Finite Group Databasebeta

← C2×#22621990 #33962711

Subgroups — C2×#22621990 #33962711

Order 18688.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989308C211yesmaximal, characteristic, complemented
2C2×#17989248C211yesmaximal, characteristic
3#22621990C2116yesmaximal, direct product factor
4C2×#17988948C211yesmaximal, characteristic, complemented
5C2×#17988926C211yesmaximal, characteristic, complemented
6C2×#17988912C211yesmaximal, characteristic, complemented
7C2×#17988880C211yesmaximal, characteristic, complemented
8C2×#17988835C211yesmaximal, characteristic, complemented
9C2×#17988825C211yesmaximal, characteristic, complemented
10C2×#17988811C211yesmaximal, characteristic, complemented
11C2×#17988748C211yesmaximal, characteristic, complemented
12C2×#17988694C211yesmaximal, characteristic, complemented
13C2×#17988661C211yesmaximal, characteristic, complemented
14C2×#17988596C211yesmaximal, characteristic, complemented
15C2×#17988582C211yesmaximal, characteristic, complemented
16C2×#451×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19C22×#11924012C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21#17989308—24no—
22#17989308C2218yescomplemented
23#17989248—24no—
24#17989248C2218yes—
25C2×#14556590C2211yescharacteristic
26C2×#14556586—21no—
27C2×#14556584—21no—
28C2×#14556580—21no—
29C2×#14556580C2211yescharacteristic
30C2×#14556577—21no—
31C2×#14556567—21no—
32C2×#14556567C2211yescharacteristic
33C2×#14556567C2211yescharacteristic
34C2×#14556565—21no—
35C2×#14556565C2211yescharacteristic
36C2×Q8×Dic73C2211yescharacteristic
37C2×Q8×Dic73C2211yescharacteristic
38C2×#14556556—21no—
39C2×C4×C22⋊D73—21no—
40C2×C4×C22⋊D73C2211yescharacteristic
41C2×#14556550C2211yescharacteristic
42C2×#14556549C2211yescharacteristic
43#17988948C2218yescomplemented
44#17988926C2218yescomplemented
45#17988912C2218yescomplemented
46#17988880C2218yescomplemented
47#17988835C2218yescomplemented
48#17988825C2218yescomplemented
49#17988811C2218yescomplemented
50#17988748C2218yescomplemented
51#17988694C2218yescomplemented
52#17988661C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556524C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57#17988596C2218yescomplemented
58#17988582C2218yescomplemented
59C2×#14556515C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C23×Q8×C73C2211yescharacteristic
70C22×Q16×C73C2211yescharacteristic
71C22×Q16×C73C2211yescharacteristic
72C2×C22⋊Q8×C73C2211yescharacteristic
73#451×C73C2218yescomplemented
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C2×#11924029—22no—
78C2×#11924029—24no—
79C2×#11924029—42no—
80C2×#11924029C2314yes—
81C22×Dic146—21no—
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×C22⋊D73—21no—
85C22×C22⋊D73D411yescharacteristic
86C22×C4×D73—21no—
87C22×C4×D73C2311yescharacteristic
88C2×#11924015—42no—
89C2×#11924015C2314yes—
90C2×#11924012—42no—
91C2×#11924012C2314yes—
92C22×#10596831C2311yescharacteristic
93C22×#10596831C2311yescharacteristic
94C2×C8×D73—42no—
95C2×C8×D73C2314yes—
96#14556590—22no—
97#14556590C2314yes—
98#14556586—28no—
99#14556584—28no—
100#14556580—28no—
101#14556580—22no—
102#14556580C2314yes—
103#14556577—28no—
104#14556567—22no—
105#14556567—22no—
106#14556567—28no—
107#14556567C2314yes—
108#14556567C2314yes—
109#14556565—28no—
110#14556565—22no—
111#14556565C2314yes—
112Q8×Dic73—22no—
113Q8×Dic73—22no—
114Q8×Dic73C2314yes—
