Finite Group Databasebeta

← C2×#22622039 #33962571

Subgroups — C2×#22622039 #33962571

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×#17989298C211yesmaximal, characteristic, complemented
2C2×#17989249C211yesmaximal, characteristic
3#22622039C2116yesmaximal, direct product factor
4C2×#17988949C211yesmaximal, characteristic, complemented
5C2×#17988907C211yesmaximal, characteristic, complemented
6C2×#17988919C211yesmaximal, characteristic, complemented
7C2×#17988846C211yesmaximal, characteristic, complemented
8C2×#17988817C211yesmaximal, characteristic, complemented
9C2×#17988810C211yesmaximal, characteristic, complemented
10C2×#17988752C211yesmaximal, characteristic, complemented
11C2×#17988744C211yesmaximal, characteristic, complemented
12C2×#17988692C211yesmaximal, characteristic, complemented
13C2×#17988657C211yesmaximal, characteristic, complemented
14C2×#17988587C211yesmaximal, characteristic, complemented
15C2×#103×D73C211yesmaximal, characteristic, complemented
16C2×#475×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×Q8×D73C2211yescharacteristic
19C22×Dic292C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924017C2211yescharacteristic
22C22×#11924011C2211yescharacteristic
23C22×C8×D73C2211yescharacteristic
24#17989298—24no—
25#17989298C2218yescomplemented
26#17989249—24no—
27#17989249C2218yes—
28C2×#14556582—21no—
29C2×#14556579—21no—
30C2×#14556579C2211yescharacteristic
31C2×#14556571—21no—
32C2×#14556571C2211yescharacteristic
33C2×#14556571C2211yescharacteristic
34C2×#14556571C2211yescharacteristic
35C2×#14556567—21no—
36C2×#14556567—21no—
37C2×#14556566—21no—
38C2×#14556566C2211yescharacteristic
39C2×C4×Dic146C2211yescharacteristic
40C2×C4×D292—21no—
41C2×C4×D292C2211yescharacteristic
42C2×#14556553—21no—
43C2×C4⋊C4×D73C2211yescharacteristic
44C2×C4⋊C4×D73C2211yescharacteristic
45#17988949C2218yescomplemented
46#17988919C2218yescomplemented
47#17988907C2218yescomplemented
48#17988846C2218yescomplemented
49#17988817C2218yescomplemented
50#17988810C2218yescomplemented
51#17988752C2218yescomplemented
52#17988744C2218yescomplemented
53#17988692C2218yescomplemented
54#17988657C2218yescomplemented
55C2×#14556522C2211yescharacteristic
56#17988587C2218yescomplemented
57C2×#14556516C2211yescharacteristic
58C2×#14556515C2211yescharacteristic
59C2×#14556514C2211yescharacteristic
60C2×#14556514C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62#103×D73C2218yescomplemented
63C2×#14556513C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556502C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71#475×C73C2218yescomplemented
72C2×#106×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C2×#11924029—22no—
78C2×#11924029—24no—
79C2×#11924029—42no—
80C2×#11924029C2314yes—
81C22×Dic146—21no—
82C22×Dic146C2311yescharacteristic
83C22×Dic146C2311yescharacteristic
84C2×Q8×D73—22no—
85C2×Q8×D73—24no—
