Finite Group Databasebeta

← C2×#22623609 #33994388

Subgroups — C2×#22623609 #33994388

Order 18688.

11438 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556639C211yesmaximal, characteristic, complemented
2C22×#41×D73C211yesmaximal, characteristic, complemented
3#22623609C2132yesmaximal, direct product factor
4C2×#17989252C212yesmaximal, complemented
5C2×#17989245C212yesmaximal, complemented
6C2×#17989240C212yesmaximal, complemented
7C2×#17989235C214yesmaximal, complemented
8C2×#17989230C212yesmaximal, complemented
9C2×#17989229C214yesmaximal, complemented
10C2×#17989167C212yesmaximal, complemented
11C2×#17989165C211yesmaximal, characteristic, complemented
12C2×#17989160C212yesmaximal, complemented
13C2×#17989100C212yesmaximal, complemented
14C2×#17989099C211yesmaximal, characteristic, complemented
15C22×#14556567C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×D73C212yesmaximal, complemented
17C2×#17989067C211yesmaximal, characteristic, complemented
18C2×#536×C73C211yesmaximal, characteristic, complemented
19C2×#14556639—216no—
20C2×#14556639C22116yescomplemented
21C22×#11924029C2211yescharacteristic
22C22×#11924029C2212yescomplemented
23C22×#11924029C2212yescomplemented
24C22×#11924028C2212yes—
25C22×#11924028C2211yescharacteristic
26C22×#11924028C2211yescharacteristic, complemented
27C22×#11924028C2214yescomplemented
28C22×#11924027C2212yes—
29C22×#11924027C2211yescharacteristic
30C2×#41×D73—216no—
31C2×#41×D73C22116yescomplemented
32C22×Q8×D73C2211yescharacteristic
33C22×Q8×D73C2212yescomplemented
34C22×Q8×D73C2212yescomplemented
35C22×D4×D73C2212yes—
36C22×D4×D73C2211yescharacteristic
37C23×C4×D73C2212yes—
38C23×C4×D73C2211yescharacteristic
39#17989252C22132yescomplemented
40#17989245C22132yescomplemented
41#17989240C22132yescomplemented
42#17989235C22164yescomplemented
43#17989230C22132yescomplemented
44#17989229C22164yescomplemented
45#17989167C22132yescomplemented
46#17989165C22116yescomplemented
47#17989160C22132yescomplemented
48C2×#14556590C2214yescomplemented
49C2×#14556577C2214yescomplemented
50#17989100C22132yescomplemented
51#17989099C22116yescomplemented
52C2×#14556576C2214yescomplemented
53C2×#14556576C2214yescomplemented
54C2×#14556575C2212yescomplemented
55C2×#14556573C2214yescomplemented
56C2×#14556571C2211yescharacteristic
57C2×#14556571C2211yescharacteristic, complemented
58C2×#14556570C2212yescomplemented
59C2×#14556569C2214yes—
60C2×#14556569C2214yescomplemented
61C2×#14556568C2214yescomplemented
62C2×#14556567C2212yes—
63C2×#14556567C2212yes—
64C2×#14556567C2212yescomplemented
65C2×#14556567C2212yescomplemented
66C2×#14556567C2212yescomplemented
67C2×#14556567C22116yescomplemented
68C22⋊Q8×D73C22132yescomplemented
69C2×#14556566C2211yescharacteristic
70C2×#14556566C2211yescharacteristic, complemented
71C2×#14556566C2214yescomplemented
72C2×#14556565C2212yescomplemented
73C2×#14556564C2214yescomplemented
74C2×#14556564C2214yescomplemented
75C2×#14556563C2214yescomplemented
76C2×#14556562C2212yescomplemented
77C2×#14556561C2212yes—
78C2×#14556561C2214yes—
79#17989067C22116yescomplemented
80C2×C4×Dic146C2212yescomplemented
81C2×C4×D292C2212yes—
82C2×C4×D292C2212yescomplemented
83C2×C4×D292C2212yescomplemented
84C2×#14556553C2214yes—
85C2×#14556551C2214yescomplemented
86C2×#14556551C2214yescomplemented
87C2×#14556549C2212yescomplemented
88C22×C4⋊Dic73C2211yescharacteristic, complemented
89C22×#11924007C2212yescomplemented
90C2×C4⋊C4×D73C2212yescomplemented
91C2×C4⋊C4×D73C2214yescomplemented
92C22×#11924005C2212yes—
93C2×C22⋊C4×D73C2214yes—
94C22×#41×C73C2211yescharacteristic
