Finite Group Databasebeta

← C2×#22620646 #33955923

Subgroups — C2×#22620646 #33955923

Order 18688.

2234 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989141C211yesmaximal, characteristic, complemented
2C2×#17989134C211yesmaximal, characteristic
3#22620646C2116yesmaximal, direct product factor
4C2×#17988991C211yesmaximal, characteristic, complemented
5C2×#17988958C211yesmaximal, characteristic, complemented
6C2×#17988936C211yesmaximal, characteristic, complemented
7C2×#17988932C211yesmaximal, characteristic, complemented
8C2×#17988836C211yesmaximal, characteristic, complemented
9C2×#17988834C211yesmaximal, characteristic, complemented
10C2×#17988832C211yesmaximal, characteristic, complemented
11C2×#17988830C211yesmaximal, characteristic, complemented
12C2×#17988689C211yesmaximal, characteristic, complemented
13C2×#17988687C211yesmaximal, characteristic, complemented
14C2×#17988685C211yesmaximal, characteristic, complemented
15C2×#17988539C211yesmaximal, characteristic, complemented
16C2×#440×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18C22×#11924017C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21C22×#11924011C2211yescharacteristic
22C22×#11924011C2211yescharacteristic
23#17989141—24no—
24#17989141C2218yescomplemented
25#17989134—24no—
26#17989134C2218yes—
27C2×#14556590C2211yescharacteristic
28C2×#14556590C2211yescharacteristic
29C2×#14556589C2211yescharacteristic
30C2×#14556587C2211yescharacteristic
31C2×#14556581—21no—
32C2×#14556577—21no—
33C2×#14556571C2211yescharacteristic
34C2×#14556569—21no—
35C2×#14556567C2211yescharacteristic
36C2×#14556566C2211yescharacteristic
37C2×#14556564—21no—
38C2×#14556562C2211yescharacteristic
39C2×C4×Dic146—21no—
40C2×C4×Dic146C2211yescharacteristic
41C2×C4×D292C2211yescharacteristic
42C2×C4×C22⋊D73—21no—
43C2×#14556548—21no—
44C2×C42×D73C2211yescharacteristic
45#17988991C2218yescomplemented
46#17988958C2218yescomplemented
47#17988936C2218yescomplemented
48#17988932C2218yescomplemented
49#17988836C2218yescomplemented
50#17988834C2218yescomplemented
51#17988832C2218yescomplemented
52#17988830C2218yescomplemented
53#17988689C2218yescomplemented
54#17988687C2218yescomplemented
55#17988685C2218yescomplemented
56C2×#14556525C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556524C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65#17988539C2218yescomplemented
66C2×#14556502C2211yescharacteristic
67C2×C8×Dic73C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#440×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C2×#11924028—28no—
78C2×#11924028—48no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146C2311yescharacteristic
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×C22⋊D73—21no—
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73D411yescharacteristic
89C22×C4×D73D411yescharacteristic
90C22×C4×D73C2311yescharacteristic
91C2×#11924017—24no—
92C2×#11924017C2314yes—