86C2×Q8×D73—42no—
87C2×Q8×D73C2314yes—
88C22×D292—21no—
89C22×D292—21no—
90C22×D292D411yescharacteristic
91C22×D292C2311yescharacteristic
92C22×C4×D73—21no—
93C22×C4×D73—21no—
94C22×C4×D73—21no—
95C22×C4×D73—21no—
96C22×C4×D73C2311yescharacteristic
97C22×C4×D73C2311yescharacteristic
98C2×Dic292—42no—
99C2×Dic292C2314yes—
100C2×#11924018—24no—
101C2×#11924018C2314yes—
102C2×#11924017—42no—
103C2×#11924017C2314yes—
104C2×#11924011—42no—
105C2×#11924011C2314yes—
106C22×#10596831C2311yescharacteristic
107C22×#10596831C2311yescharacteristic
108C2×C8×D73—42no—
109C2×C8×D73C2314yes—
110#14556582—28no—
111#14556579—28no—
112#14556579—22no—
113#14556579C2314yes—
114#14556571—22no—
115#14556571—22no—
116#14556571—22no—
117#14556571—28no—
118#14556571C2314yes—
119#14556571C2314yes—
120#14556571C2314yes—
121#14556567—28no—
122#14556567—28no—
123#14556566—28no—
124#14556566—22no—
125#14556566C2314yes—
126C4×Dic146—22no—
127C4×Dic146C2314yes—
128C4×D292—28no—
129C4×D292D414yes—
130C4×D292C2314yes—
131#14556553—28no—
132C2×C4⋊Dic73—21no—
133C2×C4⋊Dic73—21no—
134C2×C4⋊Dic73—21no—
135C2×C4⋊Dic73D411yescharacteristic
136C2×C4⋊Dic73C2311yescharacteristic
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C4⋊C4×D73—22no—
141C4⋊C4×D73—22no—
142C4⋊C4×D73C2314yes—
143C4⋊C4×D73C2314yes—
144C2×#11924005—21no—
145C2×#11924005—21no—
146C2×#11924005—21no—
147C2×#11924005—21no—
148C2×#11924005—21no—
149C2×#11924005—21no—
150C2×#11924005D411yescharacteristic
151C2×#11924005D411yescharacteristic
152C2×C4×Dic73—21no—
153#14556522C2314yes—
154#14556516C2314yes—
155#14556515C2314yes—
156#14556514C2314yes—
157#14556514C2314yes—
158#14556514C2314yes—
159#14556513C2314yes—
160#14556511C2314yes—
161#14556511C2314yes—
162#14556503C2314yes—
163#14556503C2314yes—
164#14556502C2314yes—
165C22×Q8×C73—21no—
166C22×Q8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169C4⋊Q8×C73—22no—
170C4⋊Q8×C73C2314yes—
171C4×Q8×C73—22no—
172C4×Q8×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73—21no—
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C42×C73—21no—
179C2×C42×C73C2311yescharacteristic
180#106×C73C2314yes—
181#106×C73C2314yes—
182C4⋊C8×C73C2314yes—
183#103×C73C2314yes—
184#103×C73C2314yes—
185C23×D73—21no—
186C23×D73C2×D411yescharacteristic
187C23×D73C2×D411yescharacteristic
188#11924029—28no—
189#11924029—44no—
190#11924029—48no—
191C2×Dic146—22no—
192C2×Dic146—22no—
193C2×Dic146—22no—
194C2×Dic146—22no—
195C2×Dic146—21no—
196C2×Dic146—21no—
197C2×Dic146—24no—
198C2×Dic146—44no—
199C2×Dic146C2412yes—
200C2×Dic146C2412yes—
201Q8×D73—28no—
202Q8×D73—44no—
203Q8×D73—48no—
204C2×D292—24no—
205C2×D292—22no—
206C2×D292—22no—
207C2×D292—24no—
208C2×D292—24no—
209C2×D292—21no—
210C2×D292—44no—
211C2×D292—44no—
212C2×D292C2×D414yes—
213C2×D292C2412yes—
214C22×Dic73—21no—
215C22×Dic73—21no—
216C22×Dic73—21no—
217C22×Dic73C2×D411yescharacteristic
