Finite Group Databasebeta

← C2×#22622048 #33962580

Subgroups — C2×#22622048 #33962580

Order 18688.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989295C211yesmaximal, characteristic, complemented
2C2×#17989243C211yesmaximal, characteristic
3#22622048C2116yesmaximal, direct product factor
4C2×#17988945C211yesmaximal, characteristic, complemented
5C2×#17988903C211yesmaximal, characteristic, complemented
6C2×#17988919C211yesmaximal, characteristic, complemented
7C2×#17988871C211yesmaximal, characteristic, complemented
8C2×#17988844C211yesmaximal, characteristic, complemented
9C2×#17988807C211yesmaximal, characteristic, complemented
10C2×#17988746C211yesmaximal, characteristic, complemented
11C2×#17988742C211yesmaximal, characteristic, complemented
12C2×#17988691C211yesmaximal, characteristic, complemented
13C2×#17988658C211yesmaximal, characteristic, complemented
14C2×#17988585C211yesmaximal, characteristic, complemented
15C22×#14556516C211yesmaximal, characteristic, complemented
16C2×#465×C73C211yesmaximal, characteristic, complemented
17C22×#11924027C2211yescharacteristic
18C23×Dic146C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924011C2211yescharacteristic
22#17989295—24no—
23#17989295C2218yescomplemented
24#17989243—24no—
25#17989243C2218yes—
26C2×#14556590C2211yescharacteristic
27C2×#14556581—21no—
28C2×#14556578C2211yescharacteristic
29C2×#14556577—21no—
30C2×#14556571—21no—
31C2×#14556571C2211yescharacteristic
32C2×#14556568—21no—
33C2×#14556568—21no—
34C2×#14556567C2211yescharacteristic
35C2×#14556563—21no—
36C2×Q8×Dic73C2211yescharacteristic
37C2×#14556556C2211yescharacteristic
38C2×D4×Dic73—21no—
39C2×C4×C22⋊D73C2211yescharacteristic
40C2×#14556551—21no—
41C22×C4⋊Dic73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988945C2218yescomplemented
44#17988919C2218yescomplemented
45#17988903C2218yescomplemented
46#17988871C2218yescomplemented
47#17988844C2218yescomplemented
48#17988807C2218yescomplemented
49#17988746C2218yescomplemented
50#17988742C2218yescomplemented
51#17988691C2218yescomplemented
52#17988658C2218yescomplemented
53C2×#14556522C2211yescharacteristic
54C2×#14556522C2211yescharacteristic
55C2×#14556520C2211yescharacteristic
56#17988585C2218yescomplemented
57C2×#14556516C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2218yescomplemented
62C2×#14556514C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#465×C73C2218yescomplemented
74C2×#106×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924027—24no—
78C2×#11924027—22no—
79C2×#11924027—42no—
80C2×#11924027C2314yes—
81C22×Dic146—21no—
82C22×Dic146—24no—
83C22×Dic146—22no—
84C22×Dic146—21no—
85C22×Dic146—42no—
86C22×Dic146C2311yescharacteristic
87C22×Dic146C2314yes—
88C22×Dic146C2311yescharacteristic
89C22×C22⋊D73—21no—
90C22×C22⋊D73D411yescharacteristic
91C23×Dic73—21no—
92C23×Dic73—21no—
93C23×Dic73—21no—
94C22×C4×D73—21no—
95C22×C4×D73C2311yescharacteristic
