Finite Group Databasebeta

← C2×#22623746 #33994314

Subgroups — C2×#22623746 #33994314

Order 18688.

7478 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623746C2132yesmaximal, direct product factor
2C2×#17989317C212yesmaximal, complemented
3C2×#17989314C212yesmaximal, complemented
4C2×#17989293C212yesmaximal, complemented
5C2×#17989291C214yesmaximal, complemented
6C2×#17989252C212yesmaximal, complemented
7C2×#17989250C214yesmaximal, complemented
8C2×#17989217C212yesmaximal, complemented
9C2×#17989215C211yesmaximal, characteristic, complemented
10C2×#17989214C212yesmaximal, complemented
11C2×#17989143C212yesmaximal, complemented
12C2×#17989140C211yesmaximal, characteristic, complemented
13C22×#14556590C211yesmaximal, characteristic, complemented
14C2×C4⋊Q8×D73C212yesmaximal, complemented
15C2×#17989068C211yesmaximal, characteristic
16C2×#17989067C211yesmaximal, characteristic
17C2×#17989055C211yesmaximal, characteristic
18C2×#544×C73C211yesmaximal, characteristic, complemented
19C22×#11924028C2211yescharacteristic
20C23×Dic146C2212yes—
21C22×Q8×D73C2214yes—
22#17989317C22132yescomplemented
23#17989314C22132yescomplemented
24#17989293C22132yescomplemented
25#17989291C22164yescomplemented
26#17989252C22132yescomplemented
27#17989250C22164yescomplemented
28#17989217C22132yescomplemented
29#17989215C22116yescomplemented
30#17989214C22132yescomplemented
31#17989143C22132yescomplemented
32#17989140C22116yescomplemented
33C2×#14556591C2212yes—
34C2×#14556590C2214yes—
35C2×#14556590C2212yes—
36C2×#14556590C2212yes—
37C2×#14556590C2214yes—
38C2×#14556590C2212yes—
39C2×#14556590C2212yes—
40C2×#14556590C2211yescharacteristic
41C2×#14556590C2212yes—
42C2×#14556590C2211yescharacteristic
43C2×#14556590C22116yescomplemented
44C2×#14556589C2214yes—
45C2×#14556589C2214yes—
46C4⋊Q8×D73C22132yescomplemented
47C2×#14556583C2212yes—
48C2×#14556582C2212yes—
49C2×#14556582C2211yescharacteristic
50C2×#14556582C2211yescharacteristic
51C2×#14556581C2214yes—
52C2×#14556581C2214yes—
53C2×#14556571C2214yes—
54C2×#14556569C2214yes—
55C2×#14556569C2214yes—
56C2×#14556569C2214yes—
57C2×#14556569C2214yes—
58C2×#14556568C2214yes—
59C2×#14556568C2212yes—
60C2×#14556568C2212yes—
61C2×#14556567C2214yes—
62#17989068C22116yes—
63#17989067C22116yes—
64#17989055C22116yes—
65C2×C4×Dic146C2212yes—
66C2×C4×Dic146C2212yes—
67C2×C4×Dic146C2212yes—
68C2×#14556556C2211yescharacteristic
69C2×#14556556C2212yes—
70C2×#14556556C2214yes—
71C2×#14556556C2211yescharacteristic
72C2×#14556556C2214yes—
73C2×C4×D292C2212yes—
74C2×#14556553C2211yescharacteristic
75C2×#14556553C2211yescharacteristic
76C2×#14556553C2212yes—
