Finite Group Databasebeta

← C2×#22620042 #33954166

Subgroups — C2×#22620042 #33954166

Order 18688.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989121C211yesmaximal, characteristic, complemented
2C2×C4×#11924028C211yesmaximal, characteristic, complemented
3#22620042C2116yesmaximal, direct product factor
4C2×#17988929C211yesmaximal, characteristic, complemented
5C2×#17988912C211yesmaximal, characteristic, complemented
6C2×#17988895C211yesmaximal, characteristic, complemented
7C2×#17988888C211yesmaximal, characteristic, complemented
8C2×#17988810C211yesmaximal, characteristic, complemented
9C2×#17988803C211yesmaximal, characteristic, complemented
10C2×#17988751C211yesmaximal, characteristic, complemented
11C2×#17988734C211yesmaximal, characteristic
12C2×#17988700C211yesmaximal, characteristic, complemented
13C2×#17988695C211yesmaximal, characteristic, complemented
14C2×#17988689C211yesmaximal, characteristic, complemented
15C2×#17988689C211yesmaximal, characteristic, complemented
16C2×#432×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C22×Dic292C2211yescharacteristic
19C22×#11924017C2211yescharacteristic
20C22×#11924017C2211yescharacteristic
21C22×D584C2211yescharacteristic
22#17989121—24no—
23#17989121C2218yescomplemented
24C2×#14556585—21no—
25C2×#14556583C2211yescharacteristic
26C2×#14556579C2211yescharacteristic
27C2×#14556574—21no—
28C2×#14556570C2211yescharacteristic
29C2×#14556565C2211yescharacteristic
30C4×#11924028—24no—
31C4×#11924028C2218yescomplemented
32C2×C4×Dic146C2211yescharacteristic
33C2×C4×Dic146C2211yescharacteristic
34C2×C4×Dic146C2211yescharacteristic
35C2×C4×D292C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×C4×D292C2211yescharacteristic
38C2×C4×C22⋊D73—21no—
39C2×C4×C22⋊D73—21no—
40C2×C4×C22⋊D73—21no—
41C2×#14556550C2211yescharacteristic
42C2×#14556548—21no—
43C2×#14556548—21no—
44C2×C42×D73—21no—
45#17988929C2218yescomplemented
46#17988912C2218yescomplemented
47#17988895C2218yescomplemented
48#17988888C2218yescomplemented
49#17988810C2218yescomplemented
50#17988803C2218yescomplemented
51#17988751C2218yescomplemented
52#17988734C2218yes—
53#17988700C2218yescomplemented
54#17988695C2218yescomplemented
55#17988689C2218yescomplemented
56#17988689C2218yescomplemented
57C2×#14556525C2211yescharacteristic
58C2×#14556525C2211yescharacteristic
59C2×#14556523C2211yescharacteristic
60C2×#14556523C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556513C2211yescharacteristic
67C2×#14556513C2211yescharacteristic
68C2×#14556513C2211yescharacteristic
69C22×C42×C73C2211yescharacteristic
70#432×C73C2218yescomplemented
71C2×C4⋊C8×C73C2211yescharacteristic
72C2×C4⋊C8×C73C2211yescharacteristic
73C2×C22⋊C8×C73C2211yescharacteristic
74C2×C22⋊C8×C73C2211yescharacteristic
75C2×#97×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C2×#11924028—24no—
78C2×#11924028—24no—
79C2×#11924028—22no—
80C2×#11924028C2314yes—
81C22×Dic146C2311yescharacteristic
82C22×Dic146C2311yescharacteristic
83C22×D292C2311yescharacteristic
84C22×D292C2311yescharacteristic
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73—21no—
89C22×C4×D73—21no—
90C22×C4×D73—21no—
91C2×Dic292—24no—
92C2×Dic292C2314yes—
93C2×#11924017—24no—
94C2×#11924017—24no—
95C2×#11924017C2314yes—
96C2×#11924017C2314yes—
97C2×D584—24no—
98C2×D584C2314yes—
99#14556585—28no—
100#14556583—22no—
101#14556583C2314yes—
102#14556579—22no—