96C2×#11924018—24no—
97C2×#11924018—42no—
98C2×#11924018C2314yes—
99C2×#11924018C2314yes—
100C2×#11924011—42no—
101C2×#11924011C2314yes—
102C22×#10596831C2311yescharacteristic
103C22×#10596831C2311yescharacteristic
104#14556590—22no—
105#14556590C2314yes—
106#14556581—28no—
107#14556578—22no—
108#14556578C2314yes—
109#14556577—28no—
110#14556571—22no—
111#14556571—28no—
112#14556571C2314yes—
113#14556568—28no—
114#14556568—28no—
115#14556567—22no—
116#14556567C2314yes—
117#14556563—28no—
118Q8×Dic73—22no—
119Q8×Dic73C2314yes—
120#14556556—22no—
121#14556556C2314yes—
122D4×Dic73—28no—
123C4×C22⋊D73D414yes—
124C4×C22⋊D73C2314yes—
125#14556551—28no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73—22no—
129C2×C4⋊Dic73—21no—
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×C4⋊Dic73C2314yes—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007D411yescharacteristic
138C4⋊C4×D73—22no—
139C4⋊C4×D73C2314yes—
140C2×C22⋊Dic73—21no—
141C2×C22⋊Dic73—21no—
142C2×C22⋊Dic73D411yescharacteristic
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005D411yescharacteristic
146C2×C4×Dic73—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73C2311yescharacteristic
149#14556522C2314yes—
150#14556522C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556516C2314yes—
156#14556514C2314yes—
157#14556514C2314yes—
158#14556512C2314yes—
159#14556512C2314yes—
160C22⋊#10596831C2314yes—
161#14556503C2314yes—
162#14556501C2314yes—
163C22×Q8×C73C2311yescharacteristic
164C22×D4×C73—21no—
165C22×D4×C73C2311yescharacteristic
166C23×C4×C73C2311yescharacteristic
167C2×SD16×C73—42no—
168C2×SD16×C73C2314yes—
169C22×C8×C73—42no—
170C22×C8×C73C2311yescharacteristic
171C22×C8×C73C2311yescharacteristic
172C22×C8×C73C2314yes—
173C22⋊Q8×C73—22no—
174C22⋊Q8×C73C2314yes—
175#121×C73—22no—
176#121×C73C2314yes—
177C2×C4⋊C4×C73—21no—
178C2×C4⋊C4×C73C2311yescharacteristic
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C22⋊C4×C73—21no—
181C2×C22⋊C4×C73—21no—
182#106×C73C2314yes—
183#103×C73C2314yes—
184#102×C73C2314yes—
185C23×D73C2×D411yescharacteristic
186#11924027—28no—
187#11924027—44no—
188#11924027—48no—
189C2×Dic146—21no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—22no—
193C2×Dic146—28no—
194C2×Dic146—24no—
195C2×Dic146—21no—
196C2×Dic146—24no—
197C2×Dic146—44no—
198C2×Dic146—48no—
199C2×Dic146—44no—
200C2×Dic146—82no—
201C2×Dic146#4114yes—
202C2×Dic146C2412yes—
203C2×Dic146C2412yes—
204C2×C22⋊D73—24no—
205C2×C22⋊D73—24no—
206C2×C22⋊D73—44no—
207C2×C22⋊D73C2×D414yes—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73—24no—
213C22×Dic73—24no—
214C22×Dic73—24no—
215C22×Dic73—44no—
216C22×Dic73—44no—
217C22×Dic73—82no—
218C22×Dic73C2×D411yescharacteristic
219C22×Dic73C2×D411yescharacteristic
220C22×Dic73C2×D411yescharacteristic
221C2×C4×D73—22no—
222C2×C4×D73—22no—
223C2×C4×D73—24no—
224C2×C4×D73—82no—
225C2×C4×D73C2×D412yes—
226C2×C4×D73C2412yes—
227#11924018—28no—
228#11924018—44no—