77C2×C4×C22⋊D73C2214yes—
78C2×#14556551C2212yes—
79C2×#14556551C2212yes—
80C2×#14556551C2214yes—
81C2×#14556550C2211yescharacteristic
82C2×#14556549C2212yes—
83C2×#14556549C2212yes—
84C2×#14556548C2212yes—
85C22×C4⋊Dic73C2211yescharacteristic
86C22×#11924007C2212yes—
87C2×C4⋊C4×D73C2212yes—
88C2×C4⋊C4×D73C2212yes—
89C2×C4⋊C4×D73C2214yes—
90C22×C4×Dic73C2211yescharacteristic
91C2×C42×D73C2212yes—
92#544×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2212yes—
94C2×C4⋊Q8×C73C2212yes—
95C2×#125×C73C2212yes—
96C2×#125×C73C2212yes—
97C2×C22⋊Q8×C73C2214yes—
98C2×#117×C73C2211yescharacteristic
99C2×#117×C73C2211yescharacteristic
100C22×C4⋊C4×C73C2211yescharacteristic
101C2×#11924028Q8116yescomplemented
102C2×#11924028C2318yes—
103C22×Dic146—48no—
104C22×Dic146C2312yes—
105C22×Dic146C2314yes—
106C22×Dic146C2312yes—
107C22×Dic146C2314yes—
108C22×Dic146C2314yes—
109C22×Dic146C23116yes—
110C22×Dic146C2311yescharacteristic
111C2×Q8×D73—416no—
112C2×Q8×D73C23132yes—
113C22×D292C2311yescharacteristic
114C22×C22⋊D73C2312yes—
115C23×Dic73C2311yescharacteristic
116C23×Dic73C2311yescharacteristic
117C23×Dic73C2312yes—
118C22×C4×D73C2312yes—
119C22×C4×D73C2312yes—
120C22×C4×D73C2314yes—
121C22×C4×D73C2314yes—
122C22×C4×D73C2312yes—
123#14556591C23116yes—
124#14556590C2318yes—
125#14556590C23116yes—
126#14556590C23132yes—
127#14556590C23116yes—
128#14556590C23116yes—
129#14556590C23116yes—
130#14556590C2318yes—
131#14556590C23116yes—
132#14556590C23132yes—
133#14556589C23132yes—
134#14556589C23132yes—
135#14556583C23116yes—
136#14556582C2318yes—
137#14556582C2318yes—
138#14556582C23116yes—
139#14556581C23132yes—
140#14556581C23132yes—
141#14556571C23132yes—
142#14556569C23132yes—
143#14556569C23132yes—
144#14556569C23132yes—
145#14556569C23132yes—
146#14556568C23116yes—
147#14556568C23116yes—
148#14556568C23132yes—
149#14556567C23132yes—
150C4×Dic146C23116yes—
151C4×Dic146C23116yes—
152C4×Dic146C23116yes—
153#14556556C23132yes—
154#14556556C23132yes—
155#14556556C2318yes—
156#14556556C2318yes—
157#14556556C23116yes—
158C4×D292C23116yes—
159#14556553C2318yes—
160#14556553C23116yes—
161#14556553C2318yes—
162C4×C22⋊D73C23132yes—
163#14556551C23116yes—
164#14556551C23132yes—
165#14556551C23116yes—
166#14556550C2318yes—
167#14556549C23116yes—
168#14556549C23116yes—
169#14556548C23116yes—
170C2×C4⋊Dic73C2312yes—
171C2×C4⋊Dic73C2312yes—
172C2×C4⋊Dic73C2312yes—
173C2×C4⋊Dic73C2311yescharacteristic
174C2×C4⋊Dic73C2314yes—
175C2×C4⋊Dic73C2311yescharacteristic
176C2×C4⋊Dic73C2318yes—
177C2×C4⋊Dic73C2312yes—
178C2×#11924007C2312yes—
179C2×#11924007C2312yes—
180C2×#11924007C2314yes—
181C2×#11924007C2312yes—