95C23×Q8×C73C2211yescharacteristic, complemented
96#536×C73C22116yescomplemented
97C2×C4⋊Q8×C73C2212yescomplemented
98C2×#124×C73C2212yescomplemented
99C2×#123×C73C2214yescomplemented
100C2×C22⋊Q8×C73C2212yescomplemented
101C2×C22⋊Q8×C73C2212yescomplemented
102C2×#117×C73C2211yescharacteristic, complemented
103C24×D73C2312yes—
104C24×D73C2311yescharacteristic
105#14556639—2128no—
106C2×#11924029—28no—
107C2×#11924029—216no—
108C2×#11924029—216no—
109C2×#11924029C2318yes—
110C2×#11924029C23116yescomplemented
111C2×#11924029C23116yescomplemented
112C2×#11924028—232no—
113C2×#11924028—216no—
114C2×#11924028—28no—
115C2×#11924028D4116yescomplemented
116C2×#11924028C23116yes—
117C2×#11924028C2318yes—
118C2×#11924028C2318yescomplemented
119C2×#11924028C23132yescomplemented
120C2×#11924027—28no—
121C2×#11924027—216no—
122C2×#11924027C23116yes—
123C2×#11924027C2318yes—
124#41×D73—2128no—
125C22×Dic146C2312yes—
126C22×Dic146C2314yes—
127C22×Dic146C2311yescharacteristic
128C22×Dic146C2311yescharacteristic
129C2×Q8×D73—28no—
130C2×Q8×D73—216no—
131C2×Q8×D73—216no—
132C2×Q8×D73C2318yes—
133C2×Q8×D73C23116yescomplemented
134C2×Q8×D73C23116yescomplemented
135C22×D292C2312yes—
136C22×D292C2314yes—
137C22×D292C2311yescharacteristic
138C22×D292C2312yes—
139C22×D292C2312yes—
140C22×D292C2311yescharacteristic
141C22×C22⋊D73C2312yes—
142C22×C22⋊D73C2312yes—
143C22×C22⋊D73C2312yes—
144C22×C22⋊D73C2314yes—
145C22×C22⋊D73C2312yes—
146C2×D4×D73—28no—
147C2×D4×D73—216no—
148C2×D4×D73C23116yes—
149C2×D4×D73C2318yes—
150C23×Dic73C2311yescharacteristic
151C23×Dic73C2312yes—
152C23×Dic73C2312yes—
153C22×C4×D73—216no—
154C22×C4×D73—28no—
155C22×C4×D73C2311yescharacteristic
156C22×C4×D73C2312yes—
157C22×C4×D73C2311yescharacteristic
158C22×C4×D73C23116yes—
159C22×C4×D73C2318yes—
160C22×C4×D73C2312yes—
161C22×C4×D73C2311yescharacteristic
162C22×C4×D73C2311yescharacteristic
163C22×C4×D73C2314yes—
164C22×C4×D73C2314yes—
165C22×C4×D73C2312yes—
166C22×C4×D73C2314yes—
167C22×C4×D73C2312yes—
168#14556590C23132yescomplemented
169#14556577C23132yescomplemented
170#14556576C23132yescomplemented
171#14556576C23132yescomplemented
172#14556575C23116yescomplemented
173#14556573C23132yescomplemented
174#14556571C2318yes—
175#14556571C2318yescomplemented
176#14556570C23116yescomplemented
177#14556569C23132yes—
178#14556569C23132yescomplemented
179#14556568C23132yescomplemented
180#14556567C23116yes—
181#14556567C23116yes—
182#14556567C23116yescomplemented
183#14556567C23116yescomplemented
184#14556567C23116yescomplemented
185#14556566C2318yes—
186#14556566C2318yescomplemented
187#14556566C23132yescomplemented
188#14556565C23116yescomplemented
189#14556564C23132yescomplemented
190#14556564C23132yescomplemented
191#14556563C23132yescomplemented
192#14556562C23116yescomplemented
193#14556561C23116yes—
194#14556561C23132yes—
195C4×Dic146C23116yescomplemented
196C4×D292C23116yes—
197C4×D292C23116yescomplemented
198C4×D292C23116yescomplemented
199#14556553C23132yes—
200#14556551C23132yescomplemented
201#14556551C23132yescomplemented
202#14556549C23116yescomplemented
203C2×C4⋊Dic73C2312yes—
204C2×C4⋊Dic73C2312yes—
205C2×C4⋊Dic73C2312yes—
206C2×C4⋊Dic73C2312yes—
207C2×C4⋊Dic73C2318yescomplemented
208C2×#11924007C2314yes—
209C2×#11924007C2314yes—
210C2×#11924007C2314yes—
211C2×#11924007C2314yes—
212C2×#11924007C23116yescomplemented
213C4⋊C4×D73C23116yescomplemented
214C4⋊C4×D73C23132yescomplemented
215C2×C22⋊Dic73C2314yes—
216C2×#11924005C23116yes—
217C2×#11924005C2312yes—
218C2×#11924005C2314yes—
219C2×#11924005C2314yes—
220C2×#11924005C2314yes—
221C2×#11924005C2312yes—
