Finite Group Databasebeta

← C2×#22622051 #33962696

Subgroups — C2×#22622051 #33962696

Order 18688.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989258C211yesmaximal, characteristic
2#22622051C2116yesmaximal, direct product factor
3C2×#17988953C211yesmaximal, characteristic, complemented
4C2×#17988905C211yesmaximal, characteristic, complemented
5C2×#17988911C211yesmaximal, characteristic, complemented
6C2×#17988891C211yesmaximal, characteristic, complemented
7C2×#17988835C211yesmaximal, characteristic, complemented
8C2×#17988818C211yesmaximal, characteristic, complemented
9C2×#17988787C211yesmaximal, characteristic, complemented
10C2×#17988747C211yesmaximal, characteristic, complemented
11C2×#17988747C211yesmaximal, characteristic, complemented
12C2×#17988692C211yesmaximal, characteristic, complemented
13C2×#17988659C211yesmaximal, characteristic, complemented
14C2×#17988586C211yesmaximal, characteristic, complemented
15C2×#17988581C211yesmaximal, characteristic, complemented
16C2×#552×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C22×#11924028C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21C22×#11924015C2211yescharacteristic
22C22×#11924012C2211yescharacteristic
23C23×#10596831C2211yescharacteristic
24#17989258—24no—
25#17989258C2218yes—
26C2×#14556588C2211yescharacteristic
27C2×#14556587—21no—
28C2×#14556565C2211yescharacteristic
29C2×#14556565C2211yescharacteristic
30C2×#14556564—21no—
31C2×#14556564—21no—
32C2×C4×Dic146C2211yescharacteristic
33C2×#14556553—21no—
34#17988953C2218yescomplemented
35#17988911C2218yescomplemented
36#17988905C2218yescomplemented
37#17988891C2218yescomplemented
38#17988835C2218yescomplemented
39#17988818C2218yescomplemented
40#17988787C2218yescomplemented
41#17988747C2218yescomplemented
42#17988747C2218yescomplemented
43#17988692C2218yescomplemented
44#17988659C2218yescomplemented
45C2×#14556524C2211yescharacteristic
46C2×#14556522C2211yescharacteristic
47C2×#14556522C2211yescharacteristic
48C2×C4⋊#10596831C2211yescharacteristic
49#17988586C2218yescomplemented
50#17988581C2218yescomplemented
51C2×#14556515C2211yescharacteristic
52C2×#14556514C2211yescharacteristic
53C2×#14556514C2211yescharacteristic
54C2×#14556514C2211yescharacteristic
55C2×#14556511C2211yescharacteristic
56C2×#14556511C2211yescharacteristic
57C2×#14556511C2211yescharacteristic
58C2×#14556511C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×#14556511C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×C22⋊#10596831C2211yescharacteristic
63C2×#14556502C2211yescharacteristic
64#552×C73—24no—
65#552×C73C2218yescomplemented
66C2×#126×C73—21no—
67C2×#125×C73—21no—
68C2×#125×C73C2211yescharacteristic
69C2×#123×C73—21no—
70C2×C22⋊Q8×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73C2×C4×D4×C73C2211yescharacteristic
74C2×#117×C73—21no—
75C2×#117×C73C2211yescharacteristic
76C22×C4⋊C4×C73C2211yescharacteristic
77C2×#11924028—24no—
78C2×#11924028—24no—
79C2×#11924028—22no—