103#14556579C2314yes—
104#14556574—28no—
105#14556570—22no—
106#14556570C2314yes—
107#14556565—22no—
108#14556565C2314yes—
109C4×Dic146—22no—
110C4×Dic146—22no—
111C4×Dic146—22no—
112C4×Dic146C2314yes—
113C4×Dic146C2314yes—
114C4×Dic146C2314yes—
115C4×D292—22no—
116C4×D292—22no—
117C4×D292—22no—
118C4×D292C2314yes—
119C4×D292C2314yes—
120C4×D292C2314yes—
121C4×C22⋊D73—28no—
122C4×C22⋊D73—28no—
123C4×C22⋊D73—28no—
124#14556550—22no—
125#14556550C2314yes—
126#14556548—28no—
127#14556548—28no—
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×C22⋊Dic73—21no—
139C2×C22⋊Dic73—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005—21no—
146C2×C4×Dic73—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73—21no—
149C2×C4×Dic73—21no—
150C42×D73—28no—
151#14556525C2314yes—
152#14556525C2314yes—
153#14556523C2314yes—
154#14556523C2314yes—
155#14556516C2314yes—
156#14556516C2314yes—
157#14556516C2314yes—
158#14556516C2314yes—
159#14556513C2314yes—
160#14556513C2314yes—
161#14556513C2314yes—
162#14556513C2314yes—
163C23×C4×C73D411yescharacteristic
164C23×C4×C73D411yescharacteristic
165C23×C4×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169C22×C8×C73C2311yescharacteristic
170C2×C42×C73D414yes—
171C2×C42×C73D411yescharacteristic
172C2×C42×C73D411yescharacteristic
173C2×C42×C73C2314yes—
174C2×C42×C73C2311yescharacteristic
175C2×C42×C73C2311yescharacteristic
176C4⋊C8×C73C2314yes—
177C4⋊C8×C73C2314yes—
178C22⋊C8×C73C2314yes—
179C22⋊C8×C73C2314yes—
180#97×C73C2314yes—
181#97×C73C2314yes—
182C23×D73—21no—
183C23×D73—21no—
184#11924028—216no—
185#11924028—28no—
186#11924028—28no—
187C2×Dic146—21no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—21no—
192C2×Dic146#4114yes—
193C2×Dic146C2412yes—
194C2×Dic146C2412yes—
195C2×D292—21no—
196C2×D292—22no—
197C2×D292—22no—
198C2×D292—22no—
199C2×D292—21no—
200C2×D292#4114yes—
201C2×D292C2412yes—
202C2×D292C2412yes—
203C2×C22⋊D73—28no—
204C2×C22⋊D73—24no—
205C2×C22⋊D73—24no—
206C2×C22⋊D73—44no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73—21no—
213C2×C4×D73—28no—
214C2×C4×D73—24no—
215C2×C4×D73—24no—
216C2×C4×D73—24no—
217C2×C4×D73—24no—
218C2×C4×D73—44no—
219C2×C4×D73—44no—
220C2×C4×D73—44no—
221Dic292—28no—
222#11924017—28no—
223#11924017—28no—
224D584—28no—
225C4⋊Dic73—21no—
226C4⋊Dic73—21no—
227C4⋊Dic73—21no—
228C4⋊Dic73—21no—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231C4⋊Dic73C2412yes—
232C4⋊Dic73C2412yes—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236#11924007—24no—
237#11924007—24no—
238#11924007—24no—
239C22⋊Dic73—24no—
240C22⋊Dic73—24no—
241#11924005—24no—
242#11924005—24no—
243#11924005—24no—
244#11924005—24no—
245#11924005—24no—
246#11924005—24no—
247C4×Dic73—24no—
248C4×Dic73—24no—
249C4×Dic73—24no—
250C4×Dic73—24no—
251C24×C73C2×D411yescharacteristic
252C22×C4×C73—22no—
253C22×C4×C73—22no—
254C22×C4×C73—42no—
255C22×C4×C73—42no—
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D412yes—
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2×D414yes—
263C22×C4×C73C2×D414yes—
264C22×C4×C73C2412yes—
265C22×C4×C73C2411yescharacteristic
266C2×C8×C73—22no—
267C2×C8×C73—22no—
268C2×C8×C73—22no—
269C2×C8×C73—22no—
270C2×C8×C73C2412yes—
271C2×C8×C73C2412yes—
272C2×C8×C73C2412yes—
273C2×C8×C73C2412yes—
274C42×C73C2×D414yes—
275C42×C73C2×D414yes—
276C42×C73C2×D412yes—
277C42×C73C2×D412yes—
278C42×C73C2412yes—
279C42×C73C2412yes—
