Finite Group Databasebeta

← C2×#22602731 #32905146

Subgroups — C2×#22602731 #32905146

Order 18176.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602731C2132yesmaximal, direct product factor
2C2×#17986746C214yesmaximal, complemented
3C2×#17986714C211yesmaximal, characteristic, complemented
4C2×#17986714C212yesmaximal, complemented
5C2×#17986709C211yesmaximal, characteristic, complemented
6C2×#17986695C212yesmaximal, complemented
7C2×#17986687C212yesmaximal, complemented
8C2×Q8×D284C211yesmaximal, characteristic, complemented
9C2×#17986657C212yesmaximal, complemented
10C2×#17986653C211yesmaximal, characteristic, complemented
11C2×#17986627C212yesmaximal, complemented
12C2×#17986615C214yesmaximal, complemented
13C2×#17986604C212yesmaximal, complemented
14C2×#17986578C212yesmaximal, complemented
15C2×#17986572C212yesmaximal, complemented
16C2×#17986556C211yesmaximal, characteristic, complemented
17C2×#17986549C211yesmaximal, characteristic, complemented
18C2×#529×C71C211yesmaximal, characteristic, complemented
19C22×#11765865C2212yes—
20C22×#11765864C2212yes—
21C22×Q8×D71C2212yes—
22#17986746C22164yescomplemented
23#17986714C22116yescomplemented
24#17986714C22132yescomplemented
25#17986709C22116yescomplemented
26#17986695C22132yescomplemented
27#17986687C22132yescomplemented
28Q8×D284C22116yescomplemented
29#17986657C22132yescomplemented
30#17986653C22116yescomplemented
31#17986627C22132yescomplemented
32#17986615C22164yescomplemented
33#17986604C22132yescomplemented
34#17986578C22132yescomplemented
35#17986572C22132yescomplemented
36#17986556C22116yescomplemented
37#17986549C22116yescomplemented
38C2×#14556128C2211yescharacteristic
39C2×#14556128C2212yes—
40C2×#14556128C2211yescharacteristic
41C2×#14556128C2211yescharacteristic
42C2×#14556127C2214yes—
43C2×#14556125C2211yescharacteristic
44C2×#14556123C2214yes—
45C2×#14556120C2212yes—
46C2×#14556120C2212yes—
47C2×#14556119C2214yes—
48C2×#14556116C2212yes—
49C2×#14556114C2214yes—
50C2×#14556114C2214yes—
51C2×#14556114C2214yes—
52C2×#14556113C2214yes—
53C2×#14556113C2214yes—
54C2×#14556112C2214yes—
55C2×#14556110C2214yes—
56C2×#14556108C2212yes—
57C2×#14556108C2212yes—
58C2×#14556108C2214yes—
59C2×#14556107C2212yes—
60C2×#14556107C2212yes—
61C2×#14556106C2214yes—
62C2×#14556105C2214yes—
63C2×#14556105C2214yes—
64C2×#14556104C2212yes—
65C2×#14556102C2212yes—
66C2×#14556102C2211yescharacteristic
67C2×#14556102C2212yes—
68C2×#14556102C2211yescharacteristic
69C2×#14556102C2212yes—
70C2×#14556101C2214yes—
71C2×#14556101C2214yes—
72C2×#14556100C2214yes—
73C2×#14556099C2212yes—
74C2×#14556099C2214yes—
75C2×C4×Dic142C2212yes—
76C2×C4×Dic142C2212yes—
77C2×C4×D284C2211yescharacteristic
78C2×C4×D284C2212yes—
79C2×C4×D284C2212yes—
80C2×C4×D284C2211yescharacteristic
81C2×C4×D284C2212yes—
82C2×(C22⋊D71)⋊C4C2214yes—
83C2×#14556087C2212yes—
84C2×#14556087C2212yes—
85C2×#14556086C2212yes—
86C2×#14556086C2214yes—
87C22×C4⋊Dic71C2212yes—
88C2×C4⋊C4×D71C2212yes—
89#529×C71C22116yescomplemented
90C2×#126×C71C2212yes—
91C2×#125×C71C2211yescharacteristic
92C2×#124×C71C2211yescharacteristic
93C2×#123×C71C2212yes—
94C2×C22⋊Q8×C71C2211yescharacteristic
95C2×#121×C71C2211yescharacteristic
96C2×C4×Q8×C71C2211yescharacteristic