218C22×Dic73C2×D411yescharacteristic
219C2×C4×D73—22no—
220C2×C4×D73—22no—
221C2×C4×D73—22no—
222C2×C4×D73—22no—
223C2×C4×D73—24no—
224C2×C4×D73—24no—
225C2×C4×D73—24no—
226C2×C4×D73—24no—
227C2×C4×D73—44no—
228C2×C4×D73—44no—
229C2×C4×D73—82no—
230C2×C4×D73—82no—
231C2×C4×D73C2×D412yes—
232C2×C4×D73C2×D412yes—
233C2×C4×D73C2412yes—
234C2×C4×D73C2412yes—
235Dic292—44no—
236#11924018—28no—
237#11924017—44no—
238#11924011—44no—
239C2×#10596831—22no—
240C2×#10596831—22no—
241C2×#10596831C2412yes—
242C2×#10596831C2412yes—
243C8×D73—44no—
244C4⋊Dic73—21no—
245C4⋊Dic73—24no—
246C4⋊Dic73—24no—
247C4⋊Dic73—24no—
248C4⋊Dic73C2×D414yes—
249C4⋊Dic73C2412yes—
250#11924007—24no—
251#11924007—24no—
252#11924007—24no—
253#11924005—24no—
254#11924005—24no—
255#11924005—24no—
256#11924005—24no—
257#11924005—24no—
258#11924005—24no—
259#11924005C2×D414yes—
260#11924005C2×D414yes—
261C4×Dic73—24no—
262C2×Q8×C73—21no—
263C2×Q8×C73—24no—
264C2×Q8×C73—22no—
265C2×Q8×C73—82no—
266C2×Q8×C73#4114yes—
267C2×Q8×C73C2412yes—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73C2×D411yescharacteristic
273C22×C4×C73C2×D411yescharacteristic
274C22×C4×C73C2411yescharacteristic
275C2×C8×C73—22no—
276C2×C8×C73—22no—
277C2×C8×C73C2412yes—
278C2×C8×C73C2412yes—
279C4⋊C4×C73—24no—
280C4⋊C4×C73—24no—
281C4⋊C4×C73—21no—
282C4⋊C4×C73—21no—
283C4⋊C4×C73—21no—
284C4⋊C4×C73C2412yes—
285C4⋊C4×C73C2412yes—
286C4⋊C4×C73C2412yes—
287C42×C73—24no—
288C42×C73C2×D412yes—
289C42×C73C2412yes—
290C23×C73C22×D411yescharacteristic
291C22×D73—22no—
292C22×D73—22no—
293C22×D73—22no—
294C22×D73—22no—
295C22×D73—22no—
296C22×D73—22no—
297C22×D73—42no—
298C22×D73—42no—
299C22×D73—42no—
300C22×D73#13714yes—
301C22×D73C22×D412yes—
302C22×D73C22×D412yes—
303Q8×C73—24no—
304Q8×C73—22no—
305Q8×C73—84no—
306Q8×C73C2×#4114yes—
307C2×C4×C73—24no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—42no—
317C2×C4×C73C22×D412yes—
318C2×C4×C73C22×D412yes—
319C2×C4×C73C22×D411yescharacteristic
320C2×C4×C73C2×#4112yes—
321C2×C4×C73H(5,𝔽2)12yes—
322C2×C4×C73C2511yescharacteristic
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—42no—
331C2×Dic73C22×D412yes—
332C2×Dic73C22×D412yes—
333D292—28no—
334D292—22no—
335D292—22no—
336D292—48no—
337D292—48no—
338D292—42no—
339C4×D73—24no—
340C4×D73—24no—
341C4×D73—22no—
342C4×D73—22no—
343C4×D73—22no—
344C4×D73—22no—
345C4×D73—48no—
346C4×D73—48no—
347C4×D73—84no—
348C4×D73—84no—
349Dic146—22no—
350Dic146—22no—
351Dic146—22no—
352Dic146—22no—
353Dic146—48no—
354Dic146—42no—
355Dic146—42no—
356C8×C73—22no—
357C8×C73—22no—
358#10596831—22no—
359#10596831—22no—
360C22×C73#54612yes—
361C22×C73C2×#13712yes—
362C22×C73#57712yes—
363C22×C73C23×D411yescharacteristic
364C2×D73—22no—
365C2×D73—28no—
366C2×D73—22no—
367C2×D73—22no—
368C2×D73—22no—
369C2×D73—22no—
370C2×D73—44no—
371C2×D73—42no—
372C2×D73—42no—
373C2×D73—42no—
374C2×D73—84no—