280C23×C73—22no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73C22×D412yes—
284C23×C73C22×D411yescharacteristic
285C22×D73—24no—
286C22×D73—22no—
287C22×D73—22no—
288C22×D73—42no—
289C22×D73—42no—
290C22×D73—42no—
291C22×D73—42no—
292C22×D73—42no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—24no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—44no—
302C2×C4×C73—44no—
303C2×C4×C73C22×D412yes—
304C2×C4×C73C22×D412yes—
305C2×C4×C73C22×D412yes—
306C2×C4×C73C22×D412yes—
307C2×C4×C73C22×D412yes—
308C2×C4×C73C22×D411yescharacteristic
309C2×C4×C73C2×#4112yes—
310C2×C4×C73C2×#4112yes—
311C2×C4×C73C2511yescharacteristic
312C22⋊D73—216no—
313C22⋊D73—48no—
314C2×Dic73—24no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—42no—
322C2×Dic73—42no—
323C2×Dic73—42no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326D292—24no—
327D292—22no—
328D292—22no—
329D292—22no—
330D292—42no—
331D292C2×#4114yes—
332C4×D73—216no—
333C4×D73—48no—
334C4×D73—48no—
335C4×D73—48no—
336Dic146—24no—
337Dic146—22no—
338Dic146—22no—
339Dic146—22no—
340Dic146—42no—
341Dic146C2×#4114yes—
342C8×C73—22no—
343C8×C73—22no—
344C8×C73—22no—
345C8×C73—22no—
346C22×C73—22no—
347C22×C73—22no—
348C22×C73—22no—
349C22×C73—44no—
350C22×C73#52512yes—
351C22×C73#57512yes—
352C22×C73#57512yes—
353C22×C73C23×D411yescharacteristic
354C2×D73—24no—
355C2×D73—48no—
356C2×D73—42no—
357C2×D73—42no—
358C2×D73—42no—
359C2×D73—42no—
360C2×D73—42no—
361C2×D73—84no—
362C4×C73—22no—
363C4×C73—22no—
364C4×C73—22no—
365C4×C73—22no—
366C4×C73—22no—
367C4×C73#52512yes—
368C4×C73C22×#4111yescharacteristic
369C4×C73C22×#4111yescharacteristic
370Dic73—24no—
371Dic73—42no—
372Dic73—42no—
373Dic73—42no—
374Dic73—42no—
375Dic73—42no—
376C2×#3111—731nomaximal, Sylow
377C2×C73—42no—
378C2×C73#311114yescomplemented
379C2×C73C2×#52511yescharacteristic
380C2×C73C2×#57511yescharacteristic
381C2×C73C2×#57511yescharacteristic
382D73—44no—
383D73—82no—
384C2×#529—731no—
385C2×C4×#41—731no—
386#3111—7316no—
387C2×#485—731no—
388C2×#482—731no—
389C2×#479—731no—
390C2×#478—731no—
391C2×#464—731no—
392C2×#463—731no—
393C2×#452—731no—
394C2×#449—731no—
395C2×#442—731no—
396C2×#441—731no—
397C2×#440—731no—
398C2×#440—731no—
399C2×#432D7311yescharacteristic, complemented
400C73C2×#311111yescharacteristic, complemented, Sylow
401C22×#41—731no—
402C22×Q16—731no—
403C22×SD16—731no—
404C22×SD16—731no—
405C22×D8—731no—
406#529—738no—
407#529—1464no—
408C2×#126—1461no—
409C2×#125—731no—
410C2×#124—731no—
411C2×#123—1461no—
412C2×C22⋊Q8—731no—
413C2×#121—731no—
414C4×#41—738no—
415C4×#41—1464no—
416C2×C4×Q8—731no—
417C2×C4×Q8—731no—
418C2×C4×Q8—731no—
419C2×C4×D4—731no—
420C2×C4×D4—731no—
421C2×C4×D4—731no—
422C2×C4×D4—1461no—
423C2×C4×D4—1461no—
424C2×C4×D4—1461no—
425C2×#117—731no—
426C2×#117—1461no—
427C2×#117—1461no—
428C22×C42—1461no—
429C22×C42C2×D7311yescharacteristic
430#485—738no—
431#482—738no—
432#479—738no—
433#478—738no—
434#464—738no—
435#463—738no—
436#452—738no—
437#449—738no—
438#442—738no—
439#441—738no—
440#440—738no—
441#440—738no—
442#432C2×D7318yescomplemented
443C2×#107—731no—
444C2×#107—731no—
445C2×#106—731no—
446C2×#106—731no—
447C2×C4⋊C8C2×D7311yescharacteristic
448C2×C4⋊C8C2×D7311yescharacteristic
449C2×#103—731no—
450C2×#103—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#102—731no—
454C2×#102—731no—
455C2×#102—731no—
456C2×#102—731no—