229#11924011—44no—
230C2×#10596831—22no—
231C2×#10596831—22no—
232C2×#10596831C2412yes—
233C2×#10596831C2412yes—
234C4⋊Dic73—21no—
235C4⋊Dic73—21no—
236C4⋊Dic73—24no—
237C4⋊Dic73—24no—
238C4⋊Dic73—24no—
239C4⋊Dic73C2412yes—
240C4⋊Dic73C2412yes—
241#11924007—24no—
242#11924007—24no—
243#11924007—24no—
244#11924007—24no—
245#11924007C2×D414yes—
246C22⋊Dic73—24no—
247C22⋊Dic73—24no—
248C22⋊Dic73C2×D414yes—
249#11924005—24no—
250#11924005—24no—
251#11924005C2×D414yes—
252C4×Dic73—24no—
253C4×Dic73—24no—
254C4×Dic73C2×D412yes—
255C4×Dic73C2412yes—
256C24×C73—21no—
257C24×C73C2×D411yescharacteristic
258C2×Q8×C73—21no—
259C2×Q8×C73—22no—
260C2×Q8×C73—22no—
261C2×Q8×C73C2412yes—
262C2×D4×C73—24no—
263C2×D4×C73—21no—
264C2×D4×C73—22no—
265C2×D4×C73—22no—
266C2×D4×C73—44no—
267C2×D4×C73C2412yes—
268C22×C4×C73—22no—
269C22×C4×C73—22no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73C2×D411yescharacteristic
274C22×C4×C73C2×D412yes—
275C22×C4×C73C2412yes—
276C22×C4×C73C2411yescharacteristic
277SD16×C73—44no—
278C2×C8×C73—22no—
279C2×C8×C73—22no—
280C2×C8×C73—44no—
281C2×C8×C73C2412yes—
282C2×C8×C73C2412yes—
283C4⋊C4×C73—24no—
284C4⋊C4×C73—21no—
285C4⋊C4×C73—21no—
286C4⋊C4×C73C2412yes—
287C4⋊C4×C73C2412yes—
288C22⋊C4×C73—24no—
289C22⋊C4×C73—24no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—42no—
294C23×C73—42no—
295C23×C73—42no—
296C23×C73#13714yes—
297C23×C73C22×D412yes—
298C23×C73C22×D411yescharacteristic
299C22×D73—22no—
300C22×D73—22no—
301C22×D73—22no—
302C22×D73C22×D412yes—
303Q8×C73—22no—
304Q8×C73—22no—
305Q8×C73—42no—
306D4×C73—22no—
307D4×C73—22no—
308D4×C73—48no—
309D4×C73—42no—
310C2×C4×C73—22no—
311C2×C4×C73—24no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—42no—
318C2×C4×C73—42no—
319C2×C4×C73—42no—
320C2×C4×C73C22×D412yes—
321C2×C4×C73C22×D411yescharacteristic
322C2×C4×C73C2×#4112yes—
323C2×C4×C73H(5,𝔽2)12yes—
324C2×C4×C73C2511yescharacteristic
325C22⋊D73—28no—
326C22⋊D73—48no—
327C2×Dic73—22no—
328C2×Dic73—24no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—48no—
336C2×Dic73—48no—
337C2×Dic73—42no—
338C2×Dic73—42no—
339C2×Dic73—42no—
340C2×Dic73—84no—
341C2×Dic73C22×D412yes—
342C2×Dic73C22×D412yes—
343C2×Dic73C22×D412yes—
344C4×D73—24no—
345C4×D73—22no—
346C4×D73—22no—
347C4×D73—84no—
348Dic146—24no—
349Dic146—22no—
350Dic146—22no—
351Dic146—22no—
352Dic146—48no—
353Dic146—42no—
354Dic146—84no—
355Dic146C2×#4114yes—
356C8×C73—22no—
357C8×C73—22no—
358#10596831—22no—
359#10596831—22no—
360C22×C73—22no—
361C22×C73—28no—
362C22×C73—22no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—84no—
367C22×C73#54612yes—
368C22×C73C2×#13714yes—
369C22×C73C2×#13712yes—
370C22×C73#57712yes—
371C22×C73C23×D411yescharacteristic
372C2×D73—22no—
373C2×D73—22no—
374C2×D73—22no—
375C2×D73—44no—
376C4×C73—22no—
377C4×C73—42no—
378C4×C73—42no—
379C4×C73—42no—
380C4×C73#54612yes—
381C4×C73C22×#4111yescharacteristic
382C4×C73C2×H(5,𝔽2)11yescharacteristic