182C2×#11924007C2314yes—
183C2×#11924007C2314yes—
184C2×#11924007C2314yes—
185C2×#11924007C2314yes—
186C2×#11924007C2312yes—
187C2×#11924007C23116yes—
188C2×#11924007C2312yes—
189C2×#11924007C2314yes—
190C2×#11924007C2312yes—
191C4⋊C4×D73C23116yes—
192C4⋊C4×D73C23116yes—
193C4⋊C4×D73C23132yes—
194C2×C22⋊Dic73C2312yes—
195C2×#11924005C2312yes—
196C2×#11924005C2312yes—
197C2×#11924005C2314yes—
198C2×#11924005C2314yes—
199C2×C4×Dic73C2312yes—
200C2×C4×Dic73C2314yes—
201C2×C4×Dic73C2311yescharacteristic
202C2×C4×Dic73C2312yes—
203C2×C4×Dic73C2311yescharacteristic
204C2×C4×Dic73C2311yescharacteristic
205C2×C4×Dic73C2311yescharacteristic
206C2×C4×Dic73C2314yes—
207C2×C4×Dic73C2312yes—
208C2×C4×Dic73C2318yes—
209C42×D73C23116yes—
210C22×Q8×C73C2314yes—
211C23×C4×C73C2312yes—
212C23×C4×C73C2311yescharacteristic
213C4⋊Q8×C73C23116yes—
214C4⋊Q8×C73C23116yes—
215#125×C73C23116yes—
216#125×C73C23116yes—
217C22⋊Q8×C73C23132yes—
218#117×C73C2318yes—
219#117×C73C2318yes—
220C2×C4⋊C4×C73C2312yes—
221C2×C4⋊C4×C73C2312yes—
222C2×C4⋊C4×C73C2311yescharacteristic
223C2×C4⋊C4×C73C2311yescharacteristic
224C2×C4⋊C4×C73C2311yescharacteristic
225C2×C4⋊C4×C73C2314yes—
226C2×C4⋊C4×C73C2314yes—
227C2×C4⋊C4×C73C2318yes—
228C2×C4⋊C4×C73C2311yescharacteristic
229C2×C4⋊C4×C73C2314yes—
230C2×C22⋊C4×C73C2312yes—
231C2×C22⋊C4×C73C2312yes—
232C2×C42×C73C2312yes—
233C2×C42×C73C2312yes—
234C23×D73C2412yes—
235#11924028C2×Q8164yescomplemented
236C2×Dic146—28no—
237C2×Dic146—216no—
238C2×Dic146—28no—
239C2×Dic146—432no—
240C2×Dic146—48no—
241C2×Dic146—48no—
242C2×Dic146C2×Q818yescomplemented
243C2×Dic146C2418yes—
244C2×Dic146C24116yes—
245C2×Dic146C2418yes—
246C2×Dic146C24116yes—
247C2×Dic146C24116yes—
248C2×Dic146C2414yes—
249Q8×D73—464no—
250C2×D292C2×Q818yescomplemented
251C2×D292C2414yes—
252C2×C22⋊D73C2×Q8116yescomplemented
253C2×C22⋊D73C2418yes—
254C22×Dic73—24no—
255C22×Dic73—24no—
256C22×Dic73—44no—
257C22×Dic73C2412yes—
258C22×Dic73C2411yescharacteristic
259C22×Dic73C2411yescharacteristic
260C22×Dic73C2414yes—
261C22×Dic73C2414yes—
262C22×Dic73C2414yes—
263C22×Dic73C2412yes—
264C22×Dic73C2418yes—
265C22×Dic73C2412yes—
266C22×Dic73C2411yescharacteristic
267C22×Dic73C2411yescharacteristic
268C2×C4×D73—28no—
269C2×C4×D73—28no—
270C2×C4×D73—48no—
271C2×C4×D73—48no—
272C2×C4×D73C2×Q8116yescomplemented
273C2×C4×D73C2418yes—
274C2×C4×D73C2418yes—
275C2×C4×D73C24116yes—
276C2×C4×D73C24116yes—
277C2×C4×D73C2418yes—
278C4⋊Dic73C2414yes—
279C4⋊Dic73C2418yes—
280C4⋊Dic73C24116yes—
281C4⋊Dic73C2418yes—
282C4⋊Dic73C2414yes—
283C4⋊Dic73C2418yes—
284C4⋊Dic73C2418yes—
285#11924007C2418yes—
286#11924007C24116yes—