115Q8×Dic73C2314yes—
116#14556556—28no—
117C4×C22⋊D73—28no—
118C4×C22⋊D73D414yes—
119C4×C22⋊D73C2314yes—
120#14556550—22no—
121#14556550C2314yes—
122#14556549—22no—
123#14556549C2314yes—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007D411yescharacteristic
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73D411yescharacteristic
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005D411yescharacteristic
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yes—
148#14556524C2314yes—
149#14556523C2314yes—
150#14556520C2314yes—
151#14556515C2314yes—
152#14556515C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556515C2314yes—
156#14556513C2314yes—
157#14556513C2314yes—
158#14556511C2314yes—
159#14556503C2314yes—
160#14556501C2314yes—
161C22×Q8×C73—22no—
162C22×Q8×C73—21no—
163C22×Q8×C73—24no—
164C22×Q8×C73—42no—
165C22×Q8×C73C2311yescharacteristic
166C22×Q8×C73C2311yescharacteristic
167C22×Q8×C73C2314yes—
168C22×Q8×C73C2311yescharacteristic
169C23×C4×C73—21no—
170C23×C4×C73C2311yescharacteristic
171C2×Q16×C73—24no—
172C2×Q16×C73—42no—
173C2×Q16×C73C2314yes—
174C2×Q16×C73C2314yes—
175C22×C8×C73C2311yescharacteristic
176C22×C8×C73C2311yescharacteristic
177C22⋊Q8×C73—22no—
178C22⋊Q8×C73C2314yes—
179C2×C4⋊C4×C73—21no—
180C2×C4⋊C4×C73C2311yescharacteristic
181C2×C22⋊C4×C73—21no—
182#103×C73C2314yes—
183#103×C73C2314yes—
184C22⋊C8×C73C2314yes—
185C23×D73—21no—
186C23×D73C2×D411yescharacteristic
187#11924029—28no—
188#11924029—44no—
189#11924029—48no—
190C2×Dic146—24no—
191C2×Dic146—44no—
192C2×D292—22no—
193C2×D292—22no—
194C2×D292—24no—
195C2×D292—21no—
196C2×D292—44no—
197C2×D292C2412yes—
198C2×C22⋊D73—24no—
199C2×C22⋊D73—42no—
200C2×C22⋊D73—44no—
201C2×C22⋊D73C2×D414yes—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C22×Dic73C2×D411yescharacteristic
208C2×C4×D73—22no—
209C2×C4×D73—22no—
210C2×C4×D73—24no—
211C2×C4×D73—44no—
212C2×C4×D73C2×D412yes—
213C2×C4×D73C2412yes—
214#11924015—44no—
215#11924012—44no—
216C2×#10596831—22no—
217C2×#10596831—22no—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C8×D73—44no—
221C4⋊Dic73—21no—
222C4⋊Dic73—21no—
223C4⋊Dic73—21no—
224C4⋊Dic73—24no—
225C4⋊Dic73—24no—
226C4⋊Dic73C2412yes—
227C4⋊Dic73C2412yes—
228C4⋊Dic73C2412yes—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007C2×D414yes—
233C22⋊Dic73—24no—
234C22⋊Dic73C2×D414yes—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005C2×D414yes—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C4×Dic73—24no—
246C4×Dic73C2×D412yes—
247C4×Dic73C2412yes—
248C24×C73C2×D411yescharacteristic
249C2×Q8×C73—21no—
250C2×Q8×C73—21no—
251C2×Q8×C73—24no—
252C2×Q8×C73—21no—
253C2×Q8×C73—22no—
254C2×Q8×C73—28no—
255C2×Q8×C73—22no—
256C2×Q8×C73—22no—
257C2×Q8×C73—22no—
258C2×Q8×C73—22no—
259C2×Q8×C73—44no—
260C2×Q8×C73—44no—
261C2×Q8×C73—48no—
262C2×Q8×C73#4114yes—
263C2×Q8×C73C2412yes—
264C2×Q8×C73C2412yes—
265C2×Q8×C73C2412yes—
266C22×C4×C73—21no—
267C22×C4×C73—22no—
268C22×C4×C73—22no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—24no—
273C22×C4×C73—44no—
274C22×C4×C73C2×D411yescharacteristic
275C22×C4×C73C2×D412yes—
276C22×C4×C73C2412yes—
277C22×C4×C73C2411yescharacteristic
278Q16×C73—28no—
279Q16×C73—44no—
280C2×C8×C73—22no—
281C2×C8×C73—22no—
282C2×C8×C73C2412yes—
283C2×C8×C73C2412yes—
284C4⋊C4×C73—24no—
285C4⋊C4×C73—21no—
286C4⋊C4×C73C2412yes—
287C22⋊C4×C73—24no—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73C22×D412yes—