222C2×#11924005C2314yes—
223C2×#11924005C2312yes—
224C2×#11924005C2312yes—
225C22⋊C4×D73C23132yes—
226C2×C4×Dic73C2314yes—
227C2×#41×C73—28no—
228C2×#41×C73C2318yes—
229C22×Q8×C73—28no—
230C22×Q8×C73C2311yescharacteristic
231C22×Q8×C73C2312yes—
232C22×Q8×C73C2312yes—
233C22×Q8×C73C2318yescomplemented
234C22×D4×C73C2312yes—
235C22×D4×C73C2311yescharacteristic
236C23×C4×C73C2312yes—
237C23×C4×C73C2312yes—
238C23×C4×C73C2311yescharacteristic
239C4⋊Q8×C73C23116yescomplemented
240#124×C73C23116yescomplemented
241#123×C73C23132yescomplemented
242C22⋊Q8×C73C23116yescomplemented
243C22⋊Q8×C73C23116yescomplemented
244#117×C73C2318yescomplemented
245C2×C4⋊C4×C73C2314yes—
246C2×C4⋊C4×C73C2311yescharacteristic
247C2×C4⋊C4×C73C2311yescharacteristic
248C2×C4⋊C4×C73C2314yes—
249C2×C22⋊C4×C73C2312yes—
250C2×C22⋊C4×C73C2314yes—
251C2×C22⋊C4×C73C2314yes—
252C2×C42×C73C2312yes—
253C23×D73—24no—
254C23×D73—28no—
255C23×D73—28no—
256C23×D73—24no—
257C23×D73—44no—
258C23×D73—42no—
259C23×D73C2411yescharacteristic
260C23×D73C2412yes—
261C23×D73C2418yes—
262C23×D73C2414yes—
263C23×D73C2412yes—
264C23×D73C2411yescharacteristic
265#11924029—232no—
266#11924029—264no—
267#11924029—264no—
268#11924028—232no—
269#11924028—2128no—
270#11924028—264no—
271#11924028C2×D4164yescomplemented
272#11924027—264no—
273#11924027—232no—
274C2×Dic146—24no—
275C2×Dic146—216no—
276C2×Dic146—28no—
277C2×Dic146C2×D418yes—
278C2×Dic146C24116yes—
279C2×Dic146C2418yes—
280C2×Dic146C2414yes—
281C2×Dic146C2414yes—
282Q8×D73—264no—
283Q8×D73—232no—
284Q8×D73—264no—
285C2×D292—28no—
286C2×D292—216no—
287C2×D292—28no—
288C2×D292—24no—
289C2×D292—44no—
290C2×D292C2×D418yes—
291C2×D292C2418yes—
292C2×D292C24116yes—
293C2×D292C2414yes—
294C2×D292C2418yes—
295C2×D292C2418yes—
296C2×D292C2414yes—
297C2×C22⋊D73—28no—
298C2×C22⋊D73—28no—
299C2×C22⋊D73—28no—
300C2×C22⋊D73—48no—
301C2×C22⋊D73C2×D4116yes—
302C2×C22⋊D73C2418yes—
303C2×C22⋊D73C2418yes—
304C2×C22⋊D73C2418yes—
305C2×C22⋊D73C24116yes—
306C2×C22⋊D73C2418yes—
307D4×D73—264no—
308D4×D73—232no—
309C22×Dic73—24no—
310C22×Dic73—28no—
311C22×Dic73—44no—
312C22×Dic73C2414yes—
313C22×Dic73C2412yes—
314C22×Dic73C2411yescharacteristic
315C22×Dic73C2411yescharacteristic
316C22×Dic73C2414yes—
317C22×Dic73C2418yes—
318C22×Dic73C2418yes—
319C22×Dic73C2412yes—
320C2×C4×D73—28no—
321C2×C4×D73—216no—
322C2×C4×D73—24no—
323C2×C4×D73—24no—
324C2×C4×D73—232no—
325C2×C4×D73—24no—
326C2×C4×D73—24no—
327C2×C4×D73—28no—
328C2×C4×D73—28no—
329C2×C4×D73—216no—
330C2×C4×D73—264no—
331C2×C4×D73—48no—
332C2×C4×D73C2×D4116yes—
333C2×C4×D73C24116yes—
334C2×C4×D73C2418yes—
335C2×C4×D73C24116yes—
336C2×C4×D73C2418yes—
337C2×C4×D73C2414yes—
338C2×C4×D73C2418yes—
339C2×C4×D73C2414yes—
340C2×C4×D73C2414yes—
341C2×C4×D73C2414yes—
342C2×C4×D73C24116yes—
343C2×C4×D73C2418yes—
344C4⋊Dic73C2418yes—
345C4⋊Dic73C2418yes—
346C4⋊Dic73C2418yes—
347C4⋊Dic73C2418yes—
348#11924007C24116yes—
349#11924007C24116yes—
350#11924007C24116yes—
351#11924007C24116yes—
352C22⋊Dic73C24116yes—
353#11924005C2418yes—
354#11924005C24116yes—
355#11924005C24116yes—
356#11924005C24116yes—
357#11924005C2418yes—
358#11924005C24116yes—
359#11924005C2418yes—
360#11924005C2418yes—
361C4×Dic73C24116yes—
362C24×C73C2412yes—
363C24×C73C2411yescharacteristic
364#41×C73—232no—
365C2×Q8×C73—28no—
366C2×Q8×C73—28no—
367C2×Q8×C73—232no—
368C2×Q8×C73—24no—
369C2×Q8×C73C2418yes—
370C2×Q8×C73C2418yes—
371C2×Q8×C73C2414yes—
372C2×D4×C73—28no—
373C2×D4×C73—24no—
374C2×D4×C73C2418yes—
375C2×D4×C73C2414yes—
376C22×C4×C73—28no—
377C22×C4×C73—28no—
378C22×C4×C73C2×D418yes—
379C22×C4×C73C2412yes—
