Finite Group Databasebeta

← #33102068

Subgroups — #33102068

Order 18688.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989117C211yesmaximal, characteristic
2C2×#17988665C211yesmaximal, characteristic, complemented
3#22610871C211yesmaximal, characteristic, complemented
4#22610866C211yesmaximal, characteristic, complemented
5#22610228C211yesmaximal, characteristic, complemented
6#22610226C211yesmaximal, characteristic, complemented
7#22610226C211yesmaximal, characteristic, complemented
8#22610223C211yesmaximal, characteristic, complemented
9#22610000C211yesmaximal, characteristic, complemented
10#22609997C211yesmaximal, characteristic, complemented
11#22609912C211yesmaximal, characteristic, complemented
12#22609700C211yesmaximal, characteristic, complemented
13#22609627C211yesmaximal, characteristic, complemented
14#22609624C211yesmaximal, characteristic, complemented
15C2×#435×C73C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18#17989117—24no—
19#17989117—24no—
20C2×#14556586C411yescharacteristic
21C2×#14556584C411yescharacteristic
22C2×#14556581C411yescharacteristic
23C2×#14556577C411yescharacteristic
24C2×#14556575C411yescharacteristic
25C2×#14556572C411yescharacteristic
26C2×#14556568C411yescharacteristic
27C2×#14556563C411yescharacteristic
28C2×C4×Dic146C2211yescharacteristic
29C2×C4×C22⋊D73C2211yescharacteristic
30C2×C4×C22⋊D73C2211yescharacteristic
31C2×#14556550C2211yescharacteristic
32C2×#14556548C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34#17988665—24no—
35C2×C4⋊#10596831C2211yescharacteristic
36C2×C22⋊#10596831C2211yescharacteristic
37C2×C22⋊#10596831C2211yescharacteristic
38C2×#14556503C2211yescharacteristic
39C2×#14556503C2211yescharacteristic
40C2×#14556503C2211yescharacteristic
41C2×#14556503C2211yescharacteristic
42C2×C4×#10596831C2211yescharacteristic
43#17988341C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55C22×M16×C73C2211yescharacteristic
56C23×C8×C73C2211yescharacteristic
57C2×C4×D4×C73C2211yescharacteristic
58#435×C73—24no—
59C2×C4⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C2×#97×C73C2211yescharacteristic
63C22×Dic146C2×C411yescharacteristic
64C22×C22⋊D73C2×C411yescharacteristic
65C22×C22⋊D73C2×C411yescharacteristic
66C23×Dic73C2×C411yescharacteristic
67C23×Dic73C2×C411yescharacteristic
68C22×C4×D73C2311yescharacteristic
69C2×#11924012—22no—
70C2×#11924012—22no—
71C2×#11924012—22no—
72C2×#11924012—22no—
73C2×#11924012—41no—
74C2×#11924012—41no—
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79#14556586—24no—
80#14556584—24no—
81#14556581—24no—
82#14556577—24no—
83#14556575—24no—
84#14556572—24no—
85#14556568—24no—
86#14556563—24no—
87C4×Dic146—22no—
88C4×Dic146—22no—
89C4×C22⋊D73—22no—
90C4×C22⋊D73—22no—
91C4×C22⋊D73—22no—
92C4×C22⋊D73—22no—
93#14556550—22no—
94#14556550—22no—
95#14556548—22no—
96#14556548—22no—
97C2×C4⋊Dic73C2×C411yescharacteristic
98C2×C4⋊Dic73C2×C411yescharacteristic
99C2×C4⋊Dic73C2×C411yescharacteristic
100C2×#11924007C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924007C2×C411yescharacteristic
104C2×#11924007C2×C411yescharacteristic
105C2×#11924007C2×C411yescharacteristic
106C2×C22⋊Dic73C2×C411yescharacteristic
107C2×C22⋊Dic73C2×C411yescharacteristic
108C2×C22⋊Dic73C2×C411yescharacteristic