93C2×#11924016—24no—
94C2×#11924016C2314yes—
95C2×#11924015—24no—
96C2×#11924015C2314yes—
97C2×#11924011—24no—
98C2×#11924011—24no—
99C2×#11924011C2314yes—
100C2×#11924011C2314yes—
101C22×#10596831C2311yescharacteristic
102C22×#10596831C2311yescharacteristic
103#14556590—22no—
104#14556590—22no—
105#14556590C2314yes—
106#14556590C2314yes—
107#14556589—22no—
108#14556589C2314yes—
109#14556587—22no—
110#14556587C2314yes—
111#14556581—28no—
112#14556577—28no—
113#14556571—22no—
114#14556571C2314yes—
115#14556569—28no—
116#14556567—22no—
117#14556567C2314yes—
118#14556566—22no—
119#14556566C2314yes—
120#14556564—28no—
121#14556562—22no—
122#14556562C2314yes—
123C4×Dic146—28no—
124C4×Dic146—22no—
125C4×Dic146C2314yes—
126C4×D292—22no—
127C4×D292C2314yes—
128C4×C22⋊D73—28no—
129#14556548—28no—
130C2×C4⋊Dic73—21no—
131C2×C4⋊Dic73C2311yescharacteristic
132C2×C4⋊Dic73C2311yescharacteristic
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×C22⋊Dic73—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73D411yescharacteristic
146C2×C4×Dic73D411yescharacteristic
147C2×C4×Dic73C2311yescharacteristic
148C42×D73D414yes—
149C42×D73C2314yes—
150#14556525C2314yes—
151#14556524C2314yes—
152#14556524C2314yes—
153#14556516C2314yes—
154#14556515C2314yes—
155#14556514C2314yes—
156#14556513C2314yes—
157#14556512C2314yes—
158#14556511C2314yes—
159#14556502C2314yes—
160C8×Dic73C2314yes—
161C8×Dic73C2314yes—
162C22×Q8×C73C2311yescharacteristic
163C22×D4×C73C2311yescharacteristic
164C23×C4×C73—21no—
165C2×SD16×C73—24no—
166C2×SD16×C73C2314yes—
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169C4×Q8×C73—22no—
170C4×Q8×C73C2314yes—
171C4×D4×C73—22no—
172C4×D4×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C22⋊C4×C73—21no—
177C2×C42×C73—21no—
178C2×C42×C73C2311yescharacteristic
179#107×C73C2314yes—
180#103×C73C2314yes—
181#102×C73C2314yes—
182#97×C73C2314yes—
183C23×D73—21no—
184C23×D73C2×D411yescharacteristic
185#11924028—432no—
186C2×Dic146—22no—
187C2×Dic146—22no—
188C2×Dic146—21no—
189C2×Dic146—24no—
190C2×Dic146—24no—
191C2×Dic146—44no—
192C2×Dic146—44no—
193C2×Dic146C2412yes—
194C2×D292—22no—
195C2×D292—22no—
196C2×D292—24no—
197C2×D292—21no—
198C2×D292—44no—
199C2×D292C2412yes—
200C2×C22⋊D73—24no—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—24no—
203C2×C22⋊D73—44no—
204C2×C22⋊D73—44no—
205C2×C22⋊D73—44no—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C22×Dic73C2×D411yescharacteristic
212C2×C4×D73—22no—
213C2×C4×D73—22no—
214C2×C4×D73—24no—
215C2×C4×D73—24no—
216C2×C4×D73—24no—
217C2×C4×D73—44no—
218C2×C4×D73C2×D412yes—
219C2×C4×D73C2×D414yes—
220C2×C4×D73C2×D414yes—
221C2×C4×D73C2412yes—
222#11924017—28no—
223#11924016—28no—
224#11924015—28no—
225#11924011—28no—
226#11924011—28no—
227C2×#10596831—22no—
228C2×#10596831#4114yescomplemented
229C2×#10596831C2412yes—
230C2×#10596831C2412yes—
231C4⋊Dic73—21no—
232C4⋊Dic73—21no—
233C4⋊Dic73—24no—
234C4⋊Dic73C2412yes—