383Dic73—24no—
384Dic73—22no—
385Dic73—22no—
386Dic73—22no—
387Dic73—42no—
388Dic73—42no—
389Dic73—42no—
390C2×#3316—731nomaximal, Sylow
391C2×C73—24no—
392C2×C73—82no—
393C2×C73#331614yescomplemented
394C2×C73C2×#54611yescharacteristic
395C2×C73C22×#13711yescharacteristic
396C2×C73C2×#57711yescharacteristic
397D73—42no—
398C2×#554—731no—
399C2×#548—731no—
400#3316—7316no—
401C2×#489—731no—
402C2×#481—731no—
403C2×#483—731no—
404C2×#475—731no—
405C2×#470—731no—
406C2×#465D7311yescharacteristic, complemented
407C2×#464—731no—
408C2×#452—731no—
409C2×#451—731no—
410C2×#441—731no—
411C2×#435—731no—
412C2×#417—731no—
413C22×#103—731no—
414C73C2×#331611yescharacteristic, complemented, Sylow
415C22×#41—731no—
416C23×Q8—731no—
417C22×Q16—731no—
418C22×Q16—731no—
419C22×SD16C2×D7311yescharacteristic
420C22×M16—731no—
421C23×C8C2×D7311yescharacteristic
422#554—738no—
423#554—1464no—
424#548—738no—
425#548—1464no—
426C2×C4⋊Q8—731no—
427C2×#125—1461no—
428C2×#124—731no—
429C2×#124—1461no—
430C2×C22⋊Q8—731no—
431C2×C22⋊Q8—731no—
432C2×C22⋊Q8—1461no—
433C2×C22⋊Q8—1461no—
434C2×C22⋊Q8—1461no—
435C2×C22⋊Q8C2×D7311yescharacteristic
436C2×#121—1461no—
437C2×#121C2×D7311yescharacteristic
438C2×C4×Q8—731no—
439C2×C4×Q8—731no—
440C2×C4×D4—731no—
441C2×C4×D4—1461no—
442C2×C4×D4—1461no—
443C22×C4⋊C4—731no—
444C22×C4⋊C4—731no—
445#489—738no—
446#483—738no—
447#481—738no—
448#475—738no—
449#470—738no—
450#465C2×D7318yescomplemented
451#464—738no—
452#452—738no—
453#451—738no—
454#441—738no—
455#435—738no—
456C2×#106—731no—
457C2×#106—731no—
458C2×#106C2×D7311yescharacteristic
459C2×C4⋊C8—731no—
460#417—738no—
461C2×#103—731no—
462C2×#103—731no—
463C2×#103—731no—
464C2×#103—731no—
465C2×#103—738no—
466C2×#103—731no—
467C2×#103—731no—
468C2×#103C2×D7311yescharacteristic
469C2×#102—731no—
470C2×#102—731no—
471C2×#102C2×D7311yescharacteristic
472C2×C22⋊C8—731no—
473C2×C22⋊C8—731no—
474C2×#97—731no—
475C2×#41—2922no—
476C2×#41—734no—
477C2×#41—1464no—
478C2×#41—1462no—
479C22×Q8—2922no—
480C22×Q8—734no—
481C22×Q8—731no—
482C22×Q8—731no—
483C22×Q8—1464no—
484C22×Q8—1461no—
485C22×Q8—1461no—
486C22×Q8—1462no—
487C22×Q8C22×D7311yescharacteristic
488C22×D4—21no—
489C22×D4—731no—
490C22×D4—1461no—
491C22×D4C22×D7311yescharacteristic
492C23×C4—731no—
493C23×C4—1461no—
494C23×C4—1461no—
495C23×C4—1461no—
496C23×C4—1461no—
497C23×C4C22×D7311yescharacteristic
498C2×Q16—2922no—
499C2×Q16—734no—
500C2×Q16—734no—
501C2×Q16—1464no—
502C2×SD16—42no—
503C2×SD16C22×D7314yes—
504C2×M16—2922no—
505C2×M16—734no—
506C22×C8—42no—
507C22×C8—731no—
508C22×C8—731no—
509C22×C8C22×D7311yescharacteristic
510C22×C8C22×D7311yescharacteristic
511C22×C8C22×D7314yes—
512C4⋊Q8—734no—
513C4⋊Q8—1462no—
514#125—1468no—
515#124—734no—
516#124—1462no—
517#124—1468no—
518C22⋊Q8—22no—
519C22⋊Q8—734no—
520C22⋊Q8—734no—
521C22⋊Q8—1468no—
522C22⋊Q8—1468no—
523C22⋊Q8—1468no—
524C22⋊Q8—1462no—
525C22⋊Q8—1462no—