287#11924007C24116yes—
288#11924007C24116yes—
289#11924007C24116yes—
290#11924007C2418yes—
291#11924007C2418yes—
292#11924007C2418yes—
293#11924007C24116yes—
294#11924007C24116yes—
295#11924007C2418yes—
296#11924007C2418yes—
297C22⋊Dic73C2418yes—
298#11924005C2418yes—
299#11924005C2418yes—
300#11924005C24116yes—
301#11924005C24116yes—
302C4×Dic73C2414yes—
303C4×Dic73C2418yes—
304C4×Dic73C2418yes—
305C4×Dic73C2414yes—
306C4×Dic73C2414yes—
307C4×Dic73C2414yes—
308C4×Dic73C24116yes—
309C4×Dic73C24116yes—
310C4×Dic73C2418yes—
311C24×C73C2411yescharacteristic
312C2×Q8×C73—48no—
313C2×Q8×C73C24116yes—
314C22×C4×C73—44no—
315C22×C4×C73C2×Q818yescomplemented
316C22×C4×C73C2412yes—
317C22×C4×C73C2412yes—
318C22×C4×C73C2412yes—
319C22×C4×C73C2412yes—
320C22×C4×C73C2414yes—
321C22×C4×C73C2418yes—
322C22×C4×C73C2411yescharacteristic
323C22×C4×C73C2411yescharacteristic
324C22×C4×C73C2414yes—
325C4⋊C4×C73C2418yes—
326C4⋊C4×C73C2418yes—
327C4⋊C4×C73C2414yes—
328C4⋊C4×C73C2414yes—
329C4⋊C4×C73C2414yes—
330C4⋊C4×C73C2414yes—
331C4⋊C4×C73C24116yes—
332C4⋊C4×C73C24116yes—
333C4⋊C4×C73C24116yes—
334C22⋊C4×C73C2418yes—
335C22⋊C4×C73C2418yes—
336C42×C73C2418yes—
337C42×C73C2418yes—
338C23×C73—22no—
339C23×C73—22no—
340C23×C73C22×Q814yes—
341C23×C73C2512yes—
342C23×C73C2511yescharacteristic
343C22×D73—24no—
344C22×D73—24no—
345C22×D73C22×Q818yes—
346C22×D73C2514yes—
347Q8×C73—416no—
348C2×C4×C73—28no—
349C2×C4×C73—24no—
350C2×C4×C73—24no—
351C2×C4×C73—24no—
352C2×C4×C73—24no—
353C2×C4×C73—48no—
354C2×C4×C73C22×Q814yes—
355C2×C4×C73C22×Q814yes—
356C2×C4×C73C22×Q8116yescomplemented
357C2×C4×C73C2514yes—
358C2×C4×C73C2514yes—
359C2×C4×C73C2514yes—
360C2×C4×C73C2514yes—
361C2×C4×C73C2518yes—
362C2×C4×C73C2512yes—
363C2×C4×C73C2512yes—
364C22⋊D73C22×Q8132yescomplemented
365C2×Dic73—24no—
366C2×Dic73—28no—
367C2×Dic73—22no—
368C2×Dic73—22no—
369C2×Dic73—24no—
370C2×Dic73—28no—
371C2×Dic73—28no—
372C2×Dic73—48no—
373C2×Dic73C22×Q818yes—
374C2×Dic73H(5,𝔽2)14yes—
375C2×Dic732−1+414yes—
376C2×Dic73C2514yes—
377C2×Dic73C2512yes—
378C2×Dic73C2512yes—
379C2×Dic73C2518yes—
380C2×Dic73C2514yes—
381C2×Dic73C2514yes—
382C2×Dic73C2512yes—
383C2×Dic73C2512yes—
384D292C22×Q8116yescomplemented
385C4×D73—216no—
386C4×D73—216no—
387C4×D73—416no—
388C4×D73—416no—
389C4×D73C22×Q8132yescomplemented
390Dic146—216no—
391Dic146—232no—
392Dic146—216no—
393Dic146—416no—
394Dic146—416no—
395Dic146C22×Q8116yescomplemented
396C22×C73—22no—
397C22×C73—22no—
398C22×C73—28no—
399C22×C73C23×Q814yes—
400C22×C73C23×Q812yes—
401C22×C73C2×H(5,𝔽2)12yes—
402C22×C73C2×2−1+412yes—
403C22×C73C2611yescharacteristic
404C2×D73—24no—
405C2×D73—24no—