80C2×#11924028—22no—
81C2×#11924028—42no—
82C2×#11924028—42no—
83C2×#11924028C2314yes—
84C2×#11924028C2314yes—
85C22×Dic146C2311yescharacteristic
86C22×D292—21no—
87C22×D292—21no—
88C22×D292C2311yescharacteristic
89C22×D292C2311yescharacteristic
90C22×C22⋊D73—21no—
91C22×C22⋊D73—21no—
92C22×C22⋊D73—21no—
93C22×C22⋊D73—21no—
94C22×C4×D73—21no—
95C22×C4×D73—21no—
96C2×#11924018—24no—
97C2×#11924018C2314yes—
98C2×#11924015—42no—
99C2×#11924015—42no—
100C2×#11924015C2314yes—
101C2×#11924015C2314yes—
102C2×#11924012—42no—
103C2×#11924012C2314yes—
104C22×#10596831—42no—
105C22×#10596831C2311yescharacteristic
106C22×#10596831C2311yescharacteristic
107C22×#10596831C2311yescharacteristic
108C22×#10596831C2311yescharacteristic
109C22×#10596831C2314yes—
110#14556588—22no—
111#14556588C2314yes—
112#14556587—28no—
113#14556565—22no—
114#14556565—22no—
115#14556565C2314yes—
116#14556565C2314yes—
117#14556564—28no—
118#14556564—28no—
119C4×Dic146—22no—
120C4×Dic146C2314yes—
121#14556553—28no—
122C2×C4⋊Dic73C2311yescharacteristic
123C2×#11924007—21no—
124C2×#11924005—21no—
125C2×#11924005—21no—
126C2×C4×Dic73—21no—
127#14556524C2314yes—
128#14556522C2314yes—
129#14556522C2314yes—
130C4⋊#10596831C2314yes—
131#14556515C2314yes—
132#14556514C2314yes—
133#14556514C2314yes—
134#14556514C2314yes—
135#14556511C2314yes—
136#14556511C2314yes—
137#14556511C2314yes—
138#14556511C2314yes—
139#14556511C2314yes—
140#14556511C2314yes—
141C22⋊#10596831C2314yes—
142C22⋊#10596831C2314yes—
143#14556502C2314yes—
144C22×Q8×C73C2311yescharacteristic
145C22×D4×C73D411yescharacteristic
146C23×C4×C73—21no—
147C23×C4×C73C2311yescharacteristic
148C23×C4×C73C2311yescharacteristic
149#126×C73—28no—
150#125×C73—28no—
151#125×C73—22no—
152#125×C73C2314yes—
153#123×C73—28no—
154C22⋊Q8×C73—22no—
155C22⋊Q8×C73—22no—
156C22⋊Q8×C73C2314yes—
157C22⋊Q8×C73C2314yes—
158C4×Q8×C73—22no—
159C4×Q8×C73C2314yes—
160C4×D4×C73D414yes—
161C4×D4×C73C2314yes—
162#117×C73—22no—
163#117×C73—28no—
164#117×C73C2314yes—
165C2×C4⋊C4×C73—21no—
166C2×C4⋊C4×C73—22no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73D411yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C4⋊C4×C73C2314yes—
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180C2×C22⋊C4×C73D411yescharacteristic
181C2×C22⋊C4×C73D411yescharacteristic
182C2×C42×C73—21no—
183C2×C42×C73—21no—
184C2×C42×C73C2311yescharacteristic
185C23×D73—21no—
186C23×D73—21no—
187#11924028—28no—
188#11924028—28no—
189#11924028—44no—
190#11924028—44no—
191#11924028—48no—
192#11924028—48no—
193C2×Dic146—21no—
194C2×Dic146—22no—
195C2×Dic146#4114yes—
196C2×Dic146C2412yes—
197C2×D292—22no—
198C2×D292—22no—
199C2×D292—22no—
200C2×D292—22no—
201C2×D292—24no—
202C2×D292—21no—
203C2×D292—21no—
204C2×D292—24no—
205C2×D292—44no—
206C2×D292—82no—
207C2×D292C2412yes—
208C2×D292C2412yes—
209C2×C22⋊D73—24no—
210C2×C22⋊D73—24no—
211C2×C22⋊D73—24no—
212C2×C22⋊D73—24no—
213C2×C22⋊D73—44no—
214C2×C22⋊D73—44no—
215C2×C22⋊D73—82no—
216C2×C22⋊D73—82no—