235C4⋊Dic73C2412yes—
236#11924007—24no—
237#11924007—24no—
238#11924007—24no—
239#11924007—24no—
240#11924007—24no—
241#11924007—24no—
242C22⋊Dic73—24no—
243#11924005—24no—
244#11924005—24no—
245#11924005—24no—
246#11924005—24no—
247C4×Dic73—24no—
248C4×Dic73C2×D412yes—
249C4×Dic73C2×D414yes—
250C4×Dic73C2×D414yes—
251C4×Dic73C2412yes—
252C24×C73—21no—
253C2×Q8×C73—21no—
254C2×Q8×C73—22no—
255C2×Q8×C73—22no—
256C2×Q8×C73C2412yes—
257C2×D4×C73—21no—
258C2×D4×C73—22no—
259C2×D4×C73—22no—
260C2×D4×C73C2412yes—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—24no—
265C22×C4×C73—44no—
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2411yescharacteristic
269SD16×C73—28no—
270C2×C8×C73—22no—
271C2×C8×C73#4114yescomplemented
272C2×C8×C73C2412yes—
273C2×C8×C73C2412yes—
274C4⋊C4×C73—24no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73C2412yes—
278C4⋊C4×C73C2412yes—
279C22⋊C4×C73—24no—
280C42×C73—24no—
281C42×C73C2×D412yes—
282C42×C73C2412yes—
283C23×C73—22no—
284C23×C73—42no—
285C23×C73—42no—
286C23×C73—42no—
287C23×C73C22×D411yescharacteristic
288C22×D73—22no—
289C22×D73—22no—
290C22×D73—22no—
291C22×D73—22no—
292C22×D73—42no—
293C22×D73—42no—
294C22×D73—42no—
295C22×D73C22×D412yes—
296Q8×C73—22no—
297Q8×C73—22no—
298Q8×C73—42no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—42no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—48no—
308C2×C4×C73—42no—
309C2×C4×C73—42no—
310C2×C4×C73—42no—
311C2×C4×C73C22×D412yes—
312C2×C4×C73C22×D412yes—
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C2×#4112yes—
315C2×C4×C73C2×#4112yes—
316C2×C4×C73C2511yescharacteristic
317C22⋊D73—48no—
318C22⋊D73—48no—
319C22⋊D73—48no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73AGL(1,ℤ/8)14yes—
328C2×Dic73#13714yes—
329C2×Dic73C22×D412yes—
330C2×Dic73C22×D412yes—
331C2×Dic73C22×D412yes—
332D292—22no—
333D292—22no—
334D292—48no—
335D292—42no—
336C4×D73—24no—
337C4×D73—22no—
338C4×D73—22no—
339C4×D73—28no—
340C4×D73—28no—
341C4×D73—48no—
342Dic146—22no—
343Dic146—22no—
344Dic146—42no—
345Dic146—48no—
346Dic146—48no—
347C8×C73—22no—
348C8×C73C2×#4114yescomplemented
349#10596831—22no—
350#10596831C2×#4114yescomplemented
351C22×C73—42no—
352C22×C73—42no—
353C22×C73—42no—
354C22×C73—84no—
355C22×C73#53212yes—
356C22×C73C2×AGL(1,ℤ/8)12yes—
357C22×C73C2×#13712yes—
358C22×C73C23×D411yescharacteristic
359C2×D73—22no—
360C2×D73—22no—
361C2×D73—22no—
362C2×D73—44no—
363C2×D73—42no—
364C2×D73—42no—
365C2×D73—42no—
366C2×D73—84no—
367C4×C73—22no—
368C4×C73—22no—
369C4×C73—42no—
370C4×C73—42no—
371C4×C73—42no—
372C4×C73#53212yes—
373C4×C73C22×#4111yescharacteristic
374C4×C73C22×#4111yescharacteristic
375Dic73—22no—
376Dic73—42no—
377Dic73—42no—
378Dic73—42no—
379Dic73C2×AGL(1,ℤ/8)14yes—
380Dic73C2×#13714yes—
381C2×#3182—731nomaximal, Sylow
382C2×C73—82no—
383C2×C73#318214yescomplemented
384C2×C73C2×#53211yescharacteristic
385C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
