Finite Group Databasebeta

← #33090995

Subgroups — #33090995

Order 18688.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989115C211yesmaximal, characteristic
2C2×#17988543C211yesmaximal, characteristic, complemented
3#22610870C211yesmaximal, characteristic, complemented
4#22610866C211yesmaximal, characteristic, complemented
5#22610728C211yesmaximal, characteristic, complemented
6#22610724C211yesmaximal, characteristic, complemented
7#22610226C211yesmaximal, characteristic, complemented
8#22610226C211yesmaximal, characteristic, complemented
9#22610221C211yesmaximal, characteristic, complemented
10#22610221C211yesmaximal, characteristic, complemented
11#22609700C211yesmaximal, characteristic, complemented
12#22609698C211yesmaximal, characteristic, complemented
13#22609694C211yesmaximal, characteristic, complemented
14C4×#14556503C211yesmaximal, characteristic, complemented
15C2×#433×C73C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18#17989115—24no—
19#17989115—24no—
20C2×#14556586C411yescharacteristic
21C2×#14556584C411yescharacteristic
22C2×#14556581C411yescharacteristic
23C2×#14556577C411yescharacteristic
24C2×#14556576C411yescharacteristic
25C2×#14556573C411yescharacteristic
26C2×#14556569C411yescharacteristic
27C2×#14556564C411yescharacteristic
28C2×C4×Dic146C2211yescharacteristic
29C2×C4×D292C2211yescharacteristic
30C2×C4×C22⋊D73C2211yescharacteristic
31C2×C4×C22⋊D73C2211yescharacteristic
32C2×#14556548C2211yescharacteristic
33C2×C42×D73C2211yescharacteristic
34C2×#14556503C2211yescharacteristic
35C2×#14556503C2211yescharacteristic
36C2×#14556503C2211yescharacteristic
37C2×#14556503C2211yescharacteristic
38C2×#14556503C2211yescharacteristic
39C2×#14556503C2211yescharacteristic
40C2×#14556503C2211yescharacteristic
41C2×#14556503C2211yescharacteristic
42#17988543—24no—
43C2×#14556502C2211yescharacteristic
44C2×#14556502C2211yescharacteristic
45C2×C4×#10596831C2211yescharacteristic
46C2×C4×#10596831C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55C2×#117×C73C2211yescharacteristic
56#433×C73—24no—
57C2×C4⋊C8×C73C2211yescharacteristic
58C2×C4⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C2×#97×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63C22×Dic146C2×C411yescharacteristic
64C22×D292C2×C411yescharacteristic
65C22×C22⋊D73C2×C411yescharacteristic
66C22×C22⋊D73C2×C411yescharacteristic
67C22×C4×D73C2×C411yescharacteristic
68C22×C4×D73C2×C411yescharacteristic
69C22×C4×D73C2311yescharacteristic
70C22×C4×D73C2311yescharacteristic
71C2×#11924012—22no—
72C2×#11924012—22no—
73C2×#11924012—22no—
74C22×#10596831—22no—
75C22×#10596831—22no—
76C22×#10596831—22no—
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C22×#10596831C2311yescharacteristic
81#14556586—24no—
82#14556584—24no—
83#14556581—24no—
84#14556577—24no—
85#14556576—24no—
86#14556573—24no—
87#14556569—24no—
88#14556564—24no—
89C4×Dic146—22no—
90C4×Dic146—22no—
91C4×D292—22no—
92C4×D292—22no—
93C4×C22⋊D73—22no—
94C4×C22⋊D73—22no—
95C4×C22⋊D73—22no—
96C4×C22⋊D73—22no—
97#14556548—22no—
98#14556548—22no—
99C2×C4⋊Dic73C2×C411yescharacteristic
100C2×C4⋊Dic73C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924007C2×C411yescharacteristic
104C2×#11924007C2×C411yescharacteristic
105C2×#11924007C2×C411yescharacteristic
106C2×#11924007C2×C411yescharacteristic
107C2×C22⋊Dic73C2×C411yescharacteristic