375C2×D73C2×#13714yes—
376C4×C73—24no—
377C4×C73—22no—
378C4×C73—22no—
379C4×C73—42no—
380C4×C73—42no—
381C4×C73—42no—
382C4×C73#54612yes—
383C4×C73C22×#4111yescharacteristic
384C4×C73C2×H(5,𝔽2)11yescharacteristic
385Dic73—22no—
386Dic73—22no—
387Dic73—42no—
388Dic73—42no—
389Dic73—42no—
390C2×#3316—731nomaximal, Sylow
391C2×C73#331614yescomplemented
392C2×C73C2×#54611yescharacteristic
393C2×C73C22×#13711yescharacteristic
394C2×C73C2×#57711yescharacteristic
395D73—24no—
396D73—42no—
397D73—82no—
398C2×#554—731no—
399C2×#548—731no—
400#3316—7316no—
401C2×#489—731no—
402C2×#481—731no—
403C2×#483—731no—
404C2×#475D7311yescharacteristic, complemented
405C2×#470—731no—
406C2×#465—731no—
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×SD16—731no—
420C22×M16—731no—
421C23×C8—731no—
422#554—738no—
423#554—1464no—
424#548—738no—
425#548—1464no—
426C2×C4⋊Q8C2×D7311yescharacteristic
427C2×#125—1461no—
428C2×#124—731no—
429C2×#124—1461no—
430C2×C22⋊Q8—731no—
431C2×C22⋊Q8—731no—
432C2×C22⋊Q8—731no—
433C2×C22⋊Q8—1461no—
434C2×C22⋊Q8—1461no—
435C2×C22⋊Q8—1461no—
436C2×#121—731no—
437C2×#121—1461no—
438C2×C4×Q8—731no—
439C2×C4×Q8C2×D7311yescharacteristic
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#475C2×D7318yescomplemented
449#470—738no—
450#465—738no—
451#464—738no—
452#452—738no—
453#451—738no—
454#441—738no—
455#435—738no—
456C2×#106—731no—
457C2×#106C2×D7311yescharacteristic
458C2×#106C2×D7311yescharacteristic
459C2×C4⋊C8C2×D7311yescharacteristic
460#417—738no—
461C2×#103—731no—
462C2×#103—731no—
463C2×#103—731no—
464C2×#103—731no—
465C2×#103—731no—
466C2×#103—738no—
467C2×#103C2×D7311yescharacteristic
468C2×#103C2×D7311yescharacteristic
469C2×#102—731no—
470C2×#102—731no—
471C2×#102—731no—
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—21no—
480C22×Q8—2922no—
481C22×Q8—734no—
482C22×Q8—731no—
483C22×Q8—731no—
484C22×Q8—1461no—
485C22×Q8—1464no—
486C22×Q8—1462no—
487C22×Q8C22×D7311yescharacteristic
488C22×D4—731no—
489C22×D4—731no—
490C22×D4—1461no—
491C22×D4—1461no—
492C23×C4—731no—
493C23×C4—731no—
494C23×C4—1461no—
495C23×C4—1461no—
496C23×C4—1461no—
497C23×C4—1461no—
498C2×Q16—2922no—
499C2×Q16—734no—
500C2×Q16—734no—
501C2×Q16—1464no—
502C2×SD16—2922no—
503C2×SD16—734no—
504C2×M16—2922no—
505C2×M16—734no—
506C22×C8—2922no—
507C22×C8—734no—
508C22×C8—731no—
509C22×C8—731no—
510C22×C8C22×D7311yescharacteristic
511C22×C8C22×D7311yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8C22×D7314yes—
514#125—1468no—
515#124—734no—
516#124—1468no—
517#124—1462no—
518C22⋊Q8—734no—
519C22⋊Q8—734no—
520C22⋊Q8—734no—
521C22⋊Q8—1468no—
522C22⋊Q8—1468no—
523C22⋊Q8—1468no—
524C22⋊Q8—1462no—
525C22⋊Q8—1462no—
526C22⋊Q8—1462no—
527#121—734no—
528#121—1462no—
529#121—1468no—
530C4×Q8—22no—
531C4×Q8—734no—
532C4×Q8—1462no—
533C4×Q8C22×D7314yes—
534C4×D4—734no—
535C4×D4—734no—
536C4×D4—1468no—