217C22×Dic73—21no—
218C22×Dic73—21no—
219C2×C4×D73—24no—
220C2×C4×D73—24no—
221C2×C4×D73—44no—
222C2×C4×D73—44no—
223#11924018—28no—
224#11924015—44no—
225#11924015—44no—
226#11924012—44no—
227C2×#10596831—22no—
228C2×#10596831—22no—
229C2×#10596831—22no—
230C2×#10596831—22no—
231C2×#10596831—44no—
232C2×#10596831C2412yes—
233C2×#10596831C2412yes—
234C2×#10596831C2412yes—
235C2×#10596831C2412yes—
236C4⋊Dic73—21no—
237C4⋊Dic73C2412yes—
238#11924007—24no—
239#11924005—24no—
240#11924005—24no—
241C4×Dic73—24no—
242C24×C73C2×D411yescharacteristic
243C24×C73C2×D411yescharacteristic
244C2×Q8×C73—21no—
245C2×Q8×C73—22no—
246C2×Q8×C73—22no—
247C2×Q8×C73C2412yes—
248C2×D4×C73—42no—
249C2×D4×C73C2×D414yes—
250C22×C4×C73—22no—
251C22×C4×C73—22no—
252C22×C4×C73—22no—
253C22×C4×C73—22no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—24no—
259C22×C4×C73—44no—
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2×D411yescharacteristic
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D412yes—
265C22×C4×C73C2×D412yes—
266C22×C4×C73C2412yes—
267C22×C4×C73C2412yes—
268C22×C4×C73C2411yescharacteristic
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—24no—
272C4⋊C4×C73—24no—
273C4⋊C4×C73—24no—
274C4⋊C4×C73—24no—
275C4⋊C4×C73—24no—
276C4⋊C4×C73—24no—
277C4⋊C4×C73—21no—
278C4⋊C4×C73C2×D414yes—
279C4⋊C4×C73C2412yes—
280C4⋊C4×C73C2412yes—
281C4⋊C4×C73C2412yes—
282C22⋊C4×C73—24no—
283C22⋊C4×C73—24no—
284C22⋊C4×C73—24no—
285C22⋊C4×C73C2×D414yes—
286C22⋊C4×C73C2×D414yes—
287C42×C73—24no—
288C42×C73—24no—
289C42×C73C2×D412yes—
290C42×C73C2412yes—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73C22×D412yes—
298C23×C73C22×D412yes—
299C23×C73C22×D411yescharacteristic
300C22×D73—22no—
301C22×D73—22no—
302C22×D73—42no—
303C22×D73—42no—
304C22×D73—42no—
305C22×D73—42no—
306C22×D73—42no—
307C22×D73—42no—
308Q8×C73—22no—
309Q8×C73—22no—
310Q8×C73—42no—
311D4×C73—44no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—24no—
317C2×C4×C73—24no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—48no—
327C2×C4×C73—42no—
328C2×C4×C73—42no—
329C2×C4×C73—42no—
330C2×C4×C73—42no—
331C2×C4×C73C22×D412yes—
332C2×C4×C73C22×D412yes—
333C2×C4×C73C22×D412yes—
334C2×C4×C73C22×D412yes—
335C2×C4×C73C22×D411yescharacteristic
336C2×C4×C73C2×#4112yes—
337C2×C4×C73H(5,𝔽2)12yes—
338C2×C4×C73C2511yescharacteristic
339C22⋊D73—48no—
340C22⋊D73—48no—
341C22⋊D73—84no—
342C22⋊D73—84no—
343C2×Dic73—24no—
344C2×Dic73—22no—
345C2×Dic73—22no—
346C2×Dic73—42no—
347D292—22no—
348D292—22no—
349D292—22no—
350D292—22no—
351D292—48no—
352D292—42no—
353D292—42no—
354D292—84no—
355C4×D73—48no—
356C4×D73—48no—
357Dic146—24no—
358Dic146—22no—
359Dic146C2×#4114yes—
360#10596831—22no—
361#10596831—22no—
362#10596831—22no—
363#10596831—22no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73—22no—
368C22×C73—22no—
369C22×C73—22no—
370C22×C73—44no—
371C22×C73—44no—
372C22×C73#54612yes—
373C22×C73#57512yes—
374C22×C73#57712yes—