108C2×C22⋊Dic73C2×C411yescharacteristic
109C2×#11924005C2×C411yescharacteristic
110C2×#11924005C2×C411yescharacteristic
111C2×#11924005C2×C411yescharacteristic
112C2×#11924005C2×C411yescharacteristic
113C2×#11924005C2×C411yescharacteristic
114C2×#11924005C2×C411yescharacteristic
115C2×C4×Dic73C2×C411yescharacteristic
116C2×C4×Dic73C2×C411yescharacteristic
117C2×C4×Dic73C2311yescharacteristic
118C2×C4×Dic73C2311yescharacteristic
119C42×D73—22no—
120C42×D73—22no—
121#14556503—22no—
122#14556503—22no—
123#14556503—22no—
124#14556503—22no—
125#14556503—22no—
126#14556503—22no—
127#14556503—22no—
128#14556503—22no—
129#14556502—22no—
130#14556502—22no—
131C4×#10596831—22no—
132C4×#10596831—22no—
133C23×C4×C73C2311yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C22×C8×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138#117×C73D414yes—
139#117×C73D414yes—
140C2×C4⋊C4×C73C2×C411yescharacteristic
141C2×C4⋊C4×C73C2×C411yescharacteristic
142C2×C22⋊C4×C73C2×C411yescharacteristic
143C2×C22⋊C4×C73C2×C411yescharacteristic
144C2×C42×C73C2311yescharacteristic
145C2×C42×C73C2311yescharacteristic
146C4⋊C8×C73—22no—
147C4⋊C8×C73—22no—
148C22⋊C8×C73—22no—
149C22⋊C8×C73—22no—
150#97×C73—22no—
151C4×C8×C73—22no—
152C23×D73C22×C411yescharacteristic
153C23×D73C22×C411yescharacteristic
154C2×Dic146—22no—
155C2×Dic146—22no—
156C2×Dic146—41no—
157C2×D292—22no—
158C2×D292—22no—
159C2×D292—41no—
160C2×C22⋊D73—22no—
161C2×C22⋊D73—22no—
162C2×C22⋊D73—22no—
163C2×C22⋊D73—22no—
164C2×C22⋊D73—41no—
165C2×C22⋊D73—41no—
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C22×Dic73C22×C411yescharacteristic
172C2×C4×D73—22no—
173C2×C4×D73—22no—
174C2×C4×D73—22no—
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—21no—
179C2×C4×D73—21no—
180C2×C4×D73—21no—
181C2×C4×D73—21no—
182C2×C4×D73—21no—
183C2×C4×D73—21no—
184C2×C4×D73—21no—
185C2×C4×D73—21no—
186C2×C4×D73—21no—
187C2×C4×D73—22no—
188C2×C4×D73—41no—
189C2×C4×D73—41no—
190#11924012—28no—
191C2×#10596831—28no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831—21no—
198C2×#10596831—21no—
199C2×#10596831—21no—
200C2×#10596831#4112yes—
201C2×#10596831#4112yes—
202C2×#10596831#4112yes—
203C2×#10596831#4112yes—
204C4⋊Dic73—22no—
205C4⋊Dic73—22no—
206#11924007—22no—
207#11924007—22no—
208#11924007—22no—
209#11924007—22no—
210#11924007—22no—
211#11924007—22no—
212C22⋊Dic73—22no—
213C22⋊Dic73—22no—
214#11924005—22no—
215#11924005—22no—
216#11924005—22no—
217#11924005—22no—
218#11924005—22no—
219#11924005—22no—
220C4×Dic73—22no—
221C4×Dic73—22no—
222C4×Dic73—21no—
223C4×Dic73—21no—
224C4×Dic73—21no—
225C4×Dic73—21no—
226C24×C73C22×C411yescharacteristic
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C22×C411yescharacteristic
236C22×C4×C73C2×D412yes—
237C22×C4×C73C2×D412yes—
238C22×C4×C73C2411yescharacteristic
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C4⋊C4×C73C22⋊C414yes—
252C4⋊C4×C73C22⋊C414yes—
253C22⋊C4×C73C22⋊C414yes—
254C22⋊C4×C73C22⋊C414yes—
255C42×C73C2×D412yes—
256C42×C73C2×D412yes—
257C42×C73C2×D412yes—
258C42×C73C2×D412yes—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73C2×C22⋊C412yes—
266C23×C73C23×C411yescharacteristic
267C22×D73—21no—
268C22×D73—21no—
269C22×D73—21no—
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277C22×D73—21no—
278C22×D73—21no—
279C22×D73—21no—
