Finite Group Databasebeta

← C2×#22620160 #33954263

Subgroups — C2×#22620160 #33954263

Order 18688.

2058 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×#17989208C211yesmaximal, characteristic
2#22620160C2116yesmaximal, direct product factor
3C2×#17988928C211yesmaximal, characteristic, complemented
4C2×#17988911C211yesmaximal, characteristic
5C2×#17988882C211yesmaximal, characteristic, complemented
6C2×#17988872C211yesmaximal, characteristic, complemented
7C2×#17988809C211yesmaximal, characteristic, complemented
8C2×#17988809C211yesmaximal, characteristic, complemented
9C2×#17988743C211yesmaximal, characteristic, complemented
10C2×#17988726C211yesmaximal, characteristic
11C2×#17988692C211yesmaximal, characteristic, complemented
12C2×#17988685C211yesmaximal, characteristic, complemented
13C2×C4×#11924018C211yesmaximal, characteristic, complemented
14C2×C4×#11924015C211yesmaximal, characteristic, complemented
15C2×#17988648C211yesmaximal, characteristic, complemented
16C2×#519×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924015C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21#17989208—24no—
22#17989208C2218yes—
23C2×#14556591C2211yescharacteristic
24C2×#14556586—21no—
25C2×#14556579C2211yescharacteristic
26C2×#14556577—21no—
27C2×#14556573—21no—
28C2×#14556570C2211yescharacteristic
29C2×#14556569—21no—
30C2×#14556565C2211yescharacteristic
31C2×C4×Dic146C2211yescharacteristic
32C2×C4×D292C2211yescharacteristic
33#17988928C2218yescomplemented
34#17988911C2218yes—
35#17988882C2218yescomplemented
36#17988872C2218yescomplemented
37#17988809C2218yescomplemented
38#17988809C2218yescomplemented
39#17988743C2218yescomplemented
40#17988726C2218yes—
41#17988692C2218yescomplemented
42#17988685C2218yescomplemented
43C4×#11924018C2218yescomplemented
44C4×#11924015C2218yescomplemented
45#17988648C2218yescomplemented
46C2×#14556524C2211yescharacteristic
47C2×#14556524C2211yescharacteristic
48C2×#14556522C2211yescharacteristic
49C2×#14556522C2211yescharacteristic
50C2×C4⋊#10596831C2211yescharacteristic
51C2×C4⋊#10596831C2211yescharacteristic
52C2×#14556515C2211yescharacteristic
53C2×#14556515C2211yescharacteristic
54C2×#14556515C2211yescharacteristic
55C2×#14556515C2211yescharacteristic
56C2×#14556514C2211yescharacteristic
57C2×#14556514C2211yescharacteristic
58C2×#14556511C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×C22⋊#10596831C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×#14556502C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64C23×Q8×C73C2211yescharacteristic
65#519×C73—24no—
66#519×C73C2218yescomplemented
67C2×C4×Q8×C73—21no—
68C2×C4×Q8×C73—21no—
69C2×C4×Q8×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×Q8×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73C2×#117×C73—21no—
74C2×#117×C73—21no—
75C2×#117×C73C2211yescharacteristic
76C2×#117×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×D292C2311yescharacteristic
80C22×C22⋊D73—21no—
81C22×C4×D73—21no—
82C2×#11924018—24no—
83C2×#11924018—24no—
84C2×#11924018C2314yes—
85C2×#11924018C2314yes—
86C2×#11924015—24no—
87C2×#11924015—24no—
88C2×#11924015C2314yes—
89C2×#11924015C2314yes—
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93C22×#10596831C2311yescharacteristic
94#14556591—22no—
95#14556591C2314yes—
96#14556586—28no—
97#14556579—22no—
98#14556579C2314yes—
