Finite Group Databasebeta

← C2×#22622410 #33964557

Subgroups — C2×#22622410 #33964557

Order 18688.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989283C211yesmaximal, characteristic
2#22622410C2116yesmaximal, direct product factor
3C2×#17988993C211yesmaximal, characteristic, complemented
4C2×#17988920C211yesmaximal, characteristic, complemented
5C2×#17988905C211yesmaximal, characteristic, complemented
6C2×#17988925C211yesmaximal, characteristic, complemented
7C2×#17988900C211yesmaximal, characteristic, complemented
8C2×#17988894C211yesmaximal, characteristic, complemented
9C2×#17988864C211yesmaximal, characteristic, complemented
10C2×#17988835C211yesmaximal, characteristic, complemented
11C2×#17988818C211yesmaximal, characteristic, complemented
12C2×#17988685C211yesmaximal, characteristic, complemented
13C2×#17988659C211yesmaximal, characteristic, complemented
14C2×#17988627C211yesmaximal, characteristic, complemented
15C22×#14556524C211yesmaximal, characteristic, complemented
16C2×#554×C73C211yesmaximal, characteristic, complemented
17C22×#11924015C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C23×#10596831C2211yescharacteristic
20#17989283—24no—
21#17989283C2218yes—
22C2×#14556586—21no—
23C2×#14556583C2211yescharacteristic
24C2×#14556573—21no—
25C2×#14556565C2211yescharacteristic
26C2×#14556565C2211yescharacteristic
27C2×#14556563—21no—
28C2×C4×D292C2211yescharacteristic
29C2×#14556551—21no—
30C2×#14556550C2211yescharacteristic
31C22×C4⋊Dic73C2211yescharacteristic
32#17988993C2218yescomplemented
33#17988925C2218yescomplemented
34#17988920C2218yescomplemented
35#17988905C2218yescomplemented
36#17988900C2218yescomplemented
37#17988894C2218yescomplemented
38#17988864C2218yescomplemented
39#17988835C2218yescomplemented
40#17988818C2218yescomplemented
41#17988685C2218yescomplemented
42#17988659C2218yescomplemented
43#17988627C2218yescomplemented
44C2×#14556524C2211yescharacteristic
45C2×#14556524C2211yescharacteristic
46C2×#14556524C2211yescharacteristic
47C2×#14556524C2211yescharacteristic
48C2×#14556524C2211yescharacteristic
49C2×#14556524C2211yescharacteristic
50C2×#14556524C2218yescomplemented
51C2×#14556522C2211yescharacteristic
52C2×#14556522C2211yescharacteristic
53C2×#14556522C2211yescharacteristic
54C2×C4⋊#10596831C2211yescharacteristic
55C2×#14556515C2211yescharacteristic
56C2×#14556515C2211yescharacteristic
57C2×#14556515C2211yescharacteristic
58C2×#14556511C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×#14556511C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×C22⋊#10596831C2211yescharacteristic
63C2×#14556502C2211yescharacteristic
64#554×C73—24no—
65#554×C73C2218yescomplemented
66C2×C4⋊Q8×C73C2211yescharacteristic
67C2×#125×C73—21no—
68C2×C22⋊Q8×C73—21no—
69C2×C22⋊Q8×C73—21no—
70C2×C22⋊Q8×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73C2×C4×D4×C73—21no—
74C2×C4×D4×C73C2211yescharacteristic
75C22×C4⋊C4×C73C2211yescharacteristic
76C22×C4⋊C4×C73C2211yescharacteristic
77C22×D292C2311yescharacteristic
78C22×C22⋊D73—21no—
79C22×C22⋊D73—21no—
80C23×Dic73—21no—
81C22×C4×D73—21no—
82C2×#11924015—24no—
83C2×#11924015C2314yes—
84C2×#11924012—24no—
85C2×#11924012C2314yes—
86C22×#10596831—24no—
87C22×#10596831C2311yescharacteristic
88C22×#10596831C2311yescharacteristic
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2314yes—