280C22×D73#13112yes—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73C2×C22⋊C412yes—
296C2×C4×C73C2×C22⋊C412yes—
297C2×C4×C73C2×C22⋊C412yes—
298C2×C4×C73C2×C22⋊C412yes—
299C2×C4×C73C2×C22⋊C412yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C22×D411yescharacteristic
302C2×C4×C73C2×#4111yescharacteristic
303C2×C4×C73C2×#4111yescharacteristic
304C2×C4×C73C2×#4111yescharacteristic
305C2×C4×C73C2×#4111yescharacteristic
306C22⋊D73—44no—
307C22⋊D73—44no—
308C2×Dic73—21no—
309C2×Dic73—21no—
310C2×Dic73—21no—
311C2×Dic73—21no—
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—21no—
315C2×Dic73—21no—
316C2×Dic73—21no—
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73#13112yes—
326D292—44no—
327C4×D73—44no—
328C4×D73—44no—
329C4×D73—41no—
330C4×D73—41no—
331C4×D73—41no—
332C4×D73—41no—
333C4×D73—41no—
334C4×D73—41no—
335C4×D73—41no—
336C4×D73—41no—
337Dic146—44no—
338C8×C73—41no—
339C8×C73—41no—
340C8×C73—41no—
341C8×C73—41no—
342#10596831—22no—
343#10596831—22no—
344#10596831—22no—
345#10596831—22no—
346C22×C73—22no—
347C22×C73—22no—
348C22×C73—22no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73C22×C22⋊C411yescharacteristic
354C22×C73C4×#4111yescharacteristic
355C22×C73C4×#4111yescharacteristic
356C22×C73C2×#13111yescharacteristic
357C22×C73C2×#13111yescharacteristic
358C22×C73#56811yescharacteristic
359C22×C73#56811yescharacteristic
360C2×D73—22no—
361C2×D73—22no—
362C2×D73—22no—
363C2×D73—41no—
364C2×D73—41no—
365C2×D73—41no—
366C2×D73—41no—
367C2×D73—41no—
368C2×D73—41no—
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
372C2×D73—41no—
373C2×D73—41no—
374C4×C73—22no—
375C4×C73—22no—
376C4×C73—22no—
377C4×C73—22no—
378C4×C73—22no—
379C4×C73#52511yescharacteristic
380C4×C73#52511yescharacteristic
381C4×C73#53211yescharacteristic
382C4×C73#53211yescharacteristic
383Dic73—22no—
384Dic73—41no—
385Dic73—41no—
386Dic73—41no—
387Dic73—41no—
388Dic73—41no—
389#21381—731nomaximal, Sylow
390C2×C73—42no—
391C2×C73#229711yescharacteristic
392C2×C73#288011yescharacteristic
393C2×C73#288011yescharacteristic
394C2×C73#296611yescharacteristic
395C2×C73#296711yescharacteristic
396C2×C73#296811yescharacteristic
397C2×C73#296911yescharacteristic
398D73—42no—
399D73—81no—
400C2×#529—731no—
401C2×#433D7311yescharacteristic, complemented
402C2×#405—731no—
403#1985—731no—
404#1984—731no—
405#1955—731no—
406#1954—731no—
407#1870—731no—
408#1870—731no—
409#1869—731no—
410#1869—731no—
411#1750—731no—
412#1750—731no—
413#1749—731no—
414C4×C22⋊C8—731no—
415C73#2138111yescharacteristic, complemented, Sylow
416C22×M16—731no—
417C23×C8—731no—
418#529—1464no—
419#529—1464no—
420C2×#126—731no—
421C2×#126—731no—
422C2×#125—731no—
423C2×#124—731no—
424C2×#123—731no—
425C2×#123—731no—
426C2×C22⋊Q8—731no—
427C2×#121—731no—
428C2×C4×Q8—731no—
429C2×C4×D4—731no—
430C2×C4×D4—731no—
431C2×C4×D4—731no—
432C2×#117—731no—
433C2×#117C2×D7311yescharacteristic
434C22×C42—731no—
435#433—24no—
436C2×C4⋊C8C2×D7311yescharacteristic
437C2×C4⋊C8C2×D7311yescharacteristic
438C2×C22⋊C8—731no—
439C2×C22⋊C8—731no—
440C2×C22⋊C8—731no—
441C2×C22⋊C8—731no—
442C2×C22⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C22⋊C8—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8C2×D7311yescharacteristic
447C2×C22⋊C8C2×D7311yescharacteristic
448#405—1464no—
449C2×#97—731no—
450C2×#97—731no—
451C2×#97C2×D7311yescharacteristic