537C4×D4—1468no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—731no—
541C2×C4⋊C4—731no—
542C2×C4⋊C4—734no—
543C2×C4⋊C4—734no—
544C2×C4⋊C4—1462no—
545C2×C4⋊C4—1462no—
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⋊C4C22×D7311yescharacteristic
553C2×C4⋊C4C22×D7311yescharacteristic
554C2×C4⋊C4C22×D7311yescharacteristic
555C2×C22⋊C4—731no—
556C2×C22⋊C4—731no—
557C2×C22⋊C4—1461no—
558C2×C22⋊C4—1461no—
559C2×C22⋊C4—1461no—
560C2×C22⋊C4—1461no—
561C2×C22⋊C4—1461no—
562C2×C22⋊C4—1461no—
563C2×C42—21no—
564C2×C42—1461no—
565C2×C42C22×D7311yescharacteristic
566#106—734no—
567#106C22×D7314yes—
568#106C22×D7314yes—
569C4⋊C8C22×D7314yes—
570#103—734no—
571#103—734no—
572#103—734no—
573#103—734no—
574#103—734no—
575#103C22×D7314yes—
576#103C22×D7314yes—
577#102—734no—
578#102—734no—
579#102—734no—
580C22⋊C8—734no—
581C22⋊C8—734no—
582#97—734no—
583C24—731no—
584C24—731no—
585C24—1461no—
586#41—2928no—
587#41—2924no—
588#41—1468no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—22no—
592C2×Q8—82no—
593C2×Q8—2924no—
594C2×Q8—2928no—
595C2×Q8—2924no—
596C2×Q8—732no—
597C2×Q8—732no—
598C2×Q8—1464no—
599C2×Q8—1468no—
600C2×Q8—1462no—
601C2×Q8—1462no—
602C2×Q8—1462no—
603C2×Q8—1462no—
604C2×Q8—1461no—
605C2×Q8—1461no—
606C2×Q8#1192402914yes—
607C2×Q8C23×D7312yes—
608C2×D4—2924no—
609C2×D4—2924no—
610C2×D4—734no—
611C2×D4—732no—
612C2×D4—1464no—
613C2×D4—1464no—
614C2×D4—1464no—
615C2×D4—1461no—
616C2×D4—1462no—
617C2×D4—1462no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—2924no—
623C22×C4—2924no—
624C22×C4—5842no—
625C22×C4—5842no—
626C22×C4—731no—
627C22×C4—731no—
628C22×C4—732no—
629C22×C4—732no—
630C22×C4—732no—
631C22×C4—732no—
632C22×C4—1464no—
633C22×C4—1464no—
634C22×C4—1464no—
635C22×C4—1464no—
636C22×C4—1461no—
637C22×C4—1461no—
638C22×C4—1461no—
639C22×C4—1462no—
640C22×C4—1462no—
641C22×C4—1462no—
642C22×C4—1462no—
643C22×C4D4×D7311yescharacteristic
644C22×C4D4×D7311yescharacteristic
645C22×C4C23×D7311yescharacteristic
646Q16—2924no—
647Q16—1468no—
648SD16—2924no—
649M16—2924no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—2924no—
653C2×C8—732no—
654C2×C8—732no—
655C2×C8—1462no—
656C2×C8—1462no—
657C2×C8C23×D7312yes—
658C2×C8C23×D7312yes—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—734no—
665C4⋊C4—732no—
666C4⋊C4—1464no—
667C4⋊C4—1464no—
668C4⋊C4—1464no—
669C4⋊C4—1464no—
670C4⋊C4—1464no—
671C4⋊C4—1464no—
672C4⋊C4—1461no—
673C4⋊C4C23×D7312yes—
674C4⋊C4C23×D7312yes—
675C4⋊C4C23×D7312yes—
676C22⋊C4—734no—
677C22⋊C4—734no—
678C22⋊C4—1464no—
679C22⋊C4—1464no—
680C22⋊C4—1464no—
681C22⋊C4—1464no—
682C22⋊C4—1464no—
683C22⋊C4—1464no—
684C42—24no—
685C42—1464no—
686C42D4×D7312yes—
687C42C23×D7312yes—
688C23—2922no—
689C23—2922no—
690C23—2922no—
691C23—734no—
692C23—732no—
693C23—732no—
694C23—1462no—
695C23—1462no—
696C23—1462no—
697C23—1462no—
698C23—1462no—
699C23—1462no—