375C22×C73C23×D411yescharacteristic
376C2×D73—42no—
377C2×D73—42no—
378C2×D73—42no—
379C2×D73—42no—
380C2×D73—42no—
381C2×D73—42no—
382C2×D73—84no—
383C2×D73—84no—
384C4×C73—22no—
385C4×C73—22no—
386C4×C73—22no—
387C4×C73—22no—
388C4×C73—42no—
389C4×C73—42no—
390C4×C73—42no—
391C4×C73—42no—
392C4×C73#54612yes—
393C4×C73C22×#4111yescharacteristic
394C4×C73C2×H(5,𝔽2)11yescharacteristic
395Dic73—24no—
396Dic73—42no—
397C2×#3317—731nomaximal, Sylow
398C2×C73—42no—
399C2×C73—42no—
400C2×C73#331714yescomplemented
401C2×C73C2×#54611yescharacteristic
402C2×C73C2×#57511yescharacteristic
403C2×C73C2×#57711yescharacteristic
404D73—82no—
405D73—82no—
406C2×#552D7311yescharacteristic, complemented
407C2×#550—731no—
408#3317—7316no—
409C2×#490—731no—
410C2×#481—731no—
411C2×#482—731no—
412C2×#479—731no—
413C2×#468—731no—
414C2×#465—731no—
415C2×#460—731no—
416C2×#452—731no—
417C2×#452—731no—
418C2×#441—731no—
419C2×#435—731no—
420C2×#417—731no—
421C2×#416—731no—
422C73C2×#331711yescharacteristic, complemented, Sylow
423C22×#41—731no—
424C22×#41—731no—
425C22×Q16—731no—
426C22×SD16—731no—
427C22×SD16—731no—
428C22×M16—731no—
429C23×C8—731no—
430#552—24no—
431#552C2×D7318yescomplemented
432#550—738no—
433#550—1464no—
434C2×#127—731no—
435C2×#127—1461no—
436C2×#126—21no—
437C2×#125—21no—
438C2×#125C2×D7311yescharacteristic
439C2×#123—21no—
440C2×C22⋊Q8C2×D7311yescharacteristic
441C2×C22⋊Q8C2×D7311yescharacteristic
442C2×#121—731no—
443C2×#121—731no—
444C2×#121—1461no—
445C2×#121—1461no—
446C2×C4×Q8—731no—
447C2×C4×Q8C2×D7311yescharacteristic
448C2×C4×D4—1461no—
449C2×C4×D4C2×D7311yescharacteristic
450C2×#117—21no—
451C2×#117C2×D7311yescharacteristic
452C22×C4⋊C4C2×D7311yescharacteristic
453#490—738no—
454#482—738no—
455#481—738no—
456#479—738no—
457#468—738no—
458#465—738no—
459#460—738no—
460#452—738no—
461#452—738no—
462#441—738no—
463#435—738no—
464C2×#107—731no—
465C2×#106—731no—
466C2×#106—731no—
467C2×C4⋊C8—731no—
468#417—738no—
469#416—738no—
470C2×#103—731no—
471C2×#103—731no—
472C2×#103—731no—
473C2×#103—731no—
474C2×#102—731no—
475C2×#102—731no—
476C2×#102—731no—
477C2×#102—731no—
478C2×#102—731no—
479C2×#102—731no—
480C2×C22⋊C8—731no—
481C2×C22⋊C8—731no—
482C2×#97—731no—
483C2×#41—2922no—
484C2×#41—2922no—
485C2×#41—734no—
486C2×#41—734no—
487C2×#41—1464no—
488C2×#41—1464no—
489C2×#41—1462no—
490C2×#41—1462no—
491C22×Q8—731no—
492C22×Q8C22×D7311yescharacteristic
493C22×D4—731no—
494C22×D4—731no—
495C22×D4—1461no—
496C22×D4—1461no—
497C22×D4—1461no—
498C22×D4—1461no—
499C22×D4—1461no—
500C22×D4—1461no—
501C22×D4C22⋊D7311yescharacteristic
502C23×C4—21no—
503C23×C4—1461no—
504C23×C4—1461no—
505C23×C4C22×D7311yescharacteristic
506C23×C4C22×D7311yescharacteristic
507C2×Q16—734no—
508C2×Q16—1464no—
509C2×SD16—2922no—
510C2×SD16—2922no—
511C2×SD16—734no—
512C2×SD16—734no—
513C2×M16—2922no—
514C2×M16—734no—
515C22×C8—2922no—
516C22×C8—734no—
517C22×C8—731no—
518C22×C8—731no—
519C22×C8—731no—
520C22×C8—731no—
521#127—734no—