380C22×C4×C73C2412yes—
381C22×C4×C73C2414yes—
382C22×C4×C73C2412yes—
383C22×C4×C73C2418yes—
384C22×C4×C73C2418yes—
385C22×C4×C73C2411yescharacteristic
386C22×C4×C73C2411yescharacteristic
387C22×C4×C73C2414yes—
388C4⋊C4×C73C2414yes—
389C4⋊C4×C73C2414yes—
390C4⋊C4×C73C24116yes—
391C4⋊C4×C73C24116yes—
392C22⋊C4×C73C2418yes—
393C22⋊C4×C73C24116yes—
394C22⋊C4×C73C24116yes—
395C42×C73C2418yes—
396C23×C73—22no—
397C23×C73—22no—
398C23×C73—24no—
399C23×C73—24no—
400C23×C73—24no—
401C23×C73C22×D414yes—
402C23×C73C2514yes—
403C23×C73C2512yes—
404C23×C73C2511yescharacteristic
405C22×D73—22no—
406C22×D73—24no—
407C22×D73—24no—
408C22×D73—22no—
409C22×D73—24no—
410C22×D73—28no—
411C22×D73—22no—
412C22×D73—24no—
413C22×D73—22no—
414C22×D73—24no—
415C22×D73—22no—
416C22×D73—216no—
417C22×D73—216no—
418C22×D73—28no—
419C22×D73—48no—
420C22×D73—44no—
421C22×D73—432no—
422C22×D73—416no—
423C22×D73C22×D418yes—
424C22×D732−1+414yescomplemented
425C22×D73C2512yes—
426C22×D73C2514yes—
427C22×D73C2514yes—
428C22×D73C2512yes—
429Q8×C73—216no—
430Q8×C73—216no—
431Q8×C73—28no—
432D4×C73—216no—
433D4×C73—28no—
434C2×C4×C73—24no—
435C2×C4×C73—28no—
436C2×C4×C73—216no—
437C2×C4×C73—24no—
438C2×C4×C73—24no—
439C2×C4×C73—216no—
440C2×C4×C73C22×D414yes—
441C2×C4×C73C22×D414yes—
442C2×C4×C73C22×D4116yes—
443C2×C4×C73C2514yes—
444C2×C4×C73C2514yes—
445C2×C4×C73C2518yes—
446C2×C4×C73C2514yes—
447C2×C4×C73C2512yes—
448C2×C4×C73C2512yes—
449C22⋊D73—216no—
450C22⋊D73—216no—
451C22⋊D73—216no—
452C22⋊D73—416no—
453C22⋊D73C22×D4132yes—
454C2×Dic73—22no—
455C2×Dic73—24no—
456C2×Dic73—22no—
457C2×Dic73—28no—
458C2×Dic73—28no—
459C2×Dic73—216no—
460C2×Dic73—48no—
461C2×Dic73C22×D418yes—
462C2×Dic73C2518yes—
463C2×Dic73C2514yes—
464C2×Dic73C2512yes—
465C2×Dic73C2512yes—
466C2×Dic73C2514yes—
467D292—216no—
468D292—232no—
469D292—216no—
470D292—28no—
471D292—48no—
472D292C22×D4116yes—
473C4×D73—216no—
474C4×D73—232no—
475C4×D73—28no—
476C4×D73—28no—
477C4×D73—28no—
478C4×D73—28no—
479C4×D73—216no—
480C4×D73—216no—
481C4×D73—232no—
482C4×D73—416no—
483C4×D73C22×D4132yes—
484Dic146—28no—
485Dic146—232no—
486Dic146—216no—
487Dic146C22×D4116yes—
488C22×C73—22no—
489C22×C73—22no—
490C22×C73—28no—
491C22×C73—24no—
492C22×C73—24no—
493C22×C73—24no—
494C22×C73—48no—
495C22×C73C23×D414yes—
496C22×C73C23×D412yes—
497C22×C73C2×2−1+412yes—
498C22×C73#58512yes—
499C22×C73C2611yescharacteristic
500C2×D73—22no—
501C2×D73—24no—
502C2×D73—24no—
503C2×D73—22no—
504C2×D73—28no—
505C2×D73—216no—
506C2×D73—24no—
507C2×D73—22no—
508C2×D73—24no—
509C2×D73—22no—
510C2×D73—22no—
511C2×D73—24no—
512C2×D73—432no—
513C2×D73—416no—
514C2×D73—48no—
515C2×D73—44no—
516C2×D73C23×D418yes—
517C2×D73C2×2−1+414yescomplemented
518C4×C73—24no—
519C4×C73—28no—
520C4×C73—24no—
521C4×C73—24no—
522C4×C73C23×D414yes—
523C4×C73C23×D414yes—
524Dic73—24no—
525Dic73—22no—
526Dic73—22no—
527Dic73—28no—
528Dic73C23×D418yes—
529C2×#3489—731nomaximal, Sylow
530C2×C73—24no—
531C2×C73—44no—
532C2×C73#348914yescomplemented
533C2×C73C24×D411yescharacteristic
534C2×C73C22×2−1+411yescharacteristic
535C2×C73C2×#58511yescharacteristic
536D73—24no—
537D73—28no—
538D73—44no—
539D73—42no—
540C22×2−1+4—731no—
541C23×#41—731no—
542#3489—7332no—
543C2×D4×Q8—732no—
544C2×#548—732no—
545C2×#547—732no—
546C2×#547—734no—
547C2×#546—732no—
548C2×#546—734no—
549C2×#537—731no—
550C2×#537—732no—
551C2×#536—732no—
552C2×#536D7311yescharacteristic, complemented
553C2×#525—732no—
554C2×#525—731no—
555C22×C22⋊Q8—731no—
556C22×C22⋊Q8—732no—
557C2×#520—731no—
558C73C2×#348911yescharacteristic, complemented, Sylow