457C2×C22⋊C8C2×D7311yescharacteristic
458C2×C22⋊C8C2×D7311yescharacteristic
459C2×#97C2×D7311yescharacteristic
460C2×#97C2×D7311yescharacteristic
461C2×#41—734no—
462C2×#41—1464no—
463C2×#41—1464no—
464C2×#41—1462no—
465C22×Q8—731no—
466C22×Q8—731no—
467C22×D4—731no—
468C22×D4—731no—
469C22×D4—1461no—
470C22×D4—1461no—
471C23×C4—1461no—
472C23×C4—1461no—
473C23×C4—1461no—
474C23×C4—1461no—
475C23×C4D29211yescharacteristic
476C23×C4D29211yescharacteristic
477C23×C4C22×D7311yescharacteristic
478C2×Q16—734no—
479C2×Q16—1464no—
480C2×SD16—734no—
481C2×SD16—734no—
482C2×SD16—1464no—
483C2×SD16—1464no—
484C2×D8—734no—
485C2×D8—1464no—
486C22×C8C22×D7311yescharacteristic
487C22×C8C22×D7311yescharacteristic
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490#126—1468no—
491#125—734no—
492#125—1462no—
493#124—734no—
494#124—1462no—
495#123—1468no—
496C22⋊Q8—734no—
497C22⋊Q8—1462no—
498#121—734no—
499#121—1462no—
500C4×Q8—734no—
501C4×Q8—734no—
502C4×Q8—734no—
503C4×Q8—1462no—
504C4×Q8—1462no—
505C4×Q8—1462no—
506C4×D4—734no—
507C4×D4—734no—
508C4×D4—734no—
509C4×D4—1468no—
510C4×D4—1468no—
511C4×D4—1468no—
512C4×D4—1462no—
513C4×D4—1462no—
514C4×D4—1462no—
515#117—734no—
516#117—1462no—
517#117—1468no—
518#117—1468no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C22⋊C4—1461no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
537C2×C42—1461no—
538C2×C42—1461no—
539C2×C42—1461no—
540C2×C42—1461no—
541C2×C42—1468no—
542C2×C42D29211yescharacteristic
543C2×C42D29214yes—
544C2×C42D29211yescharacteristic
545C2×C42C22×D7311yescharacteristic
546C2×C42C22×D7311yescharacteristic
547C2×C42C22×D7314yes—
548#107—734no—
549#107—734no—
550#106—734no—
551#106—734no—
552C4⋊C8C22×D7314yes—
553C4⋊C8C22×D7314yes—
554#103—734no—
555#103—734no—
556#103—734no—
557#103—734no—
558#102—734no—
559#102—734no—
560#102—734no—
561#102—734no—
562C22⋊C8C22×D7314yes—
563C22⋊C8C22×D7314yes—
564#97C22×D7314yes—
565#97C22×D7314yes—
566C24—1461no—
567C24—1461no—
568C24C2×D29211yescharacteristic
569#41—1468no—
570#41—1468no—
571#41—14616no—
572C2×Q8—734no—
573C2×Q8—732no—
574C2×Q8—732no—
575C2×Q8—1462no—
576C2×Q8—1462no—
577C2×Q8—1461no—
578C2×Q8—1461no—
579C2×Q8—1462no—
580C2×D4—2924no—
581C2×D4—734no—
582C2×D4—732no—
583C2×D4—732no—
584C2×D4—1464no—
585C2×D4—1468no—
586C2×D4—1464no—
587C2×D4—1461no—
588C2×D4—1461no—
589C2×D4—1462no—
590C2×D4—1462no—
591C2×D4—1462no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—2924no—
597C22×C4—2924no—
598C22×C4—2924no—
599C22×C4—1468no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1461no—
604C22×C4—1461no—
605C22×C4—1464no—
606C22×C4—1464no—
607C22×C4—1464no—
608C22×C4—1461no—
609C22×C4—1464no—
610C22×C4C2×D29212yes—
611C22×C4C2×D29211yescharacteristic
612C22×C4C2×D29211yescharacteristic
613C22×C4C2×D29211yescharacteristic
614C22×C4C2×D29211yescharacteristic
615C22×C4C2×D29211yescharacteristic
616C22×C4C2×D29214yes—
617C22×C4C2×D29214yes—
618C22×C4C23×D7312yes—
619C22×C4C23×D7311yescharacteristic
620Q16—1468no—
621SD16—1468no—
622SD16—1468no—
623D8—1468no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×D7312yes—
629C2×C8C23×D7312yes—
630C2×C8C23×D7312yes—
631C2×C8C23×D7312yes—
632C4⋊C4—732no—
633C4⋊C4—732no—
634C4⋊C4—732no—
635C4⋊C4—732no—
636C4⋊C4—1464no—
637C4⋊C4—1464no—
638C4⋊C4—1464no—
639C4⋊C4—1464no—
640C4⋊C4—1464no—
641C4⋊C4—1464no—
642C4⋊C4—1461no—
643C4⋊C4—1461no—
644C4⋊C4—1461no—