109C2×C22⋊Dic73C2×C411yescharacteristic
110C2×#11924005C2×C411yescharacteristic
111C2×#11924005C2×C411yescharacteristic
112C2×#11924005C2×C411yescharacteristic
113C2×#11924005C2×C411yescharacteristic
114C2×C4×Dic73—22no—
115C2×C4×Dic73—22no—
116C2×C4×Dic73C2×C411yescharacteristic
117C2×C4×Dic73C2×C411yescharacteristic
118C2×C4×Dic73C2311yescharacteristic
119C2×C4×Dic73C2311yescharacteristic
120C2×C4×Dic73C2311yescharacteristic
121C4⋊#10596831—22no—
122C22⋊#10596831—22no—
123C22⋊#10596831—22no—
124#14556503—22no—
125#14556503—22no—
126#14556503—41no—
127#14556503—41no—
128C4×#10596831—22no—
129C22×D4×C73C2×C411yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C2×M16×C73—22no—
133C2×M16×C73—22no—
134C2×M16×C73—41no—
135C22×C8×C73—22no—
136C22×C8×C73—22no—
137C22×C8×C73—41no—
138C22×C8×C73C2311yescharacteristic
139C22×C8×C73C2311yescharacteristic
140C22×C8×C73C2311yescharacteristic
141C22×C8×C73C2311yescharacteristic
142C4×D4×C73D414yes—
143C4×D4×C73D414yes—
144C2×C4⋊C4×C73C2×C411yescharacteristic
145C2×C22⋊C4×C73C2×C411yescharacteristic
146C2×C22⋊C4×C73C2×C411yescharacteristic
147C2×C42×C73C2311yescharacteristic
148C4⋊C8×C73—22no—
149C22⋊C8×C73—22no—
150C22⋊C8×C73—22no—
151#97×C73—22no—
152C23×D73C22×C411yescharacteristic
153C2×Dic146—22no—
154C2×Dic146—22no—
155C2×Dic146—41no—
156C2×C22⋊D73—22no—
157C2×C22⋊D73—22no—
158C2×C22⋊D73—22no—
159C2×C22⋊D73—41no—
160C2×C22⋊D73—41no—
161C2×C22⋊D73—41no—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—41no—
166C22×Dic73—41no—
167C22×Dic73—41no—
168C22×Dic73C22×C411yescharacteristic
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C22×Dic73C22×C411yescharacteristic
172C22×Dic73C22×C411yescharacteristic
173C22×Dic73C22×C411yescharacteristic
174C22×Dic73C22×C411yescharacteristic
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—21no—
179C2×C4×D73—21no—
180C2×C4×D73—21no—
181#11924012—44no—
182#11924012—44no—
183C2×#10596831—21no—
184C2×#10596831—21no—
185C2×#10596831—21no—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831#4112yes—
195C4⋊Dic73—22no—
196C4⋊Dic73—22no—
197C4⋊Dic73—22no—
198#11924007—22no—
199#11924007—22no—
200#11924007—22no—
201#11924007—22no—
202#11924007—22no—
203#11924007—22no—
204C22⋊Dic73—22no—
205C22⋊Dic73—22no—
206C22⋊Dic73—22no—
207C22⋊Dic73—22no—
208#11924005—22no—
209#11924005—22no—
210#11924005—22no—
211#11924005—22no—
212C4×Dic73—22no—
213C4×Dic73—22no—
214C4×Dic73—21no—
215C4×Dic73—21no—
216C4×Dic73—21no—
217C4×Dic73—21no—
218C4×Dic73—21no—
219C4×Dic73—21no—
220C24×C73C22×C411yescharacteristic
221C24×C73C22×C411yescharacteristic
222C2×D4×C73—41no—
223C2×D4×C73—41no—
224C2×D4×C73C22⋊C414yes—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C22×C411yescharacteristic
236C22×C4×C73C22×C411yescharacteristic
237C22×C4×C73C2×D412yes—
238C22×C4×C73C2×D412yes—
239C22×C4×C73C2×D412yes—
240C22×C4×C73C2×D412yes—
241C22×C4×C73C2411yescharacteristic
242M16×C73—44no—
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—
251C2×C8×C73—21no—
252C2×C8×C73—21no—
253C2×C8×C73—21no—
254C2×C8×C73—44no—
255C2×C8×C73#4112yes—
256C4⋊C4×C73C22⋊C414yes—
257C22⋊C4×C73C22⋊C414yes—
258C22⋊C4×C73C22⋊C414yes—
259C42×C73C2×D412yes—
260C42×C73C2×D412yes—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73C2×C22⋊C412yes—