559C2×2−1+4—7316no—
560C2×2−1+4—14616no—
561C22×#41—7316no—
562C22×#41—731no—
563C22×#41—732no—
564C22×#41—732no—
565C22×#41—732no—
566C22×#41—731no—
567C22×#41—731no—
568C22×#41—732no—
569C22×#41—731no—
570C22×#41—734no—
571C22×#41—14616no—
572C22×#41C2×D7311yescharacteristic
573C23×Q8—731no—
574C23×Q8—732no—
575C23×Q8—732no—
576C23×Q8C2×D7311yescharacteristic, complemented
577C23×D4—732no—
578C23×D4—731no—
579C24×C4—732no—
580C24×C4—731no—
581D4×Q8—7332no—
582#548—7332no—
583#547—7332no—
584#547—7364no—
585#546—7332no—
586#546—7364no—
587#537—7316no—
588#537—7332no—
589#536—7332no—
590#536C2×D73116yescomplemented
591C2×C4⋊Q8—734no—
592C2×C4⋊Q8C2×D7312yescomplemented
593C2×#124—734no—
594C2×#124C2×D7312yescomplemented
595#525—7332no—
596#525—7316no—
597C2×#123—734no—
598C2×#123—734no—
599C2×#123—732no—
600C2×#123—734no—
601C2×#123C2×D7314yescomplemented
602C2×C22⋊Q8—732no—
603C2×C22⋊Q8—732no—
604C2×C22⋊Q8—732no—
605C2×C22⋊Q8—732no—
606C2×C22⋊Q8—732no—
607C2×C22⋊Q8—7316no—
608C2×C22⋊Q8—732no—
609C2×C22⋊Q8—7332no—
610C2×C22⋊Q8—731no—
611C2×C22⋊Q8—734no—
612C2×C22⋊Q8—731no—
613C2×C22⋊Q8—734no—
614C2×C22⋊Q8—734no—
615C2×C22⋊Q8C2×D7312yescomplemented
616C2×C22⋊Q8C2×D7312yescomplemented
617C2×#121—734no—
618C2×#121—732no—
619C2×#121—732no—
620C2×#121—731no—
621C2×#121—731no—
622C2×#121—734no—
623C2×#121—734no—
624C2×#121—734no—
625C2×#120—734no—
626C2×#120—732no—
627#520—7316no—
628C2×C4×Q8—732no—
629C2×C4×D4—734no—
630C2×C4×D4—734no—
631C2×C4×D4—734no—
632C2×C4×D4—732no—
633C2×C4×D4—732no—
634C2×C4×D4—732no—
635C2×#117—732no—
636C2×#117C2×D7311yescharacteristic, complemented
637C22×C4⋊C4—731no—
638C22×C4⋊C4—732no—
639C22×C4⋊C4—732no—
640C22×C4⋊C4—734no—
641C22×C22⋊C4—732no—
642C22×C22⋊C4—734no—
643C25—732no—
644C25—731no—
6452−1+4—146128no—
646C2×#41—28no—
647C2×#41—7316no—
648C2×#41—7316no—
649C2×#41—738no—
650C2×#41—7316no—
651C2×#41—738no—
652C2×#41—7316no—
653C2×#41—738no—
654C2×#41—738no—
655C2×#41—7316no—
656C2×#41—7332no—
657C2×#41—14616no—
658C2×#41—14632no—
659C2×#41—14616no—
660C2×#41—14616no—
661C2×#41—1468no—
662C2×#41—1468no—
663C2×#41—14616no—
664C2×#41—146128no—
665C2×#41—1468no—
666C2×#41C22×D7318yes—
667C22×Q8—28no—
668C22×Q8—7316no—
669C22×Q8—7316no—
670C22×Q8—738no—
671C22×Q8—731no—
672C22×Q8—731no—
673C22×Q8—734no—
674C22×Q8—732no—
675C22×Q8—14616no—
676C22×Q8—1468no—
677C22×Q8—14616no—
678C22×Q8C22×D7312yes—
679C22×Q8C22×D7312yes—
680C22×Q8C22×D7311yescharacteristic
681C22×Q8C22×D7318yescomplemented
682C22×D4—734no—
683C22×D4—732no—
684C22×D4—732no—
685C22×D4—732no—
686C22×D4—732no—
687C22×D4—7316no—
688C22×D4—738no—
689C22×D4—732no—
690C22×D4—731no—
691C22×D4—732no—
692C22×D4—734no—
693C22×D4—731no—
694C22×D4—732no—
695C22×D4—14616no—
696C22×D4—1468no—
697C22×D4C22×D7312yes—
698C22×D4C22×D7311yescharacteristic
699C23×C4—732no—
700C23×C4—734no—
701C23×C4—732no—
702C23×C4—731no—
703C23×C4—732no—
704C23×C4—734no—
705C23×C4—732no—
706C23×C4—734no—
707C23×C4—732no—
708C23×C4—732no—
709C23×C4—731no—
710C23×C4—731no—
711C23×C4—731no—
712C23×C4—731no—
713C23×C4—7316no—
714C23×C4—738no—
715C23×C4—14616no—
716C23×C4—1468no—
717C23×C4C22×D7312yes—
718C23×C4C22×D7312yes—
719C23×C4C22×D7311yescharacteristic
720C4⋊Q8—7332no—
721C4⋊Q8C22×D73116yescomplemented
722#124—7332no—
723#124C22×D73116yescomplemented
724#123—7332no—
725#123—7332no—
726#123—7316no—
727#123—7332no—
728#123C22×D73132yescomplemented
729C22⋊Q8—7316no—
730C22⋊Q8—7316no—
731C22⋊Q8—7316no—
732C22⋊Q8—7316no—
733C22⋊Q8—7316no—
734C22⋊Q8—7316no—
735C22⋊Q8—738no—
736C22⋊Q8—7332no—
737C22⋊Q8—738no—
738C22⋊Q8—7332no—
739C22⋊Q8—7332no—