91C22×#10596831C2311yescharacteristic
92#14556586—28no—
93#14556583—22no—
94#14556583C2314yes—
95#14556573—28no—
96#14556565—22no—
97#14556565—22no—
98#14556565C2314yes—
99#14556565C2314yes—
100#14556563—28no—
101C4×D292—22no—
102C4×D292C2314yes—
103#14556551—28no—
104#14556550—22no—
105#14556550C2314yes—
106C2×C4⋊Dic73—22no—
107C2×C4⋊Dic73—21no—
108C2×C4⋊Dic73C2311yescharacteristic
109C2×C4⋊Dic73C2311yescharacteristic
110C2×C4⋊Dic73C2311yescharacteristic
111C2×C4⋊Dic73C2314yes—
112C2×#11924007—21no—
113C2×#11924007—21no—
114C2×C22⋊Dic73—21no—
115C2×#11924005—21no—
116C2×#11924005—21no—
117C2×#11924005—21no—
118C2×C4×Dic73—21no—
119#14556524C2314yes—
120#14556524C2314yes—
121#14556524C2314yes—
122#14556524C2314yes—
123#14556524C2314yes—
124#14556524C2314yes—
125#14556522C2314yes—
126#14556522C2314yes—
127#14556522C2314yes—
128C4⋊#10596831C2314yes—
129#14556515C2314yes—
130#14556515C2314yes—
131#14556515C2314yes—
132#14556511C2314yes—
133#14556511C2314yes—
134#14556511C2314yes—
135C22⋊#10596831C2314yes—
136C22⋊#10596831C2314yes—
137#14556502C2314yes—
138C22×Q8×C73—21no—
139C22×Q8×C73C2311yescharacteristic
140C22×D4×C73D411yescharacteristic
141C23×C4×C73—21no—
142C23×C4×C73—21no—
143C23×C4×C73C2311yescharacteristic
144C23×C4×C73C2311yescharacteristic
145C4⋊Q8×C73—22no—
146C4⋊Q8×C73C2314yes—
147#125×C73—28no—
148C22⋊Q8×C73—22no—
149C22⋊Q8×C73—22no—
150C22⋊Q8×C73—28no—
151C22⋊Q8×C73—28no—
152C22⋊Q8×C73C2314yes—
153C22⋊Q8×C73C2314yes—
154C4×Q8×C73—22no—
155C4×Q8×C73C2314yes—
156C4×D4×C73—28no—
157C4×D4×C73D414yes—
158C4×D4×C73C2314yes—
159C2×C4⋊C4×C73—21no—
160C2×C4⋊C4×C73—21no—
161C2×C4⋊C4×C73—22no—
162C2×C4⋊C4×C73—22no—
163C2×C4⋊C4×C73—21no—
164C2×C4⋊C4×C73—21no—
165C2×C4⋊C4×C73—21no—
166C2×C4⋊C4×C73—21no—
167C2×C4⋊C4×C73D411yescharacteristic
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2314yes—
172C2×C4⋊C4×C73C2314yes—
173C2×C22⋊C4×C73—21no—
174C2×C22⋊C4×C73—21no—
175C2×C22⋊C4×C73D411yescharacteristic
176C2×C22⋊C4×C73D411yescharacteristic
177C2×C42×C73—21no—
178C2×C42×C73C2311yescharacteristic
179C23×D73—21no—
180C2×D292—22no—
181C2×D292—22no—
182C2×D292—21no—
183C2×D292C2412yes—
184C2×C22⋊D73—24no—
185C2×C22⋊D73—24no—
186C2×C22⋊D73—44no—
187C2×C22⋊D73—82no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—24no—
192C22×Dic73—82no—
193C2×C4×D73—24no—
194C2×C4×D73—82no—
195#11924015—28no—
196#11924012—28no—
197C2×#10596831—22no—
198C2×#10596831—22no—
199C2×#10596831—22no—
200C2×#10596831—28no—
201C2×#10596831#4114yes—
202C2×#10596831C2412yes—
203C2×#10596831C2412yes—
204C2×#10596831C2412yes—
205C2×#10596831C2412yes—
206C4⋊Dic73—21no—
207C4⋊Dic73—21no—
208C4⋊Dic73—24no—
209C4⋊Dic73—21no—
210C4⋊Dic73C2412yes—
211C4⋊Dic73C2412yes—
212C4⋊Dic73C2412yes—
213#11924007—24no—
214#11924007—24no—
215C22⋊Dic73—24no—
216#11924005—24no—
217#11924005—24no—
218#11924005—24no—
219C4×Dic73—24no—
220C24×C73C2×D411yescharacteristic
221C24×C73C2×D411yescharacteristic
222C2×Q8×C73—21no—
223C2×Q8×C73—24no—
224C2×Q8×C73—22no—
225C2×Q8×C73—22no—
226C2×Q8×C73—82no—
227C2×Q8×C73C2412yes—
228C2×D4×C73—24no—
229C2×D4×C73C2×D414yes—
230C22×C4×C73—22no—
231C22×C4×C73—22no—
232C22×C4×C73—22no—
233C22×C4×C73—22no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—24no—
239C22×C4×C73—24no—
240C22×C4×C73—82no—
241C22×C4×C73—82no—
242C22×C4×C73C2×D411yescharacteristic
243C22×C4×C73C2×D411yescharacteristic