452C2×C4×C8—731no—
453C2×C4×C8—731no—
454C2×C4×C8C2×D7311yescharacteristic
455#336—731no—
456#336—731no—
457#336—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461#336—731no—
462#336—731no—
463C22×Q8—731no—
464C22×D4—731no—
465C22×D4—731no—
466C22×D4—731no—
467C23×C4—731no—
468C23×C4—731no—
469C23×C4—731no—
470C23×C4—731no—
471C23×C4C22×D7311yescharacteristic
472C2×M16—1462no—
473C2×M16—1462no—
474C2×M16—1462no—
475C22×C8—731no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8—731no—
479C22×C8—1462no—
480C22×C8—1462no—
481C22×C8—1462no—
482C22×C8C22×D7311yescharacteristic
483C22×C8C22×D7311yescharacteristic
484C22×C8C22×D7311yescharacteristic
485C22×C8C22×D7311yescharacteristic
486#126—1464no—
487#126—1464no—
488#125—1464no—
489#124—1464no—
490#123—1464no—
491#123—1464no—
492C22⋊Q8—1464no—
493#121—1464no—
494C4×Q8—1462no—
495C4×Q8—1462no—
496C4×D4—1462no—
497C4×D4—1462no—
498C4×D4—1462no—
499C4×D4—1462no—
500C4×D4—1462no—
501C4×D4—1462no—
502#117—1462no—
503#117—1462no—
504#117D29214yes—
505#117C22⋊D7314yes—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4C4×D7311yescharacteristic
515C2×C4⋊C4C4×D7311yescharacteristic
516C2×C22⋊C4—731no—
517C2×C22⋊C4—731no—
518C2×C22⋊C4—731no—
519C2×C22⋊C4—731no—
520C2×C22⋊C4—731no—
521C2×C22⋊C4—731no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—731no—
524C2×C22⋊C4C4×D7311yescharacteristic
525C2×C22⋊C4C4×D7311yescharacteristic
526C2×C42—731no—
527C2×C42—731no—
528C2×C42—731no—
529C2×C42—731no—
530C2×C42—1462no—
531C2×C42—1462no—
532C2×C42C22×D7311yescharacteristic
533C2×C42C22×D7311yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—1462no—
539C22⋊C8—1462no—
540C22⋊C8—1462no—
541C22⋊C8—1462no—
542C22⋊C8—1462no—
543C22⋊C8—1462no—
544C22⋊C8—1462no—
545C22⋊C8—1462no—
546#97—22no—
547#97—1462no—
548#97—1462no—
549C4×C8—22no—
550C4×C8—1462no—
551C4×C8—1462no—
552C24—731no—
553C24—731no—
554C24C2×C4×D7311yescharacteristic
555C2×Q8—2921no—
556C2×Q8—1462no—
557C2×Q8—1462no—
558C2×D4—2921no—
559C2×D4—2921no—
560C2×D4—2921no—
561C2×D4—1462no—
562C2×D4—1462no—
563C2×D4—1462no—
564C2×D4—1462no—
565C2×D4—1462no—
566C2×D4—1462no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—2921no—
572C22×C4—2921no—
573C22×C4—731no—
574C22×C4—731no—
575C22×C4—731no—
576C22×C4—731no—
577C22×C4—731no—
578C22×C4—731no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1462no—
582C22×C4—1462no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4C2×C4×D7311yescharacteristic
596C22×C4C2×C4×D7311yescharacteristic
597C22×C4C2×C4×D7311yescharacteristic
598C22×C4C2×C4×D7311yescharacteristic
599C22×C4C2×C4×D7311yescharacteristic
600C22×C4C2×C22⋊D7312yes—
601C22×C4C2×D29212yes—
602C22×C4C23×D7311yescharacteristic
603M16—1468no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—732no—
617C2×C8—732no—
618C2×C8—732no—
619C2×C8—732no—
620C2×C8—1468no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8—1461no—
626C2×C8—1461no—
627C2×C8—1461no—
628C2×C8—1461no—
629C4⋊C4—1462no—
630C4⋊C4—1462no—
631C4⋊C4—1462no—
632C4⋊C4—1462no—
633C4⋊C4—1462no—
634C4⋊C4—1462no—
635C4⋊C4—1462no—
636C4⋊C4—1462no—
637C4⋊C4#1192400514yes—
638C4⋊C4#1192400514yes—
639C22⋊C4—1462no—
640C22⋊C4—1462no—
641C22⋊C4—1462no—
642C22⋊C4—1462no—
643C22⋊C4—1462no—
644C22⋊C4—1462no—
645C22⋊C4—1462no—
646C22⋊C4—1462no—
647C22⋊C4#1192400514yes—
648C22⋊C4#1192400514yes—
649C42—1462no—