386C2×C73C22×#13711yescharacteristic
387D73—42no—
388D73—82no—
389C2×#533—731no—
390C2×#532—731no—
391#3182—7316no—
392C2×#500—731no—
393C2×#492—731no—
394C2×#487—731no—
395C2×#486—731no—
396C2×#468—731no—
397C2×#468—731no—
398C2×#468—731no—
399C2×#468—731no—
400C2×#440—731no—
401C2×#440—731no—
402C2×#440—731no—
403C2×#440D7311yescharacteristic, complemented
404C2×C4×M16—731no—
405C73C2×#318211yescharacteristic, complemented, Sylow
406C22×#41—1461no—
407C22×SD16—731no—
408C22×SD16—731no—
409C22×SD16—731no—
410C22×SD16C2×D7311yescharacteristic
411C22×M16—731no—
412C22×M16—731no—
413#533—738no—
414#533—1464no—
415#532—738no—
416#532—1464no—
417C2×C4⋊Q8—731no—
418C2×C4⋊Q8—731no—
419C2×C4⋊Q8—731no—
420C2×#127—731no—
421C2×#125—1461no—
422C2×#124—1461no—
423C2×C22⋊Q8—731no—
424C2×C22⋊Q8—731no—
425C2×C22⋊Q8—1461no—
426C2×#121—731no—
427C2×#121—731no—
428C2×#121—1461no—
429C2×C4×Q8—731no—
430C2×C4×Q8—1461no—
431C2×C4×Q8C2×D7311yescharacteristic
432C2×C4×D4—731no—
433C2×C4×D4—1461no—
434C2×C4×D4C2×D7311yescharacteristic
435C2×#117—1461no—
436C22×C42—731no—
437#500—738no—
438#492—738no—
439#487—738no—
440#486—738no—
441#468—738no—
442#468—738no—
443#468—738no—
444#468—738no—
445#440—738no—
446#440—738no—
447#440—738no—
448#440C2×D7318yescomplemented
449C2×#107—731no—
450C2×#107—731no—
451C2×#107—731no—
452C2×#107C2×D7311yescharacteristic
453C2×#103—731no—
454C2×#103—731no—
455C2×#103—731no—
456C2×#103C2×D7311yescharacteristic
457C2×#102—731no—
458C2×#102—731no—
459C2×#102—731no—
460C2×#102C2×D7311yescharacteristic
461C4×M16—738no—
462C2×#97—731no—
463C2×#97C2×D7311yescharacteristic
464C2×C4×C8—731no—
465C2×C4×C8—731no—
466C2×#41—2928no—
467C2×#41—1468no—
468C22×Q8—731no—
469C22×Q8—1461no—
470C22×Q8—1461no—
471C22×Q8C22×D7311yescharacteristic
472C22×D4—731no—
473C22×D4—1461no—
474C22×D4—1461no—
475C22×D4—1461no—
476C22×D4—1461no—
477C22×D4C22×D7311yescharacteristic
478C23×C4—21no—
479C23×C4—731no—
480C23×C4—731no—
481C23×C4—731no—
482C23×C4—1461no—
483C2×SD16—24no—
484C2×SD16—734no—
485C2×SD16—734no—
486C2×SD16—734no—
487C2×SD16—1464no—
488C2×SD16—1464no—
489C2×SD16—1464no—
490C2×SD16C22×D7314yes—
491C2×M16—734no—
492C2×M16—734no—
493C2×M16—1464no—
494C2×M16—1464no—
495C22×C8—731no—
496C22×C8—731no—
497C22×C8C22×D7311yescharacteristic
498C22×C8C22×D7311yescharacteristic
499C4⋊Q8—734no—
500C4⋊Q8—734no—
501C4⋊Q8—734no—
502C4⋊Q8—1462no—
503C4⋊Q8—1462no—
504C4⋊Q8—1462no—
505#127—734no—
506#127—1462no—
507#125—1468no—
508#124—1468no—
509C22⋊Q8—734no—
510C22⋊Q8—734no—
511C22⋊Q8—1462no—
512C22⋊Q8—1468no—
513C22⋊Q8—1462no—
514#121—734no—
515#121—734no—
516#121—1468no—
517#121—1462no—
518#121—1462no—
519C4×Q8—22no—
520C4×Q8—734no—
521C4×Q8—1468no—
522C4×Q8—1462no—
523C4×Q8C22×D7314yes—
524C4×D4—22no—
525C4×D4—734no—
526C4×D4—1468no—
527C4×D4—1462no—
528C4×D4C22×D7314yes—
529#117—1468no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—731no—
532C2×C4⋊C4—731no—