406C2×D73—216no—
407C2×D73C23×Q818yes—
408C4×C73—28no—
409C4×C73—24no—
410C4×C73—24no—
411C4×C73—24no—
412C4×C73—24no—
413C4×C73C23×Q814yes—
414C4×C73C23×Q814yes—
415Dic73—24no—
416Dic73—28no—
417Dic73—22no—
418Dic73—24no—
419Dic73—22no—
420Dic73C23×Q818yes—
421Dic73C2×H(5,𝔽2)14yes—
422Dic73C2×2−1+414yes—
423C2×#3503—731nomaximal, Sylow
424C2×C73—24no—
425C2×C73#350314yescomplemented
426C2×C73C24×Q811yescharacteristic
427C2×C73C22×H(5,𝔽2)11yescharacteristic
428C2×C73C22×2−1+411yescharacteristic
429D73—28no—
430#3503—7332no—
431C2×Q82—732no—
432C2×#557—732no—
433C2×#554—732no—
434C2×#554—734no—
435C2×D4×Q8—732no—
436C2×D4×Q8—734no—
437C2×#544—732no—
438C2×#544—732no—
439C2×#544—731no—
440C2×#544D7311yescharacteristic, complemented
441C2×#533—732no—
442C2×#533—731no—
443C22×C4⋊Q8—732no—
444C22×C4⋊Q8—731no—
445C2×#520—731no—
446C2×#520—731no—
447C2×C4×#41—731no—
448C73C2×#350311yescharacteristic, complemented, Sylow
449C22×#41—731no—
450C23×Q8—734no—
451C23×Q8—732no—
452Q82—7332no—
453#557—7332no—
454#554—7332no—
455#554—7364no—
456D4×Q8—7332no—
457D4×Q8—7364no—
458#544—7332no—
459#544—7332no—
460#544—7316no—
461#544C2×D73116yescomplemented
462#533—7332no—
463#533—7316no—
464C2×C4⋊Q8—734no—
465C2×C4⋊Q8—734no—
466C2×C4⋊Q8—7332no—
467C2×C4⋊Q8—731no—
468C2×C4⋊Q8—732no—
469C2×C4⋊Q8—732no—
470C2×C4⋊Q8—734no—
471C2×C4⋊Q8—732no—
472C2×C4⋊Q8—732no—
473C2×C4⋊Q8—731no—
474C2×C4⋊Q8—734no—
475C2×C4⋊Q8—732no—
476C2×C4⋊Q8—7316no—
477C2×C4⋊Q8—732no—
478C2×C4⋊Q8C2×D7312yes—
479C2×C4⋊Q8C2×D7312yes—
480C2×#125—731no—
481C2×#125—731no—
482C2×#125—734no—
483C2×#125—734no—
484C2×#125—732no—
485C2×#125—732no—
486C2×#125C2×D7312yes—
487C2×#125C2×D7312yes—
488C2×C22⋊Q8—734no—
489C2×C22⋊Q8—734no—
490C2×C22⋊Q8—734no—
491C2×C22⋊Q8—734no—
492C2×C22⋊Q8—734no—
493C2×C22⋊Q8—734no—
494C2×C22⋊Q8—732no—
495C2×C22⋊Q8—732no—
496C2×C22⋊Q8—734no—
497C2×C22⋊Q8C2×D7314yes—
498#520—7316no—
499#520—7316no—
500C4×#41—7316no—
501C2×C4×Q8—731no—
502C2×C4×Q8—731no—
503C2×C4×Q8—732no—
504C2×C4×Q8—734no—
505C2×C4×Q8—734no—
506C2×C4×Q8—732no—
507C2×C4×Q8—732no—
508C2×C4×Q8—732no—
509C2×C4×D4—734no—
510C2×C4×D4—731no—
511C2×C4×D4—731no—
512C2×C4×D4—732no—
513C2×C4×D4—732no—
514C2×C4×D4—732no—
515C2×C4×D4—734no—
516C2×C4×D4—732no—
517C2×#117—731no—
518C2×#117—732no—
519C2×#117—732no—
520C2×#117—732no—
521C2×#117C2×D7311yescharacteristic
522C2×#117C2×D7311yescharacteristic
523C22×C4⋊C4—731no—
524C22×C4⋊C4—732no—
525C22×C4⋊C4—732no—
526C22×C4⋊C4—732no—
527C22×C4⋊C4—734no—
528C22×C4⋊C4C2×D7311yescharacteristic
529C22×C42—731no—
530C22×C42—732no—
531C2×#41—7316no—
532C2×#41—738no—
533C22×Q8—2928no—
534C22×Q8—29216no—
535C22×Q8—7332no—