645C4⋊C4—1461no—
646C22⋊C4—1464no—
647C22⋊C4—1464no—
648C22⋊C4—1464no—
649C22⋊C4—1464no—
650C22⋊C4—1464no—
651C22⋊C4—1464no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C42—1464no—
655C42—1464no—
656C42—1464no—
657C42—1464no—
658C42C2×D29214yes—
659C42C2×D29214yes—
660C42C2×D29212yes—
661C42C2×D29212yes—
662C42C23×D7312yes—
663C42C23×D7312yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—2922no—
668C23—2922no—
669C23—2922no—
670C23—2922no—
671C23—2922no—
672C23—1462no—
673C23—1462no—
674C23—1464no—
675C23C22×D29212yes—
676C23C22×D29211yescharacteristic
677Q8—2922no—
678Q8—734no—
679Q8—1462no—
680Q8—1462no—
681Q8—1462no—
682Q8—1464no—
683D4—2928no—
684D4—2922no—
685D4—734no—
686D4—14616no—
687D4—1462no—
688D4—1462no—
689D4—1462no—
690D4—1464no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—2928no—
702C2×C4—2928no—
703C2×C4—2928no—
704C2×C4—2922no—
705C2×C4—2922no—
706C2×C4—2922no—
707C2×C4—2922no—
708C2×C4—2922no—
709C2×C4—14616no—
710C2×C4—1462no—
711C2×C4—1462no—
712C2×C4—1462no—
713C2×C4—1462no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1464no—
717C2×C4C22×D29212yes—
718C2×C4C22×D29212yes—
719C2×C4C22×D29212yes—
720C2×C4C22×D29212yes—
721C2×C4C22×D29212yes—
722C2×C4C22×D29211yescharacteristic
723C2×C4#41×D7312yes—
724C2×C4#41×D7312yes—
725C2×C4C24×D7311yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—2928no—
735C22—2922no—
736C22—2922no—
737C22—2922no—
738C22—2922no—
739C22—2922no—
740C22—5844no—
741C22—1464no—
742C22#1798909912yes—
743C22#1798938712yes—
744C22#1798938712yes—
745C22C23×D29211yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—2922no—
752C4—2922no—
753C4—2922no—
754C4—2922no—
755C4—2922no—
756C4—1464no—
757C4#1798909912yes—
758C4C2×#41×D7311yescharacteristic
759C4C2×#41×D7311yescharacteristic
760C2—42no—
761C2—2924no—
762C2—5842no—
763C2#2262004214yesdirect product factor
764C2C2×#1798909911yescharacteristic
765C2C2×#1798938711yescharacteristic
766C2C2×#1798938711yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#432×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988734C2
hypercenterC2×#432D73
hypocenterC73C2×#3111
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#17989121C2semidirect
2. C2×C4×#11924028C2semidirect
3. #22620042C2direct (N × H)
4. C2×#17988929C2semidirect
5. C2×#17988912C2semidirect
6. C2×#17988895C2semidirect
7. C2×#17988888C2semidirect
8. C2×#17988810C2semidirect
9. C2×#17988803C2semidirect
10. C2×#17988751C2semidirect
12. C2×#17988700C2semidirect
13. C2×#17988695C2semidirect
14. C2×#17988689C2semidirect
15. C2×#17988689C2semidirect
16. C2×#432×C73C2semidirect
23. #17989121C22semidirect
31. C4×#11924028C22semidirect
45. #17988929C22semidirect
46. #17988912C22semidirect
47. #17988895C22semidirect
48. #17988888C22semidirect
49. #17988810C22semidirect
50. #17988803C22semidirect
51. #17988751C22semidirect
53. #17988700C22semidirect
54. #17988695C22semidirect
55. #17988689C22semidirect
56. #17988689C22semidirect
70. #432×C73C22semidirect
378. C2×C73#3111semidirect
399. C2×#432D73semidirect
400. C73C2×#3111semidirect
442. #432C2×D73semidirect
763. C2#22620042direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891212
C2×C4×#119240282
#226200422
C2×#179889292
C2×#179889122
C2×#179888952
C2×#179888882
C2×#179888102
C2×#179888032
C2×#179887512
C2×#179887342
C2×#179887002
C2×#179886952
C2×#179886892
C2×#432×C732
C2×#311173