99#14556577—28no—
100#14556573—28no—
101#14556570—22no—
102#14556570C2314yes—
103#14556569—28no—
104#14556565—22no—
105#14556565C2314yes—
106C4×Dic146—22no—
107C4×Dic146C2314yes—
108C4×D292—22no—
109C4×D292C2314yes—
110C2×C4⋊Dic73—21no—
111C2×C4⋊Dic73C2311yescharacteristic
112C2×C4⋊Dic73C2311yescharacteristic
113C2×#11924007—21no—
114C2×#11924007—21no—
115C2×C22⋊Dic73—21no—
116C2×#11924005—21no—
117C2×#11924005—21no—
118C2×#11924005—21no—
119C2×#11924005—21no—
120C2×C4×Dic73—21no—
121#14556524C2314yes—
122#14556524C2314yes—
123#14556522C2314yes—
124#14556522C2314yes—
125C4⋊#10596831C2314yes—
126C4⋊#10596831C2314yes—
127#14556515C2314yes—
128#14556515C2314yes—
129#14556515C2314yes—
130#14556515C2314yes—
131#14556514C2314yes—
132#14556514C2314yes—
133#14556511C2314yes—
134#14556511C2314yes—
135C22⋊#10596831C2314yes—
136C22⋊#10596831C2314yes—
137#14556502C2314yes—
138C4×#10596831C2314yes—
139C22×Q8×C73—24no—
140C22×Q8×C73—24no—
141C22×Q8×C73—21no—
142C22×Q8×C73—22no—
143C22×Q8×C73C2314yes—
144C22×Q8×C73C2311yescharacteristic
145C22×Q8×C73C2311yescharacteristic
146C23×C4×C73—21no—
147C23×C4×C73C2311yescharacteristic
148C4×Q8×C73—28no—
149C4×Q8×C73—28no—
150C4×Q8×C73—22no—
151C4×Q8×C73—22no—
152C4×Q8×C73—22no—
153C4×Q8×C73—22no—
154C4×Q8×C73C2314yes—
155C4×Q8×C73C2314yes—
156C4×Q8×C73C2314yes—
157C4×Q8×C73C2314yes—
158#117×C73—22no—
159#117×C73—28no—
160#117×C73—28no—
161#117×C73D414yes—
162#117×C73C2314yes—
163#117×C73C2314yes—
164C2×C4⋊C4×C73—21no—
165C2×C4⋊C4×C73—21no—
166C2×C4⋊C4×C73—21no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73D411yescharacteristic
169C2×C4⋊C4×C73D411yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C22⋊C4×C73—21no—
173C2×C22⋊C4×C73D411yescharacteristic
174C2×C22⋊C4×C73D411yescharacteristic
175C2×C42×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73—21no—
178C2×C42×C73—21no—
179C2×C42×C73—21no—
180C2×C42×C73C2311yescharacteristic
181C2×C42×C73C2311yescharacteristic
182C23×D73—21no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—24no—
187C2×Dic146—82no—
188C2×Dic146C2412yes—
189C2×D292—22no—
190C2×D292—22no—
191C2×D292—21no—
192C2×D292C2412yes—
193C2×C22⋊D73—24no—
194C2×C22⋊D73—82no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C2×C4×D73—24no—
199C2×C4×D73—82no—
200#11924018—28no—
201#11924018—28no—
202#11924015—28no—
203#11924015—28no—
204C2×#10596831—22no—
205C2×#10596831—22no—
206C2×#10596831—22no—
207C2×#10596831—22no—
208C2×#10596831C2412yes—
209C2×#10596831C2412yes—
210C2×#10596831C2412yes—
211C2×#10596831C2412yes—
212C4⋊Dic73—24no—
213C4⋊Dic73—21no—
214C4⋊Dic73—21no—
215C4⋊Dic73C2412yes—
216C4⋊Dic73C2412yes—
217#11924007—24no—
218#11924007—24no—
219C22⋊Dic73—24no—
220#11924005—24no—
221#11924005—24no—
222#11924005—24no—
223#11924005—24no—
224C4×Dic73—24no—
225C24×C73C2×D411yescharacteristic
226C2×Q8×C73—216no—
227C2×Q8×C73—28no—
228C2×Q8×C73—28no—
229C2×Q8×C73—28no—
230C2×Q8×C73—24no—
231C2×Q8×C73—21no—
232C2×Q8×C73—21no—
233C2×Q8×C73—22no—
234C2×Q8×C73—22no—
235C2×Q8×C73#4114yes—
236C2×Q8×C73#4114yes—
237C2×Q8×C73C2412yes—
238C2×Q8×C73C2412yes—
239C22×C4×C73—28no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—24no—
243C22×C4×C73—22no—
244C22×C4×C73—22no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73C2×D411yescharacteristic
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D412yes—
253C22×C4×C73C2412yes—