536C22×Q8—734no—
537C22×Q8—734no—
538C22×Q8—7316no—
539C22×Q8—731no—
540C22×Q8—732no—
541C22×Q8—734no—
542C22×Q8—732no—
543C22×Q8C22×D7314yes—
544C22×D4—732no—
545C22×D4—731no—
546C23×C4—732no—
547C23×C4—734no—
548C23×C4—734no—
549C23×C4—732no—
550C23×C4—731no—
551C23×C4—731no—
552C23×C4—732no—
553C23×C4—732no—
554C23×C4C22×D7312yes—
555C23×C4C22×D7311yescharacteristic
556C4⋊Q8—7332no—
557C4⋊Q8—7332no—
558C4⋊Q8—738no—
559C4⋊Q8—7316no—
560C4⋊Q8—7316no—
561C4⋊Q8—7332no—
562C4⋊Q8—7316no—
563C4⋊Q8—7316no—
564C4⋊Q8—738no—
565C4⋊Q8—7332no—
566C4⋊Q8—7316no—
567C4⋊Q8—7316no—
568C4⋊Q8C22×D73116yes—
569C4⋊Q8C22×D73116yes—
570#125—738no—
571#125—738no—
572#125—7332no—
573#125—7332no—
574#125—7316no—
575#125—7316no—
576#125C22×D73116yes—
577#125C22×D73116yes—
578C22⋊Q8—7332no—
579C22⋊Q8—7332no—
580C22⋊Q8—7332no—
581C22⋊Q8—7332no—
582C22⋊Q8—7332no—
583C22⋊Q8—7332no—
584C22⋊Q8—7316no—
585C22⋊Q8—7316no—
586C22⋊Q8—7332no—
587C22⋊Q8C22×D73132yes—
588C4×Q8—738no—
589C4×Q8—738no—
590C4×Q8—7316no—
591C4×Q8—7332no—
592C4×Q8—7332no—
593C4×Q8—7316no—
594C4×Q8—7316no—
595C4×Q8—7316no—
596C4×D4—7332no—
597C4×D4—738no—
598C4×D4—738no—
599C4×D4—7316no—
600C4×D4—7316no—
601C4×D4—7316no—
602C4×D4—7332no—
603C4×D4—7316no—
604#117—738no—
605#117—7316no—
606#117—7316no—
607#117—7316no—
608#117C22×D7318yes—
609#117C22×D7318yes—
610C2×C4⋊C4—732no—
611C2×C4⋊C4—731no—
612C2×C4⋊C4—734no—
613C2×C4⋊C4—732no—
614C2×C4⋊C4—734no—
615C2×C4⋊C4—734no—
616C2×C4⋊C4—732no—
617C2×C4⋊C4—738no—
618C2×C4⋊C4—734no—
619C2×C4⋊C4—734no—
620C2×C4⋊C4—7316no—
621C2×C4⋊C4—731no—
622C2×C4⋊C4—732no—
623C2×C4⋊C4—732no—
624C2×C4⋊C4—732no—
625C2×C4⋊C4—734no—
626C2×C4⋊C4—732no—
627C2×C4⋊C4—732no—
628C2×C4⋊C4—732no—
629C2×C4⋊C4—734no—
630C2×C4⋊C4—732no—
631C2×C4⋊C4—7316no—
632C2×C4⋊C4—7316no—
633C2×C4⋊C4—7332no—
634C2×C4⋊C4C22×D7311yescharacteristic
635C2×C4⋊C4C22×D7312yes—
636C2×C4⋊C4C22×D7314yes—
637C2×C4⋊C4C22×D7312yes—
638C2×C4⋊C4C22×D7318yes—
639C2×C4⋊C4C22×D7311yescharacteristic
640C2×C4⋊C4C22×D7311yescharacteristic
641C2×C4⋊C4C22×D7311yescharacteristic
642C2×C4⋊C4C22×D7314yes—
643C2×C4⋊C4C22×D7314yes—
644C2×C22⋊C4—732no—
645C2×C22⋊C4—734no—
646C2×C22⋊C4—732no—
647C2×C22⋊C4—732no—
648C2×C22⋊C4—734no—
649C2×C22⋊C4C22×D7312yes—
650C2×C22⋊C4C22×D7312yes—
651C2×C42—731no—
652C2×C42—734no—
653C2×C42—734no—
654C2×C42—732no—
655C2×C42—732no—
656C2×C42—732no—
657C2×C42—731no—
658C2×C42—731no—
659C2×C42—738no—
660C2×C42—731no—
661C2×C42—7316no—
662C2×C42C22×D7312yes—
663C2×C42C22×D7312yes—
664C24—732no—
665C24C23×D7311yescharacteristic
666#41—7364no—
667C2×Q8—48no—
668C2×Q8—2928no—
669C2×Q8—2928no—
670C2×Q8—29232no—
671C2×Q8—29264no—
672C2×Q8—738no—