292C23×C73C22×D411yescharacteristic
293C22×D73—22no—
294C22×D73—22no—
295C22×D73—22no—
296C22×D73—22no—
297C22×D73—42no—
298C22×D73—42no—
299C22×D73—42no—
300C22×D73C22×D412yes—
301Q8×C73—24no—
302Q8×C73—22no—
303Q8×C73—22no—
304Q8×C73—22no—
305Q8×C73—22no—
306Q8×C73—22no—
307Q8×C73—48no—
308Q8×C73—42no—
309Q8×C73—42no—
310Q8×C73C2×#4114yes—
311C2×C4×C73—22no—
312C2×C4×C73—24no—
313C2×C4×C73—22no—
314C2×C4×C73—24no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—48no—
321C2×C4×C73—42no—
322C2×C4×C73—42no—
323C2×C4×C73—42no—
324C2×C4×C73C22×D412yes—
325C2×C4×C73C22×D411yescharacteristic
326C2×C4×C73C2×#4112yes—
327C2×C4×C73H(5,𝔽2)12yes—
328C2×C4×C73C2511yescharacteristic
329C22⋊D73—44no—
330C22⋊D73—48no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—42no—
338C2×Dic73—42no—
339C2×Dic73—42no—
340C2×Dic73C22×D412yes—
341C2×Dic73C22×D412yes—
342C2×Dic73C22×D412yes—
343D292—22no—
344D292—22no—
345D292—48no—
346D292—42no—
347C4×D73—24no—
348C4×D73—22no—
349C4×D73—22no—
350C4×D73—48no—
351Dic146—48no—
352C8×C73—22no—
353C8×C73—22no—
354#10596831—22no—
355#10596831—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—44no—
360C22×C73#54612yes—
361C22×C73#57512yes—
362C22×C73#57812yes—
363C22×C73C23×D411yescharacteristic
364C2×D73—22no—
365C2×D73—22no—
366C2×D73—22no—
367C2×D73—44no—
368C2×D73—42no—
369C2×D73—42no—
370C2×D73—42no—
371C2×D73—84no—
372C4×C73—24no—
373C4×C73—22no—
374C4×C73—42no—
375C4×C73—42no—
376C4×C73—42no—
377C4×C73#54612yes—
378C4×C73C22×#4111yescharacteristic
379C4×C73C2×H(5,𝔽2)11yescharacteristic
380Dic73—22no—
381Dic73—22no—
382Dic73—22no—
383Dic73—42no—
384Dic73—42no—
385Dic73—42no—
386C2×#3313—731nomaximal, Sylow
387C2×C73—42no—
388C2×C73#331314yescomplemented
389C2×C73C2×#54611yescharacteristic
390C2×C73C2×#57511yescharacteristic
391C2×C73C2×#57811yescharacteristic
392D73—42no—
393D73—82no—
394C2×#556—731no—
395C2×#548—731no—
396#3313—7316no—
397C2×#489—731no—
398C2×#485—731no—
399C2×#482—731no—
400C2×#477—731no—
401C2×#468—731no—
402C2×#467—731no—
403C2×#464—731no—
404C2×#452—731no—
405C2×#451D7311yescharacteristic, complemented
406C2×#441—731no—
407C2×#435—731no—
408C2×#419—731no—
409C2×#416—731no—
410C73C2×#331311yescharacteristic, complemented, Sylow
411C22×#41—731no—
412C23×Q8C2×D7311yescharacteristic
413C22×Q16C2×D7311yescharacteristic
414C22×Q16C2×D7311yescharacteristic
415C22×SD16—731no—
416C22×M16—731no—
417C23×C8—731no—
418#556—738no—
419#556—1464no—
420#548—738no—
421#548—1464no—
422C2×C4⋊Q8—731no—
423C2×#126—1461no—
424C2×#126—1461no—
425C2×#124—731no—
426C2×#124—1461no—
427C2×#124—1461no—
428C2×C22⋊Q8—731no—
429C2×C22⋊Q8—731no—
430C2×C22⋊Q8—1461no—
431C2×C22⋊Q8C2×D7311yescharacteristic
432C2×#121—731no—
433C2×#121—1461no—
434C2×C4×Q8—731no—
435C2×C4×Q8—731no—
436C2×C4×Q8—1461no—
437C2×C4×D4—731no—
438C2×C4×D4—1461no—
439C2×#117—731no—
440C2×#117—731no—
441#489—738no—
442#485—738no—
443#482—738no—
444#477—738no—
445#468—738no—
446#467—738no—
447#464—738no—
448#452—738no—
449#451C2×D7318yescomplemented
450#441—738no—
451#435—738no—
452C2×#107—731no—
453C2×#107—731no—
454C2×#106—731no—
455C2×C4⋊C8—731no—
456#419—738no—
457#416—738no—
458C2×#103—731no—
459C2×#103—731no—
460C2×#103—731no—
461C2×#103—731no—
462C2×#103—731no—
463C2×#103C2×D7311yescharacteristic
464C2×#103C2×D7311yescharacteristic
465C2×#102—731no—
466C2×#102—731no—
