—
444#384—732no—
445#383—732no—
446#383—732no—
447#383—732no—
448#382—732no—
449#382—731no—
450#382—731no—
451#382—732no—
452#382—732no—
453#382C2×D7312yes—
454#382C2×D7312yes—
455#382C2×D7312yes—
456#382C2×D7311yescharacteristic
457#382C2×D7311yescharacteristic
458#381—732no—
459#381—732no—
460#381—732no—
461#380—732no—
462#380—732no—
463#380—732no—
464#380—732no—
465#380—732no—
466C4×C4⋊C4—732no—
467C4×C4⋊C4—732no—
468C4×C4⋊C4—732no—
469C4×C4⋊C4—732no—
470C4×C4⋊C4—732no—
471C4×C4⋊C4—734no—
472C4×C22⋊C4—732no—
473C4×C22⋊C4—734no—
474C4×C22⋊C4—732no—
475C4×C22⋊C4—732no—
476C4×C22⋊C4—734no—
477#376—732no—
478#376—732no—
479#376—732no—
480C2×#95—732no—
481C2×#95—732no—
482C2×#95C2×D7312yes—
483C2×#95C2×D7312yes—
484C2×#41—738no—
485C2×#41—1468no—
486C22×Q8—731no—
487C22×D4—731no—
488C22×D4—731no—
489C22×D4—731no—
490C23×C4—731no—
491C23×C4—731no—
492C23×C4—734no—
493C23×C4—731no—
494C23×C4—731no—
495C23×C4—731no—
496C23×C4—731no—
497C23×C4C22×D7311yescharacteristic
498C23×C4C22×D7311yescharacteristic
499C23×C4C22×D7314yes—
500C23×C4C22×D7311yescharacteristic
501C4×Q8—738no—
502C4×Q8—738no—
503C4×D4—738no—
504C4×D4—738no—
505C4×D4—738no—
506C4×D4—738no—
507C4×D4—738no—
508C4×D4—738no—
509C4×D4—14616no—
510#117—2924no—
511#117—738no—
512#117—738no—
513#117—738no—
514C2×C4⋊C4—44no—
515C2×C4⋊C4—2924no—
516C2×C4⋊C4—734no—
517C2×C4⋊C4—734no—
518C2×C4⋊C4—731no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—732no—
525C2×C4⋊C4—734no—
526C2×C4⋊C4—732no—
527C2×C4⋊C4C22×D7312yes—
528C2×C4⋊C4C22×D7312yes—
529C2×C4⋊C4C22×D7314yes—
530C2×C22⋊C4—734no—
531C2×C22⋊C4—734no—
532C2×C22⋊C4—731no—
533C2×C22⋊C4—731no—
534C2×C22⋊C4—731no—
535C2×C22⋊C4—731no—
536C2×C22⋊C4—731no—
537C2×C22⋊C4—731no—
538C2×C22⋊C4—734no—
539C2×C22⋊C4—734no—
540C2×C42—734no—
541C2×C42—734no—
542C2×C42—734no—
543C2×C42—731no—
544C2×C42—731no—
545C2×C42—731no—
546C2×C42—731no—
547C2×C42—731no—
548C2×C42—731no—
549C2×C42—738no—
550C2×C42—738no—
551C2×C42—734no—
552C2×C42C4×D7318yescomplemented
553C2×C42C22×D7311yescharacteristic
554C2×C42C22×D7311yescharacteristic
555C2×C42C22×D7311yescharacteristic
556C2×C42C22×D7311yescharacteristic
557#95—732no—
558#95—732no—
559#95—734no—
560#95—734no—
561#95—732no—
562#95—734no—
563#95—732no—
564#95—734no—
565#95—734no—
566#95—734no—
567#95—734no—
568#95—734no—
569#95C22×D7312yes—
570#95C22×D7312yes—
571#95C22×D7312yes—
572#95C22×D7312yes—
573#95C22×D7314yes—
574#95C22×D7314yes—
575C24—731no—
576C24—731no—
577C24C23×D7311yescharacteristic
578#41—14632no—
579C2×Q8—734no—
580C2×Q8—1464no—
581C2×D4—734no—
582C2×D4—738no—
583C2×D4—734no—
584C2×D4—734no—
585C2×D4—1464no—
586C2×D4—1464no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—2922no—
595C22×C4—2922no—
596C22×C4—2924no—
597C22×C4—2924no—
598C22×C4—734no—
599C22×C4—734no—
600C22×C4—731no—
601C22×C4—731no—
602C22×C4—731no—
603C22×C4—731no—
604C22×C4—731no—
605C22×C4—731no—
606C22×C4—734no—
607C22×C4—734no—
608C22×C4—734no—
609C22×C4—734no—
610C22×C4—734no—
611C22×C4—734no—
612C22×C4—1468no—
613C22×C4—1464no—
614C22×C4—1464no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4—1462no—
618C22×C4—1462no—
619C22×C4C2×C4×D7314yes—
620C22×C4C2×C4×D7314yes—
621C22×C4C2×C4×D7314yes—
622C22×C4C23×D7314yes—
623C22×C4C23×D7314yes—
624C22×C4C23×D7311yescharacteristic
625C22×C4C23×D7311yescharacteristic
626C22×C4C23×D7311yescharacteristic
627C22×C4C23×D7311yescharacteristic
628C22×C4C23×D7311yescharacteristic
629C22×C4C23×D7311yescharacteristic
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—44no—
633C4⋊C4—2924no—
634C4⋊C4—2924no—
635C4⋊C4—734no—
636C4⋊C4—734no—
637C4⋊C4—734no—
638C4⋊C4—734no—
639C4⋊C4—734no—
640C4⋊C4—734no—
641C4⋊C4—1468no—