740C22⋊Q8C22×D73116yescomplemented
741C22⋊Q8C22×D73116yescomplemented
742#121—7332no—
743#121—7316no—
744#121—7316no—
745#121—738no—
746#121—738no—
747#121—7332no—
748#121—7332no—
749#121—7332no—
750#120—7332no—
751#120—7316no—
752C4×Q8—7316no—
753C4×D4—7332no—
754C4×D4—7332no—
755C4×D4—7332no—
756C4×D4—7316no—
757C4×D4—7316no—
758C4×D4—7316no—
759#117—7316no—
760#117C22×D7318yescomplemented
761C2×C4⋊C4—732no—
762C2×C4⋊C4—734no—
763C2×C4⋊C4—732no—
764C2×C4⋊C4—734no—
765C2×C4⋊C4—732no—
766C2×C4⋊C4—738no—
767C2×C4⋊C4—734no—
768C2×C4⋊C4—734no—
769C2×C4⋊C4—7316no—
770C2×C4⋊C4—732no—
771C2×C4⋊C4—7316no—
772C2×C4⋊C4—7332no—
773C2×C4⋊C4C22×D7311yescharacteristic
774C2×C4⋊C4C22×D7314yes—
775C2×C4⋊C4C22×D7311yescharacteristic
776C2×C4⋊C4C22×D7314yes—
777C2×C22⋊C4—734no—
778C2×C22⋊C4—734no—
779C2×C22⋊C4—732no—
780C2×C22⋊C4—734no—
781C2×C22⋊C4—7316no—
782C2×C22⋊C4—734no—
783C2×C22⋊C4—732no—
784C2×C22⋊C4—732no—
785C2×C22⋊C4—734no—
786C2×C22⋊C4—732no—
787C2×C22⋊C4—7332no—
788C2×C22⋊C4C22×D7314yes—
789C2×C22⋊C4C22×D7312yes—
790C2×C22⋊C4C22×D7314yes—
791C2×C42—734no—
792C2×C42C22×D7312yes—
793C24—2922no—
794C24—2924no—
795C24—738no—
796C24—734no—
797C24—731no—
798C24—732no—
799C24—731no—
800C24—732no—
801C24—1468no—
802C24—1464no—
803C24—1468no—
804C24—1464no—
805C24C23×D7312yes—
806C24C23×D7311yescharacteristic
807#41—232no—
808#41—7364no—
809#41—14664no—
810#41—146128no—
811#41—14664no—
812#41—14664no—
813#41—14632no—
814#41—14632no—
815#41—14664no—
816#41—14632no—
817C2×Q8—28no—
818C2×Q8—28no—
819C2×Q8—232no—
820C2×Q8—24no—
821C2×Q8—738no—
822C2×Q8—734no—
823C2×Q8—734no—
824C2×Q8—7316no—
825C2×Q8—738no—
826C2×Q8—14616no—
827C2×Q8—1468no—
828C2×Q8—14664no—
829C2×Q8—14632no—
830C2×Q8—14664no—
831C2×Q8—1464no—
832C2×Q8C23×D7318yes—
833C2×Q8C23×D7318yes—
834C2×Q8C23×D7314yes—
835C2×D4—28no—
836C2×D4—24no—
837C2×D4—2924no—
838C2×D4—2928no—
839C2×D4—7316no—
840C2×D4—7316no—
841C2×D4—738no—
842C2×D4—738no—
843C2×D4—738no—
844C2×D4—738no—
845C2×D4—738no—
846C2×D4—738no—
847C2×D4—734no—
848C2×D4—738no—
849C2×D4—7316no—
850C2×D4—734no—
851C2×D4—738no—
852C2×D4—1468no—
853C2×D4—1468no—
854C2×D4—14616no—
855C2×D4—1468no—
856C2×D4—14664no—
857C2×D4—14632no—
858C2×D4—1468no—
859C2×D4—1468no—
860C2×D4—1464no—
861C2×D4C23×D7318yes—
862C2×D4C23×D7314yes—
863C22×C4—28no—
864C22×C4—28no—
865C22×C4—2928no—
866C22×C4—2924no—
867C22×C4—738no—
868C22×C4—7316no—
869C22×C4—732no—
870C22×C4—7316no—
871C22×C4—738no—
872C22×C4—734no—
873C22×C4—738no—
874C22×C4—734no—
875C22×C4—732no—
876C22×C4—731no—
877C22×C4—731no—
878C22×C4—7316no—
879C22×C4—738no—
880C22×C4—7316no—
881C22×C4—738no—
882C22×C4—738no—
883C22×C4—734no—
884C22×C4—734no—
885C22×C4—734no—
886C22×C4—734no—
887C22×C4—1468no—
888C22×C4—14664no—
889C22×C4—14616no—
890C22×C4—1468no—
891C22×C4—14616no—
892C22×C4—1468no—
893C22×C4—1464no—
894C22×C4—1464no—
895C22×C4—1464no—
896C22×C4—1464no—
897C22×C4—1464no—
898C22×C4—14632no—
899C22×C4—1468no—
900C22×C4D4×D7318yes—
901C22×C4C23×D7318yes—
902C22×C4C23×D7318yes—
903C22×C4C23×D7312yes—
904C22×C4C23×D7312yes—
905C22×C4C23×D7314yes—
906C22×C4C23×D7312yes—
907C22×C4C23×D7314yes—
908C22×C4C23×D7311yescharacteristic
909C22×C4C23×D7311yescharacteristic
910C4⋊C4—7316no—
911C4⋊C4—7316no—
912C4⋊C4—7316no—
913C4⋊C4—7316no—
914C4⋊C4—738no—
915C4⋊C4—738no—
916C4⋊C4—738no—
917C4⋊C4—738no—
918C4⋊C4C23×D7314yes—
919C4⋊C4C23×D73116yes—
920C4⋊C4C23×D7314yes—
921C4⋊C4C23×D73116yes—
922C22⋊C4—7316no—
923C22⋊C4—7316no—
924C22⋊C4—738no—
925C22⋊C4—7316no—
926C22⋊C4—7316no—
927C22⋊C4—738no—
928C22⋊C4—738no—
929C22⋊C4—7316no—
930C22⋊C4—738no—
931C22⋊C4C23×D73116yes—
932C22⋊C4C23×D7318yes—