254C22×C4×C73C2411yescharacteristic
255C4⋊C4×C73—24no—
256C4⋊C4×C73—24no—
257C4⋊C4×C73—24no—
258C4⋊C4×C73—24no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73C2×D414yes—
262C4⋊C4×C73C2×D414yes—
263C4⋊C4×C73C2412yes—
264C4⋊C4×C73C2412yes—
265C22⋊C4×C73—24no—
266C22⋊C4×C73C2×D414yes—
267C22⋊C4×C73C2×D414yes—
268C42×C73—24no—
269C42×C73—24no—
270C42×C73—24no—
271C42×C73—24no—
272C42×C73—24no—
273C42×C73C2×D412yes—
274C42×C73C2×D412yes—
275C42×C73C2412yes—
276C42×C73C2412yes—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—22no—
280C23×C73C22×D412yes—
281C23×C73C22×D411yescharacteristic
282C22×D73—22no—
283C22×D73—42no—
284C22×D73—42no—
285C22×D73—42no—
286Q8×C73—216no—
287Q8×C73—24no—
288Q8×C73—24no—
289Q8×C73—22no—
290Q8×C73—22no—
291Q8×C73C2×#4114yes—
292Q8×C73C2×#4114yes—
293C2×C4×C73—216no—
294C2×C4×C73—24no—
295C2×C4×C73—24no—
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—24no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—42no—
309C2×C4×C73—42no—
310C2×C4×C73C22×D412yes—
311C2×C4×C73C22×D412yes—
312C2×C4×C73C22×D412yes—
313C2×C4×C73C22×D412yes—
314C2×C4×C73C22×D412yes—
315C2×C4×C73C22×D411yescharacteristic
316C2×C4×C73C2×#4112yes—
317C2×C4×C73C2×#4112yes—
318C2×C4×C73C2511yescharacteristic
319C22⋊D73—84no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—42no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326D292—22no—
327D292—22no—
328D292—42no—
329C4×D73—84no—
330Dic146—22no—
331Dic146—22no—
332Dic146—42no—
333Dic146—84no—
334#10596831—22no—
335#10596831—22no—
336#10596831—22no—
337#10596831—22no—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—44no—
342C22×C73#52512yes—
343C22×C73#57712yes—
344C22×C73#57812yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—42no—
347C2×D73—42no—
348C2×D73—42no—
349C2×D73—84no—
350C4×C73—24no—
351C4×C73—24no—
352C4×C73—22no—
353C4×C73—22no—
354C4×C73—22no—
355C4×C73—22no—
356C4×C73—22no—
357C4×C73—42no—
358C4×C73—42no—
359C4×C73#52512yes—
360C4×C73C22×#4111yescharacteristic
361C4×C73C22×#4111yescharacteristic
362Dic73—42no—
363Dic73—42no—
364Dic73—42no—
365C2×#3121—731nomaximal, Sylow
366C2×C73—42no—
367C2×C73#312114yescomplemented
368C2×C73C2×#52511yescharacteristic
369C2×C73C2×#57711yescharacteristic
370C2×C73C2×#57811yescharacteristic
371D73—82no—
372C2×#542—731no—
373C2×#519D7311yescharacteristic, complemented
374#3121—7316no—
375C2×#485—731no—
376C2×#482—731no—
377C2×#477—731no—
378C2×#475—731no—
379C2×#464—731no—
380C2×#464—731no—
381C2×#451—731no—
382C2×#448—731no—
383C2×#441—731no—
384C2×#440—731no—
385C2×C4×Q16—731no—
386C2×C4×SD16—731no—
387C2×#433—731no—
388C73C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8C2×D7311yescharacteristic
390C22×Q16—731no—
391C22×Q16—731no—
392C22×SD16—731no—
393C22×SD16—731no—
394#542—738no—
395#542—1464no—
396C2×C4⋊Q8—731no—
397C2×#126—1461no—
398C2×#124—731no—
399C2×#124—1461no—
400C2×#123—1461no—
401C2×C22⋊Q8—731no—
402C2×C22⋊Q8—1461no—
403C2×#121—731no—
404#519—24no—
405#519C2×D7318yescomplemented
406C2×C4×Q8—21no—
407C2×C4×Q8—21no—
408C2×C4×Q8—731no—
409C2×C4×Q8C2×D7311yescharacteristic
410C2×C4×Q8C2×D7311yescharacteristic
411C2×C4×Q8C2×D7311yescharacteristic
412C2×C4×Q8C2×D7311yescharacteristic
413C2×C4×D4—731no—
414C2×#117—21no—
415C2×#117—21no—
416C2×#117C2×D7311yescharacteristic
417C2×#117C2×D7311yescharacteristic