274C23×C73C2×C22⋊C412yes—
275C23×C73C23×C411yescharacteristic
276C22×D73—21no—
277C22×D73—21no—
278C22×D73—21no—
279C22×D73—21no—
280C22×D73—21no—
281C22×D73—21no—
282C22×D73—21no—
283D4×C73—44no—
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—21no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73C2×C22⋊C412yes—
301C2×C4×C73C2×C22⋊C412yes—
302C2×C4×C73C2×C22⋊C412yes—
303C2×C4×C73C2×C22⋊C412yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C2×#4111yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C73H(5,𝔽2)11yescharacteristic
309C2×C4×C732−1+411yescharacteristic
310C22⋊D73—44no—
311C22⋊D73—44no—
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—21no—
326C2×Dic73—21no—
327C2×Dic73—21no—
328C2×Dic73—21no—
329C2×Dic73—21no—
330C2×Dic73—21no—
331C2×Dic73—21no—
332C2×Dic73—44no—
333C2×Dic73—44no—
334C2×Dic73#13112yes—
335C4×D73—41no—
336C4×D73—41no—
337C4×D73—41no—
338C4×D73—41no—
339Dic146—44no—
340C8×C73—22no—
341C8×C73—41no—
342C8×C73—41no—
343C8×C73—41no—
344#10596831—22no—
345#10596831—41no—
346#10596831—41no—
347#10596831—41no—
348C22×C73—22no—
349C22×C73—22no—
350C22×C73—22no—
351C22×C73—22no—
352C22×C73—22no—
353C22×C73—22no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73C22×C22⋊C411yescharacteristic
363C22×C73C4×#4111yescharacteristic
364C22×C73#52011yescharacteristic
365C22×C73C2×#13111yescharacteristic
366C22×C73#56811yescharacteristic
367C22×C73#56811yescharacteristic
368C22×C73#56811yescharacteristic
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
372C2×D73—41no—
373C2×D73—41no—
374C2×D73—41no—
375C2×D73—41no—
376C4×C73—22no—
377C4×C73—22no—
378C4×C73—22no—
379C4×C73—22no—
380C4×C73#54611yescharacteristic
381C4×C73#54611yescharacteristic
382C4×C73#54711yescharacteristic
383C4×C73#54711yescharacteristic
384Dic73—22no—
385Dic73—41no—
386Dic73—41no—
387Dic73—41no—
388Dic73—41no—
389Dic73—41no—
390Dic73—41no—
391#22472—731nomaximal, Sylow
392C2×C73—42no—
393C2×C73—42no—
394C2×C73#233911yescharacteristic
395C2×C73#287911yescharacteristic
396C2×C73#288011yescharacteristic
397C2×C73#296711yescharacteristic
398C2×C73#296911yescharacteristic
399C2×C73#299311yescharacteristic
400C2×C73#299511yescharacteristic
401D73—81no—
402C2×#529—731no—
403C2×#436—731no—
404C2×#435D7311yescharacteristic, complemented
405#1985—731no—
406#1984—731no—
407#1870—731no—
408#1870—731no—
409#1870—731no—
410#1869—731no—
411#1818—731no—
412#1817—731no—
413#1798—731no—
414#1750—731no—
415#1729—731no—
416#1728—731no—
417C73#2247211yescharacteristic, complemented, Sylow
418C22×M16—731no—
419C22×M16—731no—
420C22×M16C2×D7311yescharacteristic
421C23×C8C2×D7311yescharacteristic
422#529—1464no—
423#529—1464no—
424C2×#126—731no—
425C2×#126—731no—
426C2×#125—731no—
427C2×#124—731no—
428C2×#123—731no—
429C2×#123—731no—
430C2×C22⋊Q8—731no—
431C2×#121—731no—
432C2×C4×Q8—731no—
433C2×C4×D4—731no—
434C2×C4×D4—731no—
435C2×C4×D4C2×D7311yescharacteristic
436C2×#117—731no—
437C2×#117—731no—
438C22×C42—731no—
439#436—1464no—
440#435—24no—
441C2×C4⋊C8—731no—
442C2×C4⋊C8C2×D7311yescharacteristic
443C2×C22⋊C8—731no—
444C2×C22⋊C8—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×C22⋊C8—731no—
449C2×C22⋊C8C2×D7311yescharacteristic
450C2×C22⋊C8C2×D7311yescharacteristic