533C2×C4⋊C4—1461no—
534C2×C4⋊C4—1461no—
535C2×C4⋊C4—1461no—
536C2×C4⋊C4—1461no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4C22×D7311yescharacteristic
541C2×C4⋊C4C22×D7311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—1461no—
544C2×C22⋊C4—1461no—
545C2×C22⋊C4—1461no—
546C2×C22⋊C4—1461no—
547C2×C22⋊C4—1461no—
548C2×C42—21no—
549C2×C42—731no—
550C2×C42—731no—
551C2×C42—731no—
552C2×C42—734no—
553C2×C42—734no—
554C2×C42—1461no—
555C2×C42C22×D7311yescharacteristic
556#107—734no—
557#107—734no—
558#107—734no—
559#107C22×D7314yes—
560#103—734no—
561#103—734no—
562#103—734no—
563#103C22×D7314yes—
564#102—734no—
565#102—734no—
566#102—734no—
567#102C22×D7314yes—
568#97—734no—
569#97C22×D7314yes—
570C4×C8—734no—
571C4×C8—734no—
572C24—21no—
573C24—731no—
574C24—1461no—
575#41—29232no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—2924no—
580C2×Q8—2924no—
581C2×Q8—732no—
582C2×Q8—1464no—
583C2×Q8—1464no—
584C2×Q8—1462no—
585C2×Q8—1462no—
586C2×Q8—1461no—
587C2×Q8C23×D7312yes—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—2924no—
592C2×D4—2924no—
593C2×D4—2924no—
594C2×D4—2924no—
595C2×D4—732no—
596C2×D4—1464no—
597C2×D4—1464no—
598C2×D4—1464no—
599C2×D4—1464no—
600C2×D4—1461no—
601C2×D4—1462no—
602C2×D4—1462no—
603C2×D4C23×D7312yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—44no—
609C22×C4—2924no—
610C22×C4—731no—
611C22×C4—731no—
612C22×C4—731no—
613C22×C4—734no—
614C22×C4—732no—
615C22×C4—734no—
616C22×C4—732no—
617C22×C4—1464no—
618C22×C4—1464no—
619C22×C4—1461no—
620C22×C4—1461no—
621C22×C4—1461no—
622C22×C4—1464no—
623C22×C4—1462no—
624C22×C4—1462no—
625C22×C4D4×D7311yescharacteristic
626C22×C4D4×D7311yescharacteristic
627C22×C4C23×D7311yescharacteristic
628SD16—28no—
629SD16—1468no—
630SD16—1468no—
631SD16—1468no—
632M16—1468no—
633M16—1468no—
634C2×C8—22no—
635C2×C8—734no—
636C2×C8—732no—
637C2×C8—732no—
638C2×C8—1462no—
639C2×C8#1192402814yescomplemented
640C2×C8C23×D7312yes—
641C2×C8C23×D7312yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—732no—
646C4⋊C4—732no—
647C4⋊C4—1464no—
648C4⋊C4—1464no—
649C4⋊C4—1464no—
650C4⋊C4—1464no—
651C4⋊C4—1464no—
652C4⋊C4—1464no—
653C4⋊C4—1464no—
654C4⋊C4—1461no—
655C4⋊C4—1461no—
656C4⋊C4C23×D7312yes—
657C4⋊C4C23×D7312yes—
658C22⋊C4—24no—
659C22⋊C4—1464no—
660C22⋊C4—1464no—
661C22⋊C4—1464no—
662C22⋊C4—1464no—
663C22⋊C4—1464no—
664C42—24no—
665C42—734no—
666C42—734no—
667C42—732no—
668C42—732no—
669C42—1464no—
670C42D4×D7312yes—
671C42C23×D7312yes—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—2922no—
677C23—2922no—
678C23—2922no—
679C23—732no—
680C23—1462no—
681C23—1462no—
682C23—1462no—
683C23—1462no—
684C23C2×D4×D7311yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—2928no—
689Q8—2928no—
690Q8—2922no—
691Q8—1462no—
692Q8—1462no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—2928no—
697D4—2928no—
698D4—2928no—
699D4—2928no—
700D4—2922no—
701D4—1462no—