418#485—738no—
419#482—738no—
420#477—738no—
421#475—738no—
422#464—738no—
423#464—738no—
424#451—738no—
425#448—738no—
426#441—738no—
427#440—738no—
428C4×Q16—738no—
429C4×SD16—738no—
430#433—738no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#106—731no—
434C2×#106—731no—
435C2×C4⋊C8—731no—
436C2×C4⋊C8—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—731no—
441C2×#103—731no—
442C2×#103—731no—
443C2×#102—731no—
444C2×#102—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×#97—731no—
448C2×C4×C8—731no—
449C22×Q8—24no—
450C22×Q8—24no—
451C22×Q8—21no—
452C22×Q8—22no—
453C22×Q8—731no—
454C22×Q8—1461no—
455C22×Q8C22×D7314yes—
456C22×Q8C22×D7311yescharacteristic
457C22×Q8C22×D7311yescharacteristic
458C22×D4—731no—
459C22×D4—1461no—
460C23×C4—21no—
461C23×C4—1461no—
462C23×C4C22×D7311yescharacteristic
463C2×Q16—734no—
464C2×Q16—734no—
465C2×Q16—1464no—
466C2×Q16—1464no—
467C2×SD16—734no—
468C2×SD16—734no—
469C2×SD16—1464no—
470C2×SD16—1464no—
471C22×C8—731no—
472C22×C8—731no—
473C22×C8—731no—
474C22×C8—731no—
475C4⋊Q8—734no—
476C4⋊Q8—1462no—
477#126—1468no—
478#124—734no—
479#124—1468no—
480#124—1462no—
481#123—1468no—
482C22⋊Q8—734no—
483C22⋊Q8—1462no—
484C22⋊Q8—1468no—
485#121—734no—
486#121—1462no—
487C4×Q8—28no—
488C4×Q8—28no—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—734no—
494C4×Q8—1462no—
495C4×Q8C22×D7314yes—
496C4×Q8C22×D7314yes—
497C4×Q8C22×D7314yes—
498C4×Q8C22×D7314yes—
499C4×D4—734no—
500C4×D4—1462no—
501#117—22no—
502#117—28no—
503#117—28no—
504#117C22⋊D7314yes—
505#117C22×D7314yes—
506#117C22×D7314yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4C22⋊D7311yescharacteristic
517C2×C4⋊C4C22⋊D7311yescharacteristic
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C4⋊C4C22×D7311yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1461no—
522C2×C22⋊C4—1461no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4C22⋊D7311yescharacteristic
527C2×C22⋊C4C22⋊D7311yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—21no—
533C2×C42—1461no—
534C2×C42C22×D7311yescharacteristic
535C2×C42C22×D7311yescharacteristic
536#107—734no—
537#107—734no—
538#106—734no—
539#106—734no—
540C4⋊C8—734no—
541C4⋊C8—734no—
542#103—734no—
543#103—734no—
544#103—734no—
545#103—734no—
546#103—734no—
547#103—734no—
548#102—734no—
549#102—734no—
550C22⋊C8—734no—
551C22⋊C8—734no—
552#97—734no—
553C4×C8—734no—
554C24—1461no—
555C24C2×C22⋊D7311yescharacteristic
556C2×Q8—216no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—5842no—
566C2×Q8—732no—
567C2×Q8—1462no—
568C2×Q8—1462no—
569C2×Q8—1461no—
570C2×Q8—1464no—
571C2×Q8#1192402814yes—
572C2×Q8#1192402814yes—
573C2×Q8C23×D7312yes—
574C2×Q8C23×D7312yes—
575C2×D4—5842no—
576C2×D4—732no—
577C2×D4—1464no—
578C2×D4—1461no—
579C2×D4—1462no—
580C2×D4—1462no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—5842no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1464no—
594C22×C4C2×C22⋊D7312yes—
595C22×C4C2×C22⋊D7311yescharacteristic
596C22×C4C2×C22⋊D7311yescharacteristic
597C22×C4C2×C22⋊D7311yescharacteristic
598C22×C4C2×C22⋊D7311yescharacteristic
599C22×C4C2×C22⋊D7311yescharacteristic
600C22×C4C23×D7312yes—
601C22×C4C23×D7311yescharacteristic
602Q16—1468no—
603Q16—1468no—
604SD16—1468no—
605SD16—1468no—
606C2×C8—732no—
607C2×C8—732no—
608C2×C8—732no—
609C2×C8—732no—
610C2×C8—1462no—
611C2×C8—1462no—
612C2×C8—1462no—