526C22⋊Q8C22×D7314yes—
527#121—22no—
528#121—1468no—
529#121C22×D7314yes—
530C4×Q8—734no—
531C4×Q8—734no—
532C4×Q8—1462no—
533C4×Q8—1462no—
534C4×D4—734no—
535C4×D4—734no—
536C4×D4—1468no—
537C4×D4—1468no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—731no—
540C2×C4⋊C4—731no—
541C2×C4⋊C4—731no—
542C2×C4⋊C4—734no—
543C2×C4⋊C4—734no—
544C2×C4⋊C4—1462no—
545C2×C4⋊C4—1461no—
546C2×C4⋊C4—1461no—
547C2×C4⋊C4—1461no—
548C2×C4⋊C4—1461no—
549C2×C4⋊C4—1461no—
550C2×C4⋊C4—1461no—
551C2×C4⋊C4—1461no—
552C2×C4⋊C4—1462no—
553C2×C4⋊C4C22×D7311yescharacteristic
554C2×C4⋊C4C22×D7311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—731no—
558C2×C22⋊C4—731no—
559C2×C22⋊C4—1461no—
560C2×C22⋊C4—1461no—
561C2×C22⋊C4—1461no—
562C2×C22⋊C4—1461no—
563C2×C42—731no—
564C2×C42—1461no—
565C2×C42—1461no—
566#106—734no—
567#106—734no—
568#106C22×D7314yes—
569C4⋊C8—734no—
570#103—734no—
571#103—734no—
572#103—734no—
573#103—734no—
574#103—734no—
575#103—734no—
576#103C22×D7314yes—
577#102—734no—
578#102—734no—
579#102C22×D7314yes—
580C22⋊C8—734no—
581C22⋊C8—734no—
582#97—734no—
583C24—21no—
584C24—731no—
585C24D4×D7311yescharacteristic
586#41—2924no—
587#41—2928no—
588#41—1468no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—2928no—
593C2×Q8—2924no—
594C2×Q8—2924no—
595C2×Q8—5842no—
596C2×Q8—734no—
597C2×Q8—732no—
598C2×Q8—732no—
599C2×Q8—1468no—
600C2×Q8—1464no—
601C2×Q8—1462no—
602C2×Q8—1462no—
603C2×Q8—1461no—
604C2×Q8—1464no—
605C2×Q8—1461no—
606C2×Q8—1462no—
607C2×Q8C23×D7312yes—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—44no—
613C2×D4—2924no—
614C2×D4—734no—
615C2×D4—1464no—
616C2×D4—1464no—
617C2×D4C23×D7312yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—2924no—
624C22×C4—2924no—
625C22×C4—5842no—
626C22×C4—5842no—
627C22×C4—731no—
628C22×C4—731no—
629C22×C4—731no—
630C22×C4—732no—
631C22×C4—732no—
632C22×C4—1464no—
633C22×C4—1464no—
634C22×C4—1464no—
635C22×C4—1461no—
636C22×C4—1461no—
637C22×C4—1461no—
638C22×C4—1464no—
639C22×C4—1461no—
640C22×C4—1462no—
641C22×C4—1462no—
642C22×C4D4×D7312yes—
643C22×C4D4×D7311yescharacteristic
644C22×C4C23×D7312yes—
645C22×C4C23×D7311yescharacteristic
646Q16—2924no—
647Q16—1468no—
648SD16—44no—
649M16—2924no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—44no—
653C2×C8—732no—
654C2×C8—732no—
655C2×C8—1462no—
656C2×C8—1462no—
657C2×C8C23×D7312yes—
658C2×C8C23×D7312yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—734no—
663C4⋊C4—732no—
664C4⋊C4—732no—
665C4⋊C4—1464no—
666C4⋊C4—1464no—
667C4⋊C4—1464no—
668C4⋊C4—1464no—
669C4⋊C4—1464no—
670C4⋊C4—1464no—
671C4⋊C4—1461no—
672C4⋊C4—1464no—
673C4⋊C4—1461no—
674C4⋊C4C23×D7312yes—
675C4⋊C4C23×D7312yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—734no—
679C22⋊C4—734no—
680C22⋊C4—1464no—
681C22⋊C4—1464no—
682C22⋊C4—1464no—
683C22⋊C4—1464no—
684C42—732no—
685C42—732no—
686C42—1464no—
687C42—1464no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—732no—
695C23—1462no—