467C2×#102—731no—
468C2×C22⋊C8—731no—
469C2×C22⋊C8C2×D7311yescharacteristic
470C2×#97—731no—
471C2×#41—2922no—
472C2×#41—734no—
473C2×#41—1464no—
474C2×#41—1462no—
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—1461no—
480C22×Q8C22×D7311yescharacteristic
481C22×Q8C22×D7311yescharacteristic
482C22×Q8C22×D7314yes—
483C22×Q8C22×D7311yescharacteristic
484C22×D4—731no—
485C22×D4—731no—
486C22×D4—1461no—
487C22×D4—1461no—
488C23×C4—21no—
489C23×C4—731no—
490C23×C4—1461no—
491C23×C4C22×D7311yescharacteristic
492C2×Q16—24no—
493C2×Q16—42no—
494C2×Q16C22×D7314yes—
495C2×Q16C22×D7314yes—
496C2×SD16—2922no—
497C2×SD16—734no—
498C2×M16—2922no—
499C2×M16—734no—
500C22×C8—2922no—
501C22×C8—734no—
502C22×C8—731no—
503C22×C8—731no—
504C22×C8C22×D7311yescharacteristic
505C22×C8C22×D7311yescharacteristic
506C4⋊Q8—734no—
507C4⋊Q8—1462no—
508#126—1468no—
509#126—1468no—
510#124—734no—
511#124—1462no—
512#124—1468no—
513#124—1468no—
514C22⋊Q8—22no—
515C22⋊Q8—734no—
516C22⋊Q8—734no—
517C22⋊Q8—1468no—
518C22⋊Q8—1462no—
519C22⋊Q8—1462no—
520C22⋊Q8C22×D7314yes—
521#121—734no—
522#121—1468no—
523#121—1462no—
524C4×Q8—734no—
525C4×Q8—734no—
526C4×Q8—1462no—
527C4×Q8—1462no—
528C4×Q8—1468no—
529C4×D4—734no—
530C4×D4—734no—
531C4×D4—1468no—
532#117—734no—
533#117—734no—
534#117—1462no—
535#117—1462no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—731no—
538C2×C4⋊C4—731no—
539C2×C4⋊C4—731no—
540C2×C4⋊C4—731no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4—1461no—
543C2×C4⋊C4—1461no—
544C2×C4⋊C4—1461no—
545C2×C4⋊C4—1461no—
546C2×C4⋊C4C22×D7311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—731no—
549C2×C22⋊C4—731no—
550C2×C22⋊C4—1461no—
551C2×C22⋊C4—1461no—
552C2×C22⋊C4—1461no—
553C2×C22⋊C4—1461no—
554C2×C22⋊C4—1461no—
555C2×C22⋊C4—1461no—
556C2×C22⋊C4—1461no—
557C2×C42—731no—
558C2×C42—1461no—
559C2×C42—1461no—
560C2×C42—1461no—
561C2×C42—1461no—
562#107—734no—
563#107—734no—
564#106—734no—
565C4⋊C8—734no—
566#103—734no—
567#103—734no—
568#103—734no—
569#103—734no—
570#103—734no—
571#103C22×D7314yes—
572#103C22×D7314yes—
573#102—734no—
574#102—734no—
575#102—734no—
576C22⋊C8—734no—
577C22⋊C8C22×D7314yes—
578#97—734no—
579C24—731no—
580C24—1461no—
581C24D4×D7311yescharacteristic
582#41—2928no—
583#41—2924no—
584#41—1468no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—28no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—44no—
596C2×Q8—44no—
597C2×Q8—48no—
598C2×Q8—2924no—
599C2×Q8—1464no—
600C2×Q8#1192402714yes—
601C2×Q8C23×D7312yes—
602C2×Q8C23×D7312yes—
603C2×Q8C23×D7312yes—
604C2×D4—2924no—
605C2×D4—2924no—
606C2×D4—2922no—
607C2×D4—734no—
608C2×D4—732no—
609C2×D4—1464no—
610C2×D4—1464no—
611C2×D4—1461no—
612C2×D4—1462no—
613C2×D4—1462no—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—44no—
622C22×C4—2924no—
623C22×C4—731no—
624C22×C4—731no—
625C22×C4—731no—
626C22×C4—732no—
627C22×C4—732no—
628C22×C4—1464no—
629C22×C4—1461no—
630C22×C4—1461no—
631C22×C4—1461no—
632C22×C4—1462no—
633C22×C4—1462no—
634C22×C4D4×D7312yes—
635C22×C4D4×D7311yescharacteristic
636C22×C4C23×D7312yes—
637C22×C4C23×D7311yescharacteristic
638Q16—28no—
639Q16—44no—
640SD16—2924no—
641M16—2924no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—2924no—
645C2×C8—732no—
646C2×C8—732no—
647C2×C8—1462no—
648C2×C8—1462no—
649C2×C8C23×D7312yes—
650C2×C8C23×D7312yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—734no—