451C2×#97C2×D7311yescharacteristic
452C2×C4×C8—731no—
453#336—731no—
454#336—731no—
455#336—731no—
456#336—731no—
457#336—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461#336—731no—
462#336—731no—
463#336—731no—
464#336—731no—
465C22×Q8—731no—
466C22×D4—731no—
467C22×D4—731no—
468C22×D4C4×D7311yescharacteristic
469C23×C4—731no—
470C23×C4—731no—
471C23×C4—731no—
472C23×C4C22×D7311yescharacteristic
473C23×C4C22×D7311yescharacteristic
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—41no—
477C2×M16—2921no—
478C2×M16—2921no—
479C2×M16—1462no—
480C2×M16—1462no—
481C2×M16—1462no—
482C2×M16—1462no—
483C22×C8—22no—
484C22×C8—22no—
485C22×C8—41no—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8—731no—
489C22×C8—731no—
490C22×C8C22×D7311yescharacteristic
491C22×C8C22×D7311yescharacteristic
492C22×C8C22×D7311yescharacteristic
493C22×C8C22×D7311yescharacteristic
494#126—1464no—
495#126—1464no—
496#125—1464no—
497#124—1464no—
498#123—1464no—
499#123—1464no—
500C22⋊Q8—1464no—
501#121—1464no—
502C4×Q8—1462no—
503C4×Q8—1462no—
504C4×D4—1462no—
505C4×D4—1462no—
506C4×D4—1462no—
507C4×D4—1462no—
508C4×D4D29214yes—
509C4×D4C22⋊D7314yes—
510#117—1462no—
511#117—1462no—
512#117—1462no—
513#117—1462no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—731no—
518C2×C4⋊C4—731no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4C4×D7311yescharacteristic
524C2×C22⋊C4—731no—
525C2×C22⋊C4—731no—
526C2×C22⋊C4—731no—
527C2×C22⋊C4—731no—
528C2×C22⋊C4—731no—
529C2×C22⋊C4—731no—
530C2×C22⋊C4—731no—
531C2×C22⋊C4—731no—
532C2×C22⋊C4C4×D7311yescharacteristic
533C2×C22⋊C4C4×D7311yescharacteristic
534C2×C42—731no—
535C2×C42—731no—
536C2×C42—731no—
537C2×C42—731no—
538C2×C42—731no—
539C2×C42—1462no—
540C2×C42—1462no—
541C2×C42C22×D7311yescharacteristic
542C4⋊C8—22no—
543C4⋊C8—1462no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—2921no—
547C22⋊C8—2921no—
548C22⋊C8—1462no—
549C22⋊C8—1462no—
550C22⋊C8—1462no—
551C22⋊C8—1462no—
552#97—22no—
553C4×C8—1462no—
554C24—731no—
555C24C2×C4×D7311yescharacteristic
556C24C2×C4×D7311yescharacteristic
557C2×Q8—2921no—
558C2×Q8—1462no—
559C2×Q8—1462no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—2921no—
563C2×D4—2921no—
564C2×D4—2921no—
565C2×D4—1462no—
566C2×D4—1462no—
567C2×D4—1462no—
568C2×D4#1192400514yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—2921no—
578C22×C4—2921no—
579C22×C4—2921no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—731no—
583C22×C4—731no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—1462no—
588C22×C4—1462no—
589C22×C4—1462no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4C2×C4×D7311yescharacteristic
597C22×C4C2×C4×D7311yescharacteristic
598C22×C4C2×C4×D7311yescharacteristic
599C22×C4C2×C4×D7311yescharacteristic
600C22×C4C2×C22⋊D7312yes—
601C22×C4C2×C22⋊D7312yes—
602C22×C4C2×D29212yes—
603C22×C4C2×D29212yes—
604C22×C4C23×D7311yescharacteristic
605M16—44no—
606M16—2924no—
607M16—2924no—
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—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—44no—
620C2×C8—732no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8—1461no—
626C2×C8—1461no—
627C2×C8—1461no—
628C2×C8—1461no—
629C2×C8—1461no—
630C2×C8—1461no—
631C2×C8—1461no—
632C2×C8#1192402712yes—