522#127—1468no—
523#127—1462no—
524#126—28no—
525#125—28no—
526#125—22no—
527#125C22×D7314yes—
528#123—28no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8C22×D7314yes—
532C22⋊Q8C22×D7314yes—
533#121—734no—
534#121—734no—
535#121—1462no—
536#121—1462no—
537#121—1468no—
538#121—1468no—
539C4×Q8—22no—
540C4×Q8—734no—
541C4×Q8—1462no—
542C4×Q8C22×D7314yes—
543C4×D4—1468no—
544C4×D4C22⋊D7314yes—
545C4×D4C22×D7314yes—
546#117—22no—
547#117—28no—
548#117C22×D7314yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—731no—
557C2×C4⋊C4—1461no—
558C2×C4⋊C4C22⋊D7311yescharacteristic
559C2×C4⋊C4C22×D7311yescharacteristic
560C2×C4⋊C4C22×D7311yescharacteristic
561C2×C4⋊C4C22×D7314yes—
562C2×C4⋊C4C22×D7311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—1461no—
567C2×C22⋊C4—1461no—
568C2×C22⋊C4C22⋊D7311yescharacteristic
569C2×C22⋊C4C22⋊D7311yescharacteristic
570C2×C42—21no—
571C2×C42—21no—
572C2×C42—1461no—
573C2×C42C22×D7311yescharacteristic
574#107—734no—
575#106—734no—
576#106—734no—
577C4⋊C8—734no—
578#103—734no—
579#103—734no—
580#103—734no—
581#103—734no—
582#102—734no—
583#102—734no—
584#102—734no—
585#102—734no—
586#102—734no—
587#102—734no—
588C22⋊C8—734no—
589C22⋊C8—734no—
590#97—734no—
591C24—1461no—
592C24—1461no—
593C24C2×C22⋊D7311yescharacteristic
594C24C2×C22⋊D7311yescharacteristic
595#41—2928no—
596#41—2928no—
597#41—2924no—
598#41—2924no—
599#41—1468no—
600#41—1468no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—734no—
605C2×Q8—732no—
606C2×Q8—1461no—
607C2×Q8—1462no—
608C2×Q8C23×D7312yes—
609C2×D4—42no—
610C2×D4—2924no—
611C2×D4—2924no—
612C2×D4—2924no—
613C2×D4—5842no—
614C2×D4—5842no—
615C2×D4—5842no—
616C2×D4—732no—
617C2×D4—732no—
618C2×D4—1464no—
619C2×D4—1464no—
620C2×D4—1464no—
621C2×D4—1464no—
622C2×D4—1464no—
623C2×D4—1461no—
624C2×D4—1461no—
625C2×D4—1464no—
626C2×D4—1462no—
627C2×D4—1462no—
628C2×D4—1462no—
629C2×D4—1462no—
630C2×D4C2×C22⋊D7314yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—44no—
641C22×C4—2924no—
642C22×C4—2924no—
643C22×C4—1461no—
644C22×C4—1464no—
645C22×C4—1464no—
646C22×C4—1461no—
647C22×C4C2×C22⋊D7312yes—
648C22×C4C2×C22⋊D7312yes—
649C22×C4C2×C22⋊D7311yescharacteristic
650C22×C4C2×C22⋊D7311yescharacteristic
651C22×C4C2×C22⋊D7311yescharacteristic
652C22×C4C2×C22⋊D7311yescharacteristic
653C22×C4C23×D7312yes—
654C22×C4C23×D7312yes—
655C22×C4C23×D7311yescharacteristic
656Q16—1468no—
657SD16—2924no—
658SD16—2924no—
659M16—2924no—
660C2×C8—2924no—
661C2×C8—732no—
662C2×C8—732no—
663C2×C8—732no—
664C2×C8—732no—
665C2×C8—1462no—
666C2×C8—1462no—
667C2×C8—1462no—
668C2×C8—1462no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—732no—
679C4⋊C4—1464no—
680C4⋊C4—1461no—
681C4⋊C4C2×C22⋊D7314yes—
682C4⋊C4C23×D7312yes—
683C4⋊C4C23×D7312yes—
684C4⋊C4C23×D7312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—1464no—
689C22⋊C4—1464no—
690C22⋊C4C2×C22⋊D7314yes—
691C22⋊C4C2×C22⋊D7314yes—
692C42—24no—
693C42—24no—
694C42—1464no—
695C42C2×C22⋊D7312yes—