702D4—1462no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—2928no—
713C2×C4—2922no—
714C2×C4—2922no—
715C2×C4—2922no—
716C2×C4—734no—
717C2×C4—732no—
718C2×C4—732no—
719C2×C4—734no—
720C2×C4—732no—
721C2×C4—1468no—
722C2×C4—1468no—
723C2×C4—1462no—
724C2×C4—1462no—
725C2×C4—1462no—
726C2×C4—1462no—
727C2×C4—1464no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4C2×D4×D7312yes—
731C2×C4C2×D4×D7312yes—
732C2×C4C2×D4×D7311yescharacteristic
733C2×C4#41×D7312yes—
734C2×C4C2×#1192402812yes—
735C2×C4C24×D7311yescharacteristic
736C8—22no—
737C8—734no—
738C8—1462no—
739C8C2×#1192402814yescomplemented
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—2924no—
745C22—2922no—
746C22—2922no—
747C22—2922no—
748C22—5844no—
749C22—1462no—
750C22—1462no—
751C22—1462no—
752C22#1798913412yes—
753C22AGL(1,ℤ/8)×D7312yes—
754C22#137×D7312yes—
755C22C22×D4×D7311yescharacteristic
756C4—22no—
757C4—22no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—2922no—
762C4—2922no—
763C4—2922no—
764C4—734no—
765C4—734no—
766C4—1462no—
767C4#1798913412yes—
768C4C2×#41×D7311yescharacteristic
769C4C22×#1192402811yescharacteristic
770C2—82no—
771C2—2922no—
772C2—5842no—
773C2#2262064614yesdirect product factor
774C2C2×#1798913411yescharacteristic
775C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
776C2C2×#137×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#440×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989134C2
hypercenterC2×#440D73
hypocenterC73C2×#3182
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#17989141C2semidirect
3. #22620646C2direct (N × H)
4. C2×#17988991C2semidirect
5. C2×#17988958C2semidirect
6. C2×#17988936C2semidirect
7. C2×#17988932C2semidirect
8. C2×#17988836C2semidirect
9. C2×#17988834C2semidirect
10. C2×#17988832C2semidirect
11. C2×#17988830C2semidirect
12. C2×#17988689C2semidirect
13. C2×#17988687C2semidirect
14. C2×#17988685C2semidirect
15. C2×#17988539C2semidirect
16. C2×#440×C73C2semidirect
24. #17989141C22semidirect
45. #17988991C22semidirect
46. #17988958C22semidirect
47. #17988936C22semidirect
48. #17988932C22semidirect
49. #17988836C22semidirect
50. #17988834C22semidirect
51. #17988832C22semidirect
52. #17988830C22semidirect
53. #17988689C22semidirect
54. #17988687C22semidirect
55. #17988685C22semidirect
65. #17988539C22semidirect
72. #440×C73C22semidirect
228. C2×#10596831#41semidirect
271. C2×C8×C73#41semidirect
348. C8×C73C2×#41semidirect
350. #10596831C2×#41semidirect
383. C2×C73#3182semidirect
403. C2×#440D73semidirect
405. C73C2×#3182semidirect
448. #440C2×D73semidirect
639. C2×C8#11924028semidirect
739. C8C2×#11924028semidirect
773. C2#22620646direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891412
C2×#179891342
#226206462
C2×#179889912
C2×#179889582
C2×#179889362
C2×#179889322
C2×#179888362
C2×#179888342
C2×#179888322
C2×#179888302
C2×#179886892
C2×#179886872
C2×#179886852
C2×#179885392
C2×#440×C732
C2×#318273