633C4⋊C4—1462no—
634C4⋊C4—1462no—
635C4⋊C4—1462no—
636C4⋊C4—1462no—
637C4⋊C4—1462no—
638C4⋊C4—1462no—
639C4⋊C4—1462no—
640C4⋊C4—1462no—
641C4⋊C4—1462no—
642C4⋊C4#1192400514yes—
643C22⋊C4—1462no—
644C22⋊C4—1462no—
645C22⋊C4—1462no—
646C22⋊C4—1462no—
647C22⋊C4—1462no—
648C22⋊C4—1462no—
649C22⋊C4—1462no—
650C22⋊C4—1462no—
651C22⋊C4#1192400514yes—
652C22⋊C4#1192400514yes—
653C42—1462no—
654C42—1462no—
655C42—1461no—
656C42—1461no—
657C42—1461no—
658C42—1461no—
659C42—1461no—
660C42—1461no—
661C42C2×C22⋊D7312yes—
662C42C2×D29212yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23—1461no—
679C23—1461no—
680C23—1461no—
681C23—1461no—
682C23C2×#1192400512yes—
683C23C2×#1192400512yes—
684C23C22×C4×D7311yescharacteristic
685Q8—2924no—
686D4—44no—
687D4—2924no—
688D4—2924no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—2924no—
706C2×C4—2924no—
707C2×C4—2921no—
708C2×C4—2921no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—732no—
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×C4—1461no—
728C2×C4—1461no—
729C2×C4—1461no—
730C2×C4—1461no—
731C2×C4—1461no—
732C2×C4C2×#1192400512yes—
733C2×C4C2×#1192400512yes—
734C2×C4C2×#1192400512yes—
735C2×C4C2×#1192400512yes—
736C2×C4C22×C22⋊D7311yescharacteristic
737C2×C4C22×D29211yescharacteristic
738C2×C4#41×D7311yescharacteristic
739C2×C4C2×#1192402711yescharacteristic
740C2×C4#1455663611yescharacteristic
741C2×C4#1455663811yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—2921no—
747C8—2921no—
748C8—2921no—
749C8—1462no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—2921no—
765C22—2921no—
766C22—2921no—
767C22—2921no—
768C22—2921no—
769C22—2921no—
770C22—2921no—
771C22C22×#1192400511yescharacteristic
772C22C4×#1192402711yescharacteristic
773C22#1798906611yescharacteristic
774C22#131×D7311yescharacteristic
775C22#1798935211yescharacteristic
776C22#1798935311yescharacteristic
777C22#1798935311yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—2921no—
783C4—2921no—
784C4—2921no—
785C4—2921no—
786C4—2921no—
787C4—2921no—
788C4—1462no—
789C4#1798923111yescharacteristic
790C4#1798923211yescharacteristic
791C4#1798923611yescharacteristic
792C4#1798924111yescharacteristic
793C2—42no—
794C2—42no—
795C2—5841no—
796C2#2261275611yescharacteristic
797C2#2261837511yescharacteristic
798C2#2261837811yescharacteristic
799C2#2261891011yescharacteristic
800C2#2261892811yescharacteristic
801C2#2261907311yescharacteristic
802C2#2261910211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#435×C73C2
prime radicalC2×#14556563C4
cosocleC22×C4×C73C24
hypercenterC2×#435D73
hypocenterC73#22472
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#17988665C2semidirect
3. #22610871C2semidirect
4. #22610866C2semidirect
5. #22610228C2semidirect
6. #22610226C2semidirect
7. #22610226C2semidirect
8. #22610223C2semidirect
9. #22610000C2semidirect
10. #22609997C2semidirect
11. #22609912C2semidirect
12. #22609700C2semidirect
13. #22609627C2semidirect
14. #22609624C2semidirect
15. C2×#435×C73C2semidirect
404. C2×#435D73semidirect
417. C73#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#179891172
C2×#179886652
#226108712
#226108662
#226102282
#226102262
#226102232
#226100002
#226099972
#226099122
#226097002
#226096272
#226096242
C2×#435×C732
#2247273