673C2×Q8—7316no—
674C2×Q8—7316no—
675C2×Q8—734no—
676C2×Q8—738no—
677C2×Q8—7316no—
678C2×Q8—738no—
679C2×Q8—14616no—
680C2×Q8—1468no—
681C2×Q8—1468no—
682C2×Q8C23×D73116yes—
683C2×D4—7316no—
684C2×D4—738no—
685C2×D4—738no—
686C2×D4—734no—
687C22×C4—44no—
688C22×C4—2928no—
689C22×C4—2928no—
690C22×C4—2924no—
691C22×C4—738no—
692C22×C4—7316no—
693C22×C4—7316no—
694C22×C4—732no—
695C22×C4—731no—
696C22×C4—731no—
697C22×C4—7316no—
698C22×C4—738no—
699C22×C4—734no—
700C22×C4—734no—
701C22×C4—732no—
702C22×C4—731no—
703C22×C4—731no—
704C22×C4—734no—
705C22×C4—732no—
706C22×C4—738no—
707C22×C4—738no—
708C22×C4—1468no—
709C22×C4—1468no—
710C22×C4—1464no—
711C22×C4—1464no—
712C22×C4Q8×D7318yescomplemented
713C22×C4C23×D7312yes—
714C22×C4C23×D7312yes—
715C22×C4C23×D7312yes—
716C22×C4C23×D7314yes—
717C22×C4C23×D7312yes—
718C22×C4C23×D7318yes—
719C22×C4C23×D7311yescharacteristic
720C22×C4C23×D7311yescharacteristic
721C22×C4C23×D7314yes—
722C4⋊C4—7316no—
723C4⋊C4—738no—
724C4⋊C4—7316no—
725C4⋊C4—7316no—
726C4⋊C4—7316no—
727C4⋊C4—738no—
728C4⋊C4—738no—
729C4⋊C4—738no—
730C4⋊C4—7316no—
731C4⋊C4—738no—
732C4⋊C4—738no—
733C4⋊C4—7316no—
734C4⋊C4—734no—
735C4⋊C4—738no—
736C4⋊C4—738no—
737C4⋊C4—7316no—
738C4⋊C4—734no—
739C4⋊C4—738no—
740C4⋊C4—738no—
741C4⋊C4C23×D7314yes—
742C4⋊C4C23×D7318yes—
743C4⋊C4C23×D73116yes—
744C4⋊C4C23×D7318yes—
745C4⋊C4C23×D7314yes—
746C4⋊C4C23×D7314yes—
747C4⋊C4C23×D7314yes—
748C4⋊C4C23×D73116yes—
749C4⋊C4C23×D73116yes—
750C22⋊C4—738no—
751C22⋊C4—7316no—
752C22⋊C4—738no—
753C22⋊C4—738no—
754C22⋊C4—7316no—
755C22⋊C4C23×D7318yes—
756C22⋊C4C23×D7318yes—
757C42—734no—
758C42—734no—
759C42—738no—
760C42—738no—
761C42—734no—
762C42—734no—
763C42—7316no—
764C42—7316no—
765C42—738no—
766C42C23×D7318yes—
767C42C23×D7318yes—
768C23—22no—
769C23—22no—
770C23—738no—
771C23—734no—
772C23—1464no—
773C23—1464no—
774C23C2×Q8×D7314yes—
775C23C24×D7312yes—
776C23C24×D7311yescharacteristic
777Q8—416no—
778Q8—29216no—
779Q8—29216no—
780Q8—7316no—
781Q8—14632no—
782Q8—14616no—
783Q8—14616no—
784D4—7332no—
785D4—7316no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—48no—
792C2×C4—29216no—
793C2×C4—29216no—
794C2×C4—2928no—
795C2×C4—738no—
796C2×C4—734no—
797C2×C4—734no—
798C2×C4—734no—
799C2×C4—732no—
800C2×C4—732no—
801C2×C4—7332no—
802C2×C4—734no—
803C2×C4—732no—
804C2×C4—732no—
805C2×C4—734no—
806C2×C4—738no—
807C2×C4—14616no—
808C2×C4—14616no—
809C2×C4—1468no—
810C2×C4—1468no—
811C2×C4—1464no—
812C2×C4—1468no—
813C2×C4—1462no—
814C2×C4—1462no—
815C2×C4—1464no—
816C2×C4C2×Q8×D7314yes—
817C2×C4C2×Q8×D7314yes—
818C2×C4C2×Q8×D73116yescomplemented
819C2×C4C24×D7314yes—
820C2×C4C24×D7314yes—