642C4⋊C4—1464no—
643C4⋊C4—1464no—
644C22⋊C4—2924no—
645C22⋊C4—2924no—
646C22⋊C4—734no—
647C22⋊C4—734no—
648C22⋊C4—734no—
649C22⋊C4—734no—
650C22⋊C4—734no—
651C22⋊C4—734no—
652C22⋊C4—1468no—
653C22⋊C4—1468no—
654C42—2924no—
655C42—2924no—
656C42—2924no—
657C42—734no—
658C42—734no—
659C42—734no—
660C42—734no—
661C42—734no—
662C42—734no—
663C42—1468no—
664C42C2×C4×D7314yes—
665C42C2×C4×D7314yes—
666C42C2×C4×D7314yes—
667C42C2×C4×D7314yes—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—732no—
672C23—734no—
673C23—732no—
674C23—1462no—
675C23—1461no—
676C23—1461no—
677C23—1462no—
678C23—1461no—
679C23—1461no—
680C23—1462no—
681C23C22×C4×D7312yes—
682C23#41×D7314yes—
683C23C24×D7311yescharacteristic
684Q8—1468no—
685D4—7316no—
686D4—1468no—
687D4—1468no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—44no—
703C2×C4—88no—
704C2×C4—2924no—
705C2×C4—2924no—
706C2×C4—5848no—
707C2×C4—732no—
708C2×C4—734no—
709C2×C4—732no—
710C2×C4—732no—
711C2×C4—732no—
712C2×C4—732no—
713C2×C4—732no—
714C2×C4—1468no—
715C2×C4—1468no—
716C2×C4—1464no—
717C2×C4—1464no—
718C2×C4—1464no—
719C2×C4—1464no—
720C2×C4—1464no—
721C2×C4—1464no—
722C2×C4—1462no—
723C2×C4—1461no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4—1461no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1468no—
730C2×C4—1468no—
731C2×C4C22×C4×D7312yes—
732C2×C4C22×C4×D7312yes—
733C2×C4C22×C4×D7312yes—
734C2×C4C22×C4×D7312yes—
735C2×C4C22×C4×D7312yes—
736C2×C4C22×C4×D7312yes—
737C2×C4#1455663612yes—
738C2×C4#1455663912yes—
739C22—24no—
740C22—22no—
741C22—22no—
742C22—24no—
743C22—2922no—
744C22—2922no—
745C22—734no—
746C22—1462no—
747C22—1462no—
748C22—1462no—
749C22—1464no—
750C22—1462no—
751C22—1462no—
752C22—1464no—
753C22#117×D7314yes—
754C22C23×C4×D7311yescharacteristic
755C22C2×#41×D7312yes—
756C22C2×#1455663611yescharacteristic
757C22C2×#1455663911yescharacteristic
758C22#1798942312yes—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—44no—
765C4—44no—
766C4—2924no—
767C4—2924no—
768C4—734no—
769C4—1462no—
770C4—1462no—
771C4—1462no—
772C4—1462no—
773C4—1462no—
774C4#1798906814yes—
775C2—24no—
776C2—2922no—
777C2—1464no—
778C2C2×#117×D7311yescharacteristic
779C2C2×#1798906811yescharacteristic
780C2#2262313211yescharacteristic
781C2#2262388612yes—
782C2#2262390312yes—
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC2×#382×C73C2
socle, cosocleC23×C73C25
prime radicalC22×#11924028C22
hypercenterC2×#382D73
hypocenterC73#34191
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #22612883C2semidirect
3. #22612857C2semidirect
4. #22612856C2semidirect
5. C4⋊C4×C22⋊D73C2semidirect
6. #22612811C2semidirect
7. #22612787C2semidirect
8. #22612784C2semidirect
10. #22612579C2semidirect
11. #22612567C2semidirect
12. #22612565C2semidirect
13. #22612337C2semidirect
14. #22612329C2semidirect
15. #22612324C2semidirect
16. #22612324C2semidirect
17. #382×D73C2semidirect
18. #22612289C2semidirect
19. C2×#382×C73C2semidirect
21. C4×#11924028C4semidirect
105. C4×Dic146C2×C4semidirect
106. C4×Dic146C2×C4semidirect
107. C4×D292C2×C4semidirect
108. C4×D292C2×C4semidirect
112. C4×C22⋊D73C2×C4semidirect
113. C4×C22⋊D73C2×C4semidirect
114. #14556550C2×C4semidirect
116. #14556548C2×C4semidirect
117. #14556548C2×C4semidirect
150. C42×D73C2×C4semidirect
151. C42×D73C2×C4semidirect
172. C2×C42×C73C2×C4semidirect
317. C22⋊D73#117semidirect
409. C2×#382D73semidirect
411. C73#34191semidirect
552. C2×C42C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#119240282
#226128832
#226128572
#226128562
C4⋊C4×C22⋊D732
#226128112
#226127872
#226127842
#226127582
#226125792
#226125672
#226125652
#226123372
#226123292
#226123242
#382×D732
#226122892
C2×#382×C732
#3419173