613C2×C8—1462no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—732no—
621C4⋊C4—732no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C4⋊C4—1464no—
627C4⋊C4C2×C22⋊D7314yes—
628C4⋊C4C2×C22⋊D7314yes—
629C4⋊C4C23×D7312yes—
630C4⋊C4C23×D7312yes—
631C22⋊C4—24no—
632C22⋊C4—1464no—
633C22⋊C4—1464no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4C2×C22⋊D7314yes—
638C22⋊C4C2×C22⋊D7314yes—
639C42—24no—
640C42—24no—
641C42—24no—
642C42—24no—
643C42—24no—
644C42—1464no—
645C42C2×C22⋊D7312yes—
646C42C2×C22⋊D7312yes—
647C42C23×D7312yes—
648C42C23×D7312yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—2922no—
653C23—2922no—
654C23—2922no—
655C23—1462no—
656C23C22×C22⋊D7312yes—
657C23C22×C22⋊D7311yescharacteristic
658Q8—216no—
659Q8—22no—
660Q8—22no—
661Q8—24no—
662Q8—24no—
663Q8—2922no—
664Q8—5844no—
665Q8—1462no—
666Q8—1462no—
667Q8C2×#1192402814yes—
668Q8C2×#1192402814yes—
669D4—2922no—
670D4—5844no—
671D4—1462no—
672D4—1462no—
673C2×C4—216no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—2922no—
691C2×C4—2922no—
692C2×C4—2922no—
693C2×C4—5844no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4C22×C22⋊D7312yes—
698C2×C4C22×C22⋊D7312yes—
699C2×C4C22×C22⋊D7312yes—
700C2×C4C22×C22⋊D7312yes—
701C2×C4C22×C22⋊D7312yes—
702C2×C4C22×C22⋊D7311yescharacteristic
703C2×C4C2×#1192402812yes—
704C2×C4C2×#1192402812yes—
705C2×C4C24×D7311yescharacteristic
706C8—1462no—
707C8—1462no—
708C8—1462no—
709C8—1462no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—2922no—
715C22—2922no—
716C22—2922no—
717C22—5844no—
718C22#1798909812yes—
719C22#1798939512yes—
720C22#1798940212yes—
721C22C23×C22⋊D7311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—24no—
727C4—24no—
728C4—22no—
729C4—42no—
730C4—42no—
731C4—2922no—
732C4—2922no—
733C4—2922no—
734C4#1798909812yes—
735C4C22×#1192402811yescharacteristic
736C4C22×#1192402811yescharacteristic
737C2—42no—
738C2—5842no—
739C2#2262016014yesdirect product factor
740C2C2×#1798909811yescharacteristic
741C2C2×#1798939511yescharacteristic
742C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#519×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
hypercenterC2×#519D73
hypocenterC73C2×#3121
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. #22620160C2direct (N × H)
3. C2×#17988928C2semidirect
5. C2×#17988882C2semidirect
6. C2×#17988872C2semidirect
7. C2×#17988809C2semidirect
8. C2×#17988809C2semidirect
9. C2×#17988743C2semidirect
11. C2×#17988692C2semidirect
12. C2×#17988685C2semidirect
13. C2×C4×#11924018C2semidirect
14. C2×C4×#11924015C2semidirect
15. C2×#17988648C2semidirect
16. C2×#519×C73C2semidirect
33. #17988928C22semidirect
35. #17988882C22semidirect
36. #17988872C22semidirect
37. #17988809C22semidirect
38. #17988809C22semidirect
39. #17988743C22semidirect
41. #17988692C22semidirect
42. #17988685C22semidirect
43. C4×#11924018C22semidirect
44. C4×#11924015C22semidirect
45. #17988648C22semidirect
66. #519×C73C22semidirect
367. C2×C73#3121semidirect
373. C2×#519D73semidirect
388. C73C2×#3121semidirect
405. #519C2×D73semidirect
739. C2#22620160direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892082
#226201602
C2×#179889282
C2×#179889112
C2×#179888822
C2×#179888722
C2×#179888092
C2×#179887432
C2×#179887262
C2×#179886922
C2×#179886852
C2×C4×#119240182
C2×C4×#119240152
C2×#179886482
C2×#519×C732
C2×#312173