821C2×C4C24×D7314yes—
822C2×C4C24×D7318yes—
823C2×C4C24×D7314yes—
824C2×C4C24×D7312yes—
825C2×C4C24×D7312yes—
826C22—28no—
827C22—22no—
828C22—22no—
829C22—738no—
830C22—14616no—
831C22—1464no—
832C22—1464no—
833C22C22×Q8×D7314yes—
834C22C22×Q8×D7312yes—
835C22H(5,𝔽2)×D7312yes—
836C222−1+4×D7312yes—
837C22C25×D7311yescharacteristic
838C4—28no—
839C4—24no—
840C4—24no—
841C4—24no—
842C4—24no—
843C4—738no—
844C4—734no—
845C4—734no—
846C4—1464no—
847C4—1468no—
848C4—1462no—
849C4—1462no—
850C4—1464no—
851C4C22×Q8×D7314yes—
852C4C22×Q8×D7314yes—
853C2—24no—
854C2—1468no—
855C2#2262374614yesdirect product factor
856C2C23×Q8×D7311yescharacteristic
857C2C2×H(5,𝔽2)×D7311yescharacteristic
858C2C2×2−1+4×D7311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#544×C73C2
socleC23×C73C25
prime radicalC22×#11924028C22
hypercenterC2×#544D73
hypocenterC73C2×#3503
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #22623746C2direct (N × H)
2. C2×#17989317C2semidirect
3. C2×#17989314C2semidirect
4. C2×#17989293C2semidirect
5. C2×#17989291C2semidirect
6. C2×#17989252C2semidirect
7. C2×#17989250C2semidirect
8. C2×#17989217C2semidirect
9. C2×#17989215C2semidirect
10. C2×#17989214C2semidirect
11. C2×#17989143C2semidirect
12. C2×#17989140C2semidirect
13. C22×#14556590C2semidirect
14. C2×C4⋊Q8×D73C2semidirect
18. C2×#544×C73C2semidirect
22. #17989317C22semidirect
23. #17989314C22semidirect
24. #17989293C22semidirect
25. #17989291C22semidirect
26. #17989252C22semidirect
27. #17989250C22semidirect
28. #17989217C22semidirect
29. #17989215C22semidirect
30. #17989214C22semidirect
31. #17989143C22semidirect
32. #17989140C22semidirect
43. C2×#14556590C22semidirect
46. C4⋊Q8×D73C22semidirect
92. #544×C73C22semidirect
101. C2×#11924028Q8semidirect
235. #11924028C2×Q8semidirect
242. C2×Dic146C2×Q8semidirect
250. C2×D292C2×Q8semidirect
252. C2×C22⋊D73C2×Q8semidirect
272. C2×C4×D73C2×Q8semidirect
315. C22×C4×C73C2×Q8semidirect
356. C2×C4×C73C22×Q8semidirect
364. C22⋊D73C22×Q8semidirect
384. D292C22×Q8semidirect
389. C4×D73C22×Q8semidirect
395. Dic146C22×Q8semidirect
425. C2×C73#3503semidirect
440. C2×#544D73semidirect
448. C73C2×#3503semidirect
461. #544C2×D73semidirect
712. C22×C4Q8×D73semidirect
818. C2×C4C2×Q8×D73semidirect
855. C2#22623746direct (N × H)

Maximal subgroups

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

subgroupindex
#226237462
C2×#179893172
C2×#179893142
C2×#179892932
C2×#179892912
C2×#179892522
C2×#179892502
C2×#179892172
C2×#179892152
C2×#179892142
C2×#179891432
C2×#179891402
C22×#145565902
C2×C4⋊Q8×D732
C2×#179890682
C2×#179890672
C2×#179890552
C2×#544×C732
C2×#350373