244C22×C4×C73C2×D411yescharacteristic
245C22×C4×C73C2×D411yescharacteristic
246C22×C4×C73C2×D412yes—
247C22×C4×C73C2×D412yes—
248C22×C4×C73C2412yes—
249C22×C4×C73C2412yes—
250C22×C4×C73C2411yescharacteristic
251C4⋊C4×C73—21no—
252C4⋊C4×C73—24no—
253C4⋊C4×C73—24no—
254C4⋊C4×C73—21no—
255C4⋊C4×C73—21no—
256C4⋊C4×C73—24no—
257C4⋊C4×C73—24no—
258C4⋊C4×C73—24no—
259C4⋊C4×C73—24no—
260C4⋊C4×C73C2×D414yes—
261C4⋊C4×C73C2412yes—
262C4⋊C4×C73C2412yes—
263C4⋊C4×C73C2412yes—
264C22⋊C4×C73—24no—
265C22⋊C4×C73—24no—
266C22⋊C4×C73C2×D414yes—
267C22⋊C4×C73C2×D414yes—
268C42×C73—24no—
269C42×C73C2×D412yes—
270C42×C73C2412yes—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73#13714yes—
277C23×C73C22×D412yes—
278C23×C73C22×D412yes—
279C23×C73C22×D411yescharacteristic
280C22×D73—22no—
281C22×D73—42no—
282C22×D73—42no—
283C22×D73—42no—
284Q8×C73—22no—
285Q8×C73—22no—
286Q8×C73—42no—
287Q8×C73—84no—
288D4×C73—28no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—24no—
294C2×C4×C73—24no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—42no—
304C2×C4×C73—42no—
305C2×C4×C73—42no—
306C2×C4×C73—42no—
307C2×C4×C73—84no—
308C2×C4×C73—84no—
309C2×C4×C73C22×D412yes—
310C2×C4×C73C22×D412yes—
311C2×C4×C73C22×D412yes—
312C2×C4×C73C22×D412yes—
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C2×#4112yes—
315C2×C4×C732−1+412yes—
316C2×C4×C73C2511yescharacteristic
317C22⋊D73—48no—
318C22⋊D73—84no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—42no—
323C2×Dic73—42no—
324C2×Dic73—42no—
325C2×Dic73—84no—
326D292—22no—
327D292—22no—
328D292—42no—
329C4×D73—84no—
330#10596831—22no—
331#10596831—22no—
332#10596831—22no—
333#10596831C2×#4114yes—
334C22×C73—28no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—44no—
341C22×C73#54712yes—
342C22×C73C2×#13714yes—
343C22×C73C2×#13712yes—
344C22×C73#57612yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—42no—
347C2×D73—42no—
348C2×D73—42no—
349C2×D73—84no—
350C4×C73—22no—
351C4×C73—22no—
352C4×C73—22no—
353C4×C73—22no—
354C4×C73—42no—
355C4×C73—42no—
356C4×C73—42no—
357C4×C73—42no—
358C4×C73#54712yes—
359C4×C73C22×#4111yescharacteristic
360C4×C73C2×2−1+411yescharacteristic
361Dic73—42no—
362Dic73—42no—
363Dic73—42no—
364C2×#3346—731nomaximal, Sylow
365C2×C73—24no—
366C2×C73—42no—
367C2×C73#334614yescomplemented
368C2×C73C2×#54711yescharacteristic
369C2×C73C22×#13711yescharacteristic
370C2×C73C2×#57611yescharacteristic
371D73—82no—
372C2×#554D7311yescharacteristic, complemented
373C2×#553—731no—
374#3346—7316no—
375C2×#501—731no—
376C2×#484—731no—
377C2×#481—731no—
378C2×#485—731no—
379C2×#480—731no—
380C2×#479—731no—
381C2×#474—731no—
382C2×#468—731no—
383C2×#465—731no—
384C2×#440—731no—
385C2×#435—731no—
386C2×#428—731no—
387C22×#107—731no—
388C73C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—731no—
390C22×M16—731no—
391C23×C8—731no—
392#554—24no—
393#554C2×D7318yescomplemented
394#553—738no—
395#553—1464no—
396C2×C4⋊Q8C2×D7311yescharacteristic
397C2×#126—1461no—
398C2×#125—21no—
399C2×#125—731no—
400C2×#123—1461no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8C2×D7311yescharacteristic
404C2×C22⋊Q8C2×D7311yescharacteristic
405C2×#121—731no—
406C2×#121—731no—
407C2×#121—1461no—
408C2×C4×Q8C2×D7311yescharacteristic
409C2×C4×D4—21no—
410C2×C4×D4—731no—
411C2×C4×D4—1461no—
412C2×C4×D4C2×D7311yescharacteristic
413C2×#117—731no—