654C4⋊C4—732no—
655C4⋊C4—732no—
656C4⋊C4—732no—
657C4⋊C4—1464no—
658C4⋊C4—1464no—
659C4⋊C4—1464no—
660C4⋊C4—1464no—
661C4⋊C4—1464no—
662C4⋊C4—1461no—
663C4⋊C4—1461no—
664C4⋊C4—1461no—
665C4⋊C4C23×D7312yes—
666C22⋊C4—24no—
667C22⋊C4—734no—
668C22⋊C4—734no—
669C22⋊C4—1464no—
670C22⋊C4—1464no—
671C22⋊C4—1464no—
672C22⋊C4—1464no—
673C22⋊C4—1464no—
674C22⋊C4—1464no—
675C22⋊C4—1464no—
676C42—732no—
677C42—732no—
678C42—1464no—
679C42—1464no—
680C42—1464no—
681C42—1464no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—2922no—
686C23—2922no—
687C23—2922no—
688C23—732no—
689C23—1462no—
690C23—1462no—
691C23—1462no—
692C23—1462no—
693C23C2×D4×D7312yes—
694C23C2×D4×D7311yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—48no—
702Q8—42no—
703Q8—42no—
704Q8—2928no—
705Q8C2×#1192402714yes—
706D4—2928no—
707D4—2928no—
708D4—2924no—
709D4—2922no—
710D4—1462no—
711D4—1462no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—2928no—
726C2×C4—2922no—
727C2×C4—2922no—
728C2×C4—2922no—
729C2×C4—732no—
730C2×C4—732no—
731C2×C4—732no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1464no—
741C2×C4C2×D4×D7312yes—
742C2×C4C2×D4×D7311yescharacteristic
743C2×C4C2×#1192402712yes—
744C2×C4#1455663612yes—
745C2×C4C24×D7311yescharacteristic
746C8—22no—
747C8—22no—
748C8—1462no—
749C8—1462no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—2924no—
755C22—2922no—
756C22—2922no—
757C22—2922no—
758C22—5844no—
759C22—1462no—
760C22—1462no—
761C22—1462no—
762C22#1798922412yes—
763C22#1798938612yes—
764C22#1798940012yes—
765C22C22×D4×D7311yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—2922no—
772C4—2922no—
773C4—2922no—
774C4—1462no—
775C4—1462no—
776C4—1462no—
777C4#1798922412yes—
778C4C22×#1192402711yescharacteristic
779C4C2×#1455663611yescharacteristic
780C2—42no—
781C2—2922no—
782C2—5842no—
783C2#2262199014yesdirect product factor
784C2C2×#1798922411yescharacteristic
785C2C2×#1798938611yescharacteristic
786C2C2×#1798940011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#451×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989248C2
hypercenterC2×#451D73
hypocenterC73C2×#3313
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#17989308C2semidirect
3. #22621990C2direct (N × H)
4. C2×#17988948C2semidirect
5. C2×#17988926C2semidirect
6. C2×#17988912C2semidirect
7. C2×#17988880C2semidirect
8. C2×#17988835C2semidirect
9. C2×#17988825C2semidirect
10. C2×#17988811C2semidirect
11. C2×#17988748C2semidirect
12. C2×#17988694C2semidirect
13. C2×#17988661C2semidirect
14. C2×#17988596C2semidirect
15. C2×#17988582C2semidirect
16. C2×#451×C73C2semidirect
22. #17989308C22semidirect
43. #17988948C22semidirect
44. #17988926C22semidirect
45. #17988912C22semidirect
46. #17988880C22semidirect
47. #17988835C22semidirect
48. #17988825C22semidirect
49. #17988811C22semidirect
50. #17988748C22semidirect
51. #17988694C22semidirect
52. #17988661C22semidirect
57. #17988596C22semidirect
58. #17988582C22semidirect
73. #451×C73C22semidirect
388. C2×C73#3313semidirect
405. C2×#451D73semidirect
410. C73C2×#3313semidirect
449. #451C2×D73semidirect
783. C2#22621990direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893082
C2×#179892482
#226219902
C2×#179889482
C2×#179889262
C2×#179889122
C2×#179888802
C2×#179888352
C2×#179888252
C2×#179888112
C2×#179887482
C2×#179886942
C2×#179886612
C2×#179885962
C2×#179885822
C2×#451×C732
C2×#331373