696C42C23×D7312yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—2922no—
704C23—2922no—
705C23—2922no—
706C23—2922no—
707C23—2922no—
708C23—2922no—
709C23—1462no—
710C23—1462no—
711C23C22×C22⋊D7312yes—
712C23C22×C22⋊D7312yes—
713C23C22×C22⋊D7311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—734no—
718Q8—1462no—
719Q8—1464no—
720D4—44no—
721D4—2928no—
722D4—2928no—
723D4—2928no—
724D4—2922no—
725D4—2922no—
726D4—5844no—
727D4—5844no—
728D4—5844no—
729D4—1462no—
730D4—1462no—
731D4—1462no—
732D4—1462no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—2928no—
753C2×C4—2928no—
754C2×C4—2922no—
755C2×C4—1462no—
756C2×C4—1462no—
757C2×C4—1464no—
758C2×C4C22×C22⋊D7312yes—
759C2×C4C22×C22⋊D7312yes—
760C2×C4C22×C22⋊D7312yes—
761C2×C4C22×C22⋊D7312yes—
762C2×C4C22×C22⋊D7311yescharacteristic
763C2×C4#41×D7312yes—
764C2×C4#1455663712yes—
765C2×C4C24×D7311yescharacteristic
766C8—1462no—
767C8—1462no—
768C8—1462no—
769C8—1462no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—2922no—
779C22—2922no—
780C22—2922no—
781C22—2922no—
782C22—2922no—
783C22—2922no—
784C22—5844no—
785C22—5844no—
786C22#1798922512yes—
787C22#1798938512yes—
788C22#1798939512yes—
789C22C23×C22⋊D7311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—2922no—
799C4—1464no—
800C4#1798922512yes—
801C4C2×#41×D7311yescharacteristic
802C4C2×#1455663711yescharacteristic
803C2—42no—
804C2—42no—
805C2—5842no—
806C2—5842no—
807C2#2262205114yesdirect product factor
808C2C2×#1798922511yescharacteristic
809C2C2×#1798938511yescharacteristic
810C2C2×#1798939511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#552×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989258C2
hypercenterC2×#552D73
hypocenterC73C2×#3317
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #22622051C2direct (N × H)
3. C2×#17988953C2semidirect
4. C2×#17988905C2semidirect
5. C2×#17988911C2semidirect
6. C2×#17988891C2semidirect
7. C2×#17988835C2semidirect
8. C2×#17988818C2semidirect
9. C2×#17988787C2semidirect
10. C2×#17988747C2semidirect
11. C2×#17988747C2semidirect
12. C2×#17988692C2semidirect
13. C2×#17988659C2semidirect
14. C2×#17988586C2semidirect
15. C2×#17988581C2semidirect
16. C2×#552×C73C2semidirect
34. #17988953C22semidirect
35. #17988911C22semidirect
36. #17988905C22semidirect
37. #17988891C22semidirect
38. #17988835C22semidirect
39. #17988818C22semidirect
40. #17988787C22semidirect
41. #17988747C22semidirect
42. #17988747C22semidirect
43. #17988692C22semidirect
44. #17988659C22semidirect
49. #17988586C22semidirect
50. #17988581C22semidirect
65. #552×C73C22semidirect
400. C2×C73#3317semidirect
406. C2×#552D73semidirect
422. C73C2×#3317semidirect
431. #552C2×D73semidirect
807. C2#22622051direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892582
#226220512
C2×#179889532
C2×#179889052
C2×#179889112
C2×#179888912
C2×#179888352
C2×#179888182
C2×#179887872
C2×#179887472
C2×#179886922
C2×#179886592
C2×#179885862
C2×#179885812
C2×#552×C732
C2×#331773