414C22×C4⋊C4—731no—
415C22×C4⋊C4C2×D7311yescharacteristic
416C22×C4⋊C4C2×D7311yescharacteristic
417#501—738no—
418#485—738no—
419#484—738no—
420#481—738no—
421#480—738no—
422#479—738no—
423#474—738no—
424#468—738no—
425#465—738no—
426#440—738no—
427#435—738no—
428#428—738no—
429C2×#107—731no—
430C2×#107—731no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#107—731no—
434C2×#107—731no—
435C2×#107—738no—
436C2×#106—731no—
437C2×#106—731no—
438C2×#106—731no—
439C2×C4⋊C8—731no—
440C2×#103—731no—
441C2×#103—731no—
442C2×#103—731no—
443C2×#102—731no—
444C2×#102—731no—
445C2×#102—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×#97—731no—
449C22×Q8—21no—
450C22×Q8C22×D7311yescharacteristic
451C22×D4—731no—
452C22×D4—1461no—
453C22×D4—1461no—
454C22×D4C22⋊D7311yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—1461no—
458C23×C4—1461no—
459C23×C4C22×D7311yescharacteristic
460C23×C4C22×D7311yescharacteristic
461C2×SD16—734no—
462C2×SD16—1464no—
463C2×M16—734no—
464C2×M16—1464no—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8—734no—
468C22×C8—731no—
469C22×C8—731no—
470C22×C8—1464no—
471C4⋊Q8—22no—
472C4⋊Q8C22×D7314yes—
473#126—1468no—
474#125—28no—
475#125—734no—
476#125—1462no—
477#123—1468no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8C22×D7314yes—
483C22⋊Q8C22×D7314yes—
484#121—734no—
485#121—734no—
486#121—1468no—
487#121—1462no—
488#121—1462no—
489C4×Q8—22no—
490C4×Q8C22×D7314yes—
491C4×D4—28no—
492C4×D4—734no—
493C4×D4—1468no—
494C4×D4—1462no—
495C4×D4C22⋊D7314yes—
496C4×D4C22×D7314yes—
497#117—734no—
498#117—1462no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—734no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1462no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4C22⋊D7311yescharacteristic
516C2×C4⋊C4C22×D7311yescharacteristic
517C2×C4⋊C4C22×D7311yescharacteristic
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C4⋊C4C22×D7314yes—
520C2×C4⋊C4C22×D7314yes—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4C22⋊D7311yescharacteristic
528C2×C22⋊C4C22⋊D7311yescharacteristic
529C2×C42—21no—
530C2×C42—1461no—
531C2×C42C22×D7311yescharacteristic
532#107—734no—
533#107—734no—
534#107—734no—
535#107—734no—
536#107—734no—
537#107—734no—
538#106—734no—
539#106—734no—
540#106—734no—
541C4⋊C8—734no—
542#103—734no—
543#103—734no—
544#103—734no—
545#102—734no—
546#102—734no—
547#102—734no—
548C22⋊C8—734no—
549C22⋊C8—734no—
550#97—734no—
551C24—1461no—
552C24C2×C22⋊D7311yescharacteristic
553C24C2×C22⋊D7311yescharacteristic
554C2×Q8—21no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—82no—
559C2×Q8C23×D7312yes—
560C2×D4—24no—
561C2×D4—2924no—
562C2×D4—5842no—
563C2×D4—732no—
564C2×D4—1464no—
565C2×D4—1464no—
566C2×D4—1461no—
567C2×D4—1462no—
568C2×D4—1462no—
569C2×D4C2×C22⋊D7314yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—5842no—
583C22×C4—5842no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4—1464no—
588C22×C4—1464no—
589C22×C4C2×C22⋊D7312yes—
590C22×C4C2×C22⋊D7312yes—
591C22×C4C2×C22⋊D7311yescharacteristic
592C22×C4C2×C22⋊D7311yescharacteristic
593C22×C4C2×C22⋊D7311yescharacteristic
594C22×C4C2×C22⋊D7311yescharacteristic
595C22×C4C23×D7312yes—
596C22×C4C23×D7312yes—
597C22×C4C23×D7311yescharacteristic
598SD16—1468no—
599M16—1468no—
600C2×C8—734no—
601C2×C8—732no—
602C2×C8—732no—
603C2×C8—732no—
604C2×C8—732no—