696C23—1462no—
697C23—1462no—
698C23#1455662014yes—
699C23C2×D4×D7312yes—
700C23C2×D4×D7311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—2928no—
705Q8—2922no—
706Q8—5844no—
707Q8—734no—
708Q8—1462no—
709Q8—1462no—
710Q8—1462no—
711Q8—1464no—
712D4—22no—
713D4—22no—
714D4—48no—
715D4—42no—
716D4—2928no—
717D4—1468no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—2922no—
729C2×C4—2922no—
730C2×C4—2922no—
731C2×C4—2928no—
732C2×C4—2928no—
733C2×C4—5844no—
734C2×C4—5844no—
735C2×C4—732no—
736C2×C4—732no—
737C2×C4—732no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1464no—
746C2×C4—1462no—
747C2×C4—1462no—
748C2×C4—1464no—
749C2×C4C2×D4×D7312yes—
750C2×C4C2×D4×D7311yescharacteristic
751C2×C4#41×D7312yes—
752C2×C4#1455663612yes—
753C2×C4C24×D7311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1462no—
757C8—1462no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—84no—
765C22—2924no—
766C22—1462no—
767C22—1462no—
768C22—1462no—
769C22#1798922612yes—
770C22C2×#1455662014yes—
771C22C2×#1455662012yes—
772C22#1798939412yes—
773C22C22×D4×D7311yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—2922no—
779C4—2922no—
780C4—2922no—
781C4—1462no—
782C4—1464no—
783C4—1462no—
784C4—1462no—
785C4#1798922612yes—
786C4C2×#41×D7311yescharacteristic
787C4C2×#1455663611yescharacteristic
788C2—24no—
789C2—82no—
790C2—2922no—
791C2#2262204814yesdirect product factor
792C2C2×#1798922611yescharacteristic
793C2C22×#1455662011yescharacteristic
794C2C2×#1798939411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#465×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989243C2
hypercenterC2×#465D73
hypocenterC73C2×#3316
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#17989295C2semidirect
3. #22622048C2direct (N × H)
4. C2×#17988945C2semidirect
5. C2×#17988903C2semidirect
6. C2×#17988919C2semidirect
7. C2×#17988871C2semidirect
8. C2×#17988844C2semidirect
9. C2×#17988807C2semidirect
10. C2×#17988746C2semidirect
11. C2×#17988742C2semidirect
12. C2×#17988691C2semidirect
13. C2×#17988658C2semidirect
14. C2×#17988585C2semidirect
15. C22×#14556516C2semidirect
16. C2×#465×C73C2semidirect
23. #17989295C22semidirect
43. #17988945C22semidirect
44. #17988919C22semidirect
45. #17988903C22semidirect
46. #17988871C22semidirect
47. #17988844C22semidirect
48. #17988807C22semidirect
49. #17988746C22semidirect
50. #17988742C22semidirect
51. #17988691C22semidirect
52. #17988658C22semidirect
56. #17988585C22semidirect
61. C2×#14556516C22semidirect
73. #465×C73C22semidirect
393. C2×C73#3316semidirect
406. C2×#465D73semidirect
414. C73C2×#3316semidirect
450. #465C2×D73semidirect
791. C2#22622048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892952
C2×#179892432
#226220482
C2×#179889452
C2×#179889032
C2×#179889192
C2×#179888712
C2×#179888442
C2×#179888072
C2×#179887462
C2×#179887422
C2×#179886912
C2×#179886582
C2×#179885852
C22×#145565162
C2×#465×C732
C2×#331673