650C42—1462no—
651C42—1461no—
652C42—1461no—
653C42—1461no—
654C42—1461no—
655C42C2×C22⋊D7312yes—
656C42C2×C22⋊D7312yes—
657C42C2×D29212yes—
658C42C2×D29212yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—732no—
666C23—1461no—
667C23—1461no—
668C23—1461no—
669C23—1461no—
670C23—1461no—
671C23—1461no—
672C23—1461no—
673C23—1461no—
674C23—1461no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23—1461no—
679C23C2×#1192400512yes—
680C23C22×C4×D7311yescharacteristic
681Q8—2924no—
682D4—2924no—
683D4—2924no—
684D4—2924no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—2924no—
700C2×C4—2924no—
701C2×C4—2921no—
702C2×C4—2921no—
703C2×C4—2921no—
704C2×C4—2921no—
705C2×C4—2921no—
706C2×C4—2921no—
707C2×C4—2921no—
708C2×C4—2921no—
709C2×C4—732no—
710C2×C4—1461no—
711C2×C4—1461no—
712C2×C4—1461no—
713C2×C4—1461no—
714C2×C4—1461no—
715C2×C4—1461no—
716C2×C4—1461no—
717C2×C4—1461no—
718C2×C4—1461no—
719C2×C4—1461no—
720C2×C4—1461no—
721C2×C4—1461no—
722C2×C4—1461no—
723C2×C4—1461no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4—1461no—
727C2×C4C2×#1192400512yes—
728C2×C4C2×#1192400512yes—
729C2×C4C2×#1192400512yes—
730C2×C4C2×#1192400512yes—
731C2×C4C2×#1192400512yes—
732C2×C4C22×C22⋊D7311yescharacteristic
733C2×C4C22×D29211yescharacteristic
734C2×C4#41×D7311yescharacteristic
735C2×C4#41×D7311yescharacteristic
736C2×C4#41×D7311yescharacteristic
737C2×C4#41×D7311yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—1462no—
743C8—1462no—
744C8—1462no—
745C8—1462no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—2921no—
754C22—2921no—
755C22—2921no—
756C22—2921no—
757C22—2921no—
758C22—2921no—
759C22—2921no—
760C22—2921no—
761C22—2921no—
762C22—2921no—
763C22—2921no—
764C22—1462no—
765C22—1462no—
766C22—1462no—
767C22C22×#1192400511yescharacteristic
768C22#1798905511yescharacteristic
769C22#1798905511yescharacteristic
770C22#131×D7311yescharacteristic
771C22#131×D7311yescharacteristic
772C22#1798935211yescharacteristic
773C22#1798935211yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—2921no—
780C4—2921no—
781C4—2921no—
782C4—2921no—
783C4—2921no—
784C4—1462no—
785C4#1798909911yescharacteristic
786C4#1798909911yescharacteristic
787C4#1798913311yescharacteristic
788C4#1798913311yescharacteristic
789C2—42no—
790C2—2922no—
791C2—5841no—
792C2#2261241911yescharacteristic
793C2#2261837811yescharacteristic
794C2#2261837811yescharacteristic
795C2#2261890411yescharacteristic
796C2#2261891411yescharacteristic
797C2#2261892311yescharacteristic
798C2#2261893311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#433×C73C2
prime radicalC2×#14556564C4
cosocleC22×C4×C73C24
hypercenterC2×#433D73
hypocenterC73#21381
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. C2×#17988543C2semidirect
3. #22610870C2semidirect
4. #22610866C2semidirect
5. #22610728C2semidirect
6. #22610724C2semidirect
7. #22610226C2semidirect
8. #22610226C2semidirect
9. #22610221C2semidirect
10. #22610221C2semidirect
11. #22609700C2semidirect
12. #22609698C2semidirect
13. #22609694C2semidirect
14. C4×#14556503C2semidirect
15. C2×#433×C73C2semidirect
401. C2×#433D73semidirect
415. C73#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#179891152
C2×#179885432
#226108702
#226108662
#226107282
#226107242
#226102262
#226102212
#226097002
#226096982
#226096942
C4×#145565032
C2×#433×C732
#2138173