605C2×C8—1468no—
606C2×C8—1462no—
607C2×C8—1462no—
608C2×C8—1462no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—732no—
619C4⋊C4—732no—
620C4⋊C4—732no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1461no—
624C4⋊C4—1461no—
625C4⋊C4—1464no—
626C4⋊C4—1461no—
627C4⋊C4C2×C22⋊D7314yes—
628C4⋊C4C23×D7312yes—
629C4⋊C4C23×D7312yes—
630C4⋊C4C23×D7312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1464no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4C2×C22⋊D7314yes—
638C22⋊C4C2×C22⋊D7314yes—
639C42—24no—
640C42—1464no—
641C42C2×C22⋊D7312yes—
642C42C23×D7312yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—2922no—
649C23—2922no—
650C23—2922no—
651C23—1462no—
652C23#1455662214yes—
653C23C22×C22⋊D7312yes—
654C23C22×C22⋊D7312yes—
655C23C22×C22⋊D7311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—2928no—
662D4—2922no—
663D4—5844no—
664D4—1462no—
665D4—1462no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—2922no—
687C2×C4—2922no—
688C2×C4—2922no—
689C2×C4—5844no—
690C2×C4—5844no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4C22×C22⋊D7312yes—
695C2×C4C22×C22⋊D7312yes—
696C2×C4C22×C22⋊D7312yes—
697C2×C4C22×C22⋊D7312yes—
698C2×C4C22×C22⋊D7311yescharacteristic
699C2×C4#41×D7312yes—
700C2×C4#1455663812yes—
701C2×C4C24×D7311yescharacteristic
702C8—734no—
703C8—1462no—
704C8—1462no—
705C8—1462no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—2922no—
714C22—2922no—
715C22—2922no—
716C22—5844no—
717C22#1798923612yes—
718C22C2×#1455662214yes—
719C22C2×#1455662212yes—
720C22#1798939012yes—
721C22C23×C22⋊D7311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—2922no—
731C4—2922no—
732C4—2922no—
733C4#1798923612yes—
734C4C2×#41×D7311yescharacteristic
735C4C2×#1455663811yescharacteristic
736C2—24no—
737C2—42no—
738C2—5842no—
739C2#2262241014yesdirect product factor
740C2C2×#1798923611yescharacteristic
741C2C22×#1455662211yescharacteristic
742C2C2×#1798939011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#554×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989283C2
hypercenterC2×#554D73
hypocenterC73C2×#3346
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #22622410C2direct (N × H)
3. C2×#17988993C2semidirect
4. C2×#17988920C2semidirect
5. C2×#17988905C2semidirect
6. C2×#17988925C2semidirect
7. C2×#17988900C2semidirect
8. C2×#17988894C2semidirect
9. C2×#17988864C2semidirect
10. C2×#17988835C2semidirect
11. C2×#17988818C2semidirect
12. C2×#17988685C2semidirect
13. C2×#17988659C2semidirect
14. C2×#17988627C2semidirect
15. C22×#14556524C2semidirect
16. C2×#554×C73C2semidirect
32. #17988993C22semidirect
33. #17988925C22semidirect
34. #17988920C22semidirect
35. #17988905C22semidirect
36. #17988900C22semidirect
37. #17988894C22semidirect
38. #17988864C22semidirect
39. #17988835C22semidirect
40. #17988818C22semidirect
41. #17988685C22semidirect
42. #17988659C22semidirect
43. #17988627C22semidirect
50. C2×#14556524C22semidirect
65. #554×C73C22semidirect
367. C2×C73#3346semidirect
372. C2×#554D73semidirect
388. C73C2×#3346semidirect
393. #554C2×D73semidirect
739. C2#22622410direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892832
#226224102
C2×#179889932
C2×#179889202
C2×#179889052
C2×#179889252
C2×#179889002
C2×#179888942
C2×#179888642
C2×#179888352
C2×#179888182
C2×#179886852
C2×#179886592
C2×#179886272
C22×#145565242
C2×#554×C732
C2×#334673