700C23C2×D4×D7311yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—84no—
704Q8—2928no—
705Q8—2922no—
706Q8—2922no—
707Q8—1462no—
708Q8—1462no—
709Q8—1462no—
710Q8—1462no—
711Q8C2×#1192402914yes—
712D4—2928no—
713D4—2928no—
714D4—2922no—
715D4—1468no—
716D4—1462no—
717D4—1462no—
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—2928no—
729C2×C4—2928no—
730C2×C4—2922no—
731C2×C4—2922no—
732C2×C4—2922no—
733C2×C4—5844no—
734C2×C4—5844no—
735C2×C4—732no—
736C2×C4—732no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1462no—
746C2×C4—1464no—
747C2×C4—1464no—
748C2×C4C2×D4×D7312yes—
749C2×C4C2×D4×D7312yes—
750C2×C4C2×D4×D7311yescharacteristic
751C2×C4C2×#1192402912yes—
752C2×C4#1455663712yes—
753C2×C4C24×D7311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1462no—
757C8—1462no—
758C22—2924no—
759C22—2922no—
760C22—2922no—
761C22—2922no—
762C22—5844no—
763C22—734no—
764C22—1462no—
765C22—1462no—
766C22—1462no—
767C22—1468no—
768C22—1462no—
769C22—1462no—
770C22#1798922812yes—
771C22#137×D7312yes—
772C22#1798939312yes—
773C22C22×D4×D7311yescharacteristic
774C4—24no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—2922no—
781C4—2922no—
782C4—2922no—
783C4—1462no—
784C4—1462no—
785C4#1798922812yes—
786C4C22×#1192402911yescharacteristic
787C4C2×#1455663711yescharacteristic
788C2—2922no—
789C2—5842no—
790C2—1464no—
791C2#2262203914yesdirect product factor
792C2C2×#1798922811yescharacteristic
793C2C2×#137×D7311yescharacteristic
794C2C2×#1798939311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#475×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989249C2
hypercenterC2×#475D73
hypocenterC73C2×#3316
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#17989298C2semidirect
3. #22622039C2direct (N × H)
4. C2×#17988949C2semidirect
5. C2×#17988907C2semidirect
6. C2×#17988919C2semidirect
7. C2×#17988846C2semidirect
8. C2×#17988817C2semidirect
9. C2×#17988810C2semidirect
10. C2×#17988752C2semidirect
11. C2×#17988744C2semidirect
12. C2×#17988692C2semidirect
13. C2×#17988657C2semidirect
14. C2×#17988587C2semidirect
15. C2×#103×D73C2semidirect
16. C2×#475×C73C2semidirect
25. #17989298C22semidirect
45. #17988949C22semidirect
46. #17988919C22semidirect
47. #17988907C22semidirect
48. #17988846C22semidirect
49. #17988817C22semidirect
50. #17988810C22semidirect
51. #17988752C22semidirect
52. #17988744C22semidirect
53. #17988692C22semidirect
54. #17988657C22semidirect
56. #17988587C22semidirect
62. #103×D73C22semidirect
71. #475×C73C22semidirect
391. C2×C73#3316semidirect
404. C2×#475D73semidirect
414. C73C2×#3316semidirect
448. #475C2×D73semidirect
791. C2#22622039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892982
C2×#179892492
#226220392
C2×#179889492
C2×#179889072
C2×#179889192
C2×#179888462
C2×#179888172
C2×#179888102
C2×#179887522
C2×#179887442
C2×#179886922
C2×#179886572
C2×#179885872
C2×#103×D732
C2×#475×C732
C2×#331673