933C22⋊C4C23×D73116yes—
934C42—7316no—
935C42C23×D7318yes—
936C23—22no—
937C23—22no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—29216no—
942C23—2924no—
943C23—2928no—
944C23—29232no—
945C23—738no—
946C23—734no—
947C23—732no—
948C23—734no—
949C23—732no—
950C23—734no—
951C23—14616no—
952C23—1468no—
953C23—14616no—
954C23—1464no—
955C23—1468no—
956C23—1462no—
957C23—1464no—
958C23—1462no—
959C23—1464no—
960C23—1462no—
961C23—1462no—
962C23—1464no—
963C23—1464no—
964C23—1462no—
965C23C2×D4×D7314yes—
966C23C24×D7314yes—
967C23C24×D7312yes—
968C23C24×D7311yescharacteristic
969Q8—216no—
970Q8—216no—
971Q8—28no—
972Q8—7316no—
973Q8—14632no—
974Q8—14616no—
975Q8—1468no—
976D4—216no—
977D4—28no—
978D4—2928no—
979D4—29216no—
980D4—7332no—
981D4—7316no—
982D4—14616no—
983D4—14632no—
984D4—14616no—
985D4—14616no—
986D4—14616no—
987D4—14616no—
988D4—1468no—
989C2×C4—24no—
990C2×C4—28no—
991C2×C4—216no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—216no—
995C2×C4—29216no—
996C2×C4—2928no—
997C2×C4—738no—
998C2×C4—734no—
999C2×C4—7332no—
1000C2×C4—738no—
1001C2×C4—734no—
1002C2×C4—732no—
1003C2×C4—732no—
1004C2×C4—14616no—
1005C2×C4—14632no—
1006C2×C4—14616no—
1007C2×C4—14632no—
1008C2×C4—14616no—
1009C2×C4—1462no—
1010C2×C4—1462no—
1011C2×C4—1464no—
1012C2×C4—1468no—
1013C2×C4—1468no—
1014C2×C4—1468no—
1015C2×C4—1468no—
1016C2×C4—1468no—
1017C2×C4—1468no—
1018C2×C4—14616no—
1019C2×C4C2×D4×D7314yes—
1020C2×C4C2×D4×D7314yes—
1021C2×C4C2×D4×D73116yes—
1022C2×C4C24×D7314yes—
1023C2×C4C24×D7314yes—
1024C2×C4C24×D7318yes—
1025C2×C4C24×D7314yes—
1026C2×C4C24×D7312yes—
1027C2×C4C24×D7312yes—
1028C22—28no—
1029C22—22no—
1030C22—22no—
1031C22—24no—
1032C22—24no—
1033C22—24no—
1034C22—48no—
1035C22—29216no—
1036C22—29232no—
1037C22—2924no—
1038C22—2928no—
1039C22—738no—
1040C22—734no—
1041C22—1464no—
1042C22—1462no—
1043C22—1464no—
1044C22—1462no—
1045C22—1464no—
1046C22—1462no—
1047C22—1468no—
1048C22—14616no—
1049C22—1462no—
1050C22—1464no—
1051C22—1464no—
1052C22—1462no—
1053C22C22×D4×D7314yes—
1054C22C22×D4×D7312yes—
1055C222−1+4×D7312yes—
1056C22#1798942412yes—
1057C22C25×D7311yescharacteristic
1058C4—24no—
1059C4—28no—
1060C4—24no—
1061C4—24no—
1062C4—738no—
1063C4—1462no—
1064C4—1462no—
1065C4—1464no—
1066C4—1468no—
1067C4C22×D4×D7314yes—
1068C4C22×D4×D7314yes—
1069C2—24no—
1070C2—44no—
1071C2—2922no—
1072C2—2924no—
1073C2—1464no—
1074C2—1468no—
1075C2#2262360914yesdirect product factor
1076C2C23×D4×D7311yescharacteristic
1077C2C2×2−1+4×D7311yescharacteristic
1078C2C2×#1798942411yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#536×C73C2
socleC23×C73C25
hypercenterC2×#536D73
hypocenterC73C2×#3489
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C22×#14556639C2semidirect
2. C22×#41×D73C2semidirect
3. #22623609C2direct (N × H)
4. C2×#17989252C2semidirect
5. C2×#17989245C2semidirect
6. C2×#17989240C2semidirect
7. C2×#17989235C2semidirect
8. C2×#17989230C2semidirect
9. C2×#17989229C2semidirect
10. C2×#17989167C2semidirect
11. C2×#17989165C2semidirect
12. C2×#17989160C2semidirect
13. C2×#17989100C2semidirect
14. C2×#17989099C2semidirect
15. C22×#14556567C2semidirect
16. C2×C22⋊Q8×D73C2semidirect
17. C2×#17989067C2semidirect
18. C2×#536×C73C2semidirect
20. C2×#14556639C22semidirect
22. C22×#11924029C22semidirect
23. C22×#11924029C22semidirect
26. C22×#11924028C22semidirect
27. C22×#11924028C22semidirect
31. C2×#41×D73C22semidirect
33. C22×Q8×D73C22semidirect
34. C22×Q8×D73C22semidirect
39. #17989252C22semidirect
40. #17989245C22semidirect
41. #17989240C22semidirect
42. #17989235C22semidirect
43. #17989230C22semidirect
44. #17989229C22semidirect
45. #17989167C22semidirect
46. #17989165C22semidirect
47. #17989160C22semidirect
48. C2×#14556590C22semidirect
49. C2×#14556577C22semidirect
50. #17989100C22semidirect
51. #17989099C22semidirect
52. C2×#14556576C22semidirect
53. C2×#14556576C22semidirect
54. C2×#14556575C22semidirect
55. C2×#14556573C22semidirect
57. C2×#14556571C22semidirect
58. C2×#14556570C22semidirect
60. C2×#14556569C22semidirect
61. C2×#14556568C22semidirect
64. C2×#14556567C22semidirect
65. C2×#14556567C22semidirect
66. C2×#14556567C22semidirect
67. C2×#14556567C22semidirect
68. C22⋊Q8×D73C22semidirect
70. C2×#14556566C22semidirect
71. C2×#14556566C22semidirect
72. C2×#14556565C22semidirect
73. C2×#14556564C22semidirect
74. C2×#14556564C22semidirect
75. C2×#14556563C22semidirect
76. C2×#14556562C22semidirect
79. #17989067C22semidirect
80. C2×C4×Dic146C22semidirect
82. C2×C4×D292C22semidirect
83. C2×C4×D292C22semidirect
85. C2×#14556551C22semidirect
86. C2×#14556551C22semidirect
87. C2×#14556549C22semidirect
88. C22×C4⋊Dic73C22semidirect
89. C22×#11924007C22semidirect
90. C2×C4⋊C4×D73C22semidirect
91. C2×C4⋊C4×D73C22semidirect
95. C23×Q8×C73C22semidirect
96. #536×C73C22semidirect
97. C2×C4⋊Q8×C73C22semidirect
98. C2×#124×C73C22semidirect
99. C2×#123×C73C22semidirect
100. C2×C22⋊Q8×C73C22semidirect
101. C2×C22⋊Q8×C73C22semidirect
102. C2×#117×C73C22semidirect
110. C2×#11924029C23semidirect
111. C2×#11924029C23semidirect
115. C2×#11924028D4semidirect
118. C2×#11924028C23semidirect
119. C2×#11924028C23semidirect
133. C2×Q8×D73C23semidirect
134. C2×Q8×D73C23semidirect
168. #14556590C23semidirect
169. #14556577C23semidirect
170. #14556576C23semidirect
171. #14556576C23semidirect
172. #14556575C23semidirect
173. #14556573C23semidirect
175. #14556571C23semidirect
176. #14556570C23semidirect
178. #14556569C23semidirect
179. #14556568C23semidirect
182. #14556567C23semidirect
183. #14556567C23semidirect
184. #14556567C23semidirect
186. #14556566C23semidirect
187. #14556566C23semidirect
188. #14556565C23semidirect
189. #14556564C23semidirect
190. #14556564C23semidirect
191. #14556563C23semidirect
192. #14556562C23semidirect
195. C4×Dic146C23semidirect
197. C4×D292C23semidirect
198. C4×D292C23semidirect
200. #14556551C23semidirect
201. #14556551C23semidirect
202. #14556549C23semidirect
207. C2×C4⋊Dic73C23semidirect
212. C2×#11924007C23semidirect
213. C4⋊C4×D73C23semidirect
214. C4⋊C4×D73C23semidirect
233. C22×Q8×C73C23semidirect
239. C4⋊Q8×C73C23semidirect
240. #124×C73C23semidirect
241. #123×C73C23semidirect
242. C22⋊Q8×C73C23semidirect
243. C22⋊Q8×C73C23semidirect
244. #117×C73C23semidirect
271. #11924028C2×D4semidirect
424. C22×D732−1+4semidirect
517. C2×D73C2×2−1+4semidirect
532. C2×C73#3489semidirect
552. C2×#536D73semidirect
558. C73C2×#3489semidirect
576. C23×Q8C2×D73semidirect
590. #536C2×D73semidirect
592. C2×C4⋊Q8C2×D73semidirect
594. C2×#124C2×D73semidirect
601. C2×#123C2×D73semidirect
615. C2×C22⋊Q8C2×D73semidirect
616. C2×C22⋊Q8C2×D73semidirect
636. C2×#117C2×D73semidirect
681. C22×Q8C22×D73semidirect
721. C4⋊Q8C22×D73semidirect
723. #124C22×D73semidirect
728. #123C22×D73semidirect
740. C22⋊Q8C22×D73semidirect
741. C22⋊Q8C22×D73semidirect
760. #117C22×D73semidirect
1075. C2#22623609direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566392
C22×#41×D732
#226236092
C2×#179892522
C2×#179892452
C2×#179892402
C2×#179892352
C2×#179892302
C2×#179892292
C2×#179891672
C2×#179891652
C2×#179891602
C2×#179891002
C2×#179890992
C22×#145565672
C2×C22⋊Q8×D732
C2×#179890672
C2×#536×C732
C2×#348973