97C2×C4×D4×C71C2211yescharacteristic
98C2×C4×D4×C71C2212yes—
99C2×#117×C71C2212yes—
100C22×C42×C71C2211yescharacteristic
101C2×#11765865—48no—
102C2×#11765865C23116yes—
103C2×#11765864—48no—
104C2×#11765864C23116yes—
105C22×Dic142C2312yes—
106C22×Dic142C2314yes—
107C22×Dic142C2312yes—
108C22×Dic142C2312yes—
109C2×Q8×D71—48no—
110C2×Q8×D71C23116yes—
111C22×D284C2311yescharacteristic
112C22×D284C2311yescharacteristic
113C22×D284C2312yes—
114C22×D284C2312yes—
115C22×C22⋊D71C2314yes—
116C22×C22⋊D71C2312yes—
117C22×C22⋊D71C2312yes—
118C22×C22⋊D71C2314yes—
119C23×Dic71C2314yes—
120C22×C4×D71C2312yes—
121C22×C4×D71C2312yes—
122C22×C4×D71C2314yes—
123C22×C4×D71C2314yes—
124#14556128C2318yes—
125#14556128C23116yes—
126#14556128C2318yes—
127#14556128C2318yes—
128#14556127C23132yes—
129#14556125C2318yes—
130#14556123C23132yes—
131#14556120C23116yes—
132#14556120C23116yes—
133#14556119C23132yes—
134#14556116C23116yes—
135#14556114C23132yes—
136#14556114C23132yes—
137#14556114C23132yes—
138#14556113C23132yes—
139#14556113C23132yes—
140#14556112C23132yes—
141#14556110C23132yes—
142#14556108C23116yes—
143#14556108C23116yes—
144#14556108C23132yes—
145#14556107C23116yes—
146#14556107C23116yes—
147#14556106C23132yes—
148#14556105C23132yes—
149#14556105C23132yes—
150#14556104C23116yes—
151#14556102C23116yes—
152#14556102C23116yes—
153#14556102C2318yes—
154#14556102C2318yes—
155#14556102C23116yes—
156#14556101C23132yes—
157#14556101C23132yes—
158#14556100C23132yes—
159#14556099C23116yes—
160#14556099C23132yes—
161C4×Dic142C23116yes—
162C4×Dic142C23116yes—
163C4×D284C23116yes—
164C4×D284C23116yes—
165C4×D284C2318yes—
166C4×D284C23116yes—
167C4×D284C2318yes—
168(C22⋊D71)⋊C4C23132yes—
169#14556087C23116yes—
170#14556087C23116yes—
171#14556086C23116yes—
172#14556086C23132yes—
173C2×C4⋊Dic71C23116yes—
174C2×C4⋊Dic71C2312yes—
175C2×C4⋊Dic71C2311yescharacteristic
176C2×C4⋊Dic71C2312yes—
177C2×C4⋊Dic71C2314yes—
178C2×C4⋊Dic71C2314yes—
179C2×C4⋊Dic71C2312yes—
180C2×C4⋊Dic71C2311yescharacteristic
181C2×C4⋊Dic71C2312yes—
182C2×C4⋊Dic71C2312yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2314yes—
185C2×Dic71⋊C4C2314yes—
186C2×Dic71⋊C4C2314yes—
187C4⋊C4×D71C23116yes—
188C2×C22⋊Dic71C2314yes—
189C2×C22⋊Dic71C2314yes—
190C2×(C2×D71)⋊C4C2312yes—
191C2×(C2×D71)⋊C4C2314yes—
192C2×(C2×D71)⋊C4C2314yes—
193C2×(C2×D71)⋊C4C2312yes—
194C2×(C2×D71)⋊C4C2314yes—
195C2×(C2×D71)⋊C4C2314yes—
196C2×(C2×D71)⋊C4C2312yes—
197C2×(C2×D71)⋊C4C2312yes—
198C2×C4×Dic71C2314yes—
199C2×C4×Dic71C2314yes—
200C22×Q8×C71C2311yescharacteristic
201C22×D4×C71C2311yescharacteristic
202C22×D4×C71C2312yes—
203C23×C4×C71C2311yescharacteristic
204C23×C4×C71C2311yescharacteristic
205C23×C4×C71C2312yes—
206C23×C4×C71C2311yescharacteristic
207#126×C71C23116yes—
208#125×C71C2318yes—
209#124×C71C2318yes—
210#123×C71C23116yes—
211C22⋊Q8×C71C2318yes—
212#121×C71C2318yes—
213C4×Q8×C71C2318yes—
214C4×D4×C71C2318yes—
215C4×D4×C71C23116yes—
216#117×C71C23116yes—
217C2×C4⋊C4×C71C2312yes—
218C2×C4⋊C4×C71C2312yes—
219C2×C4⋊C4×C71C2311yescharacteristic
220C2×C4⋊C4×C71C2312yes—
221C2×C4⋊C4×C71C2311yescharacteristic
222C2×C4⋊C4×C71C2312yes—
223C2×C22⋊C4×C71C2312yes—
224C2×C22⋊C4×C71C2312yes—
225C2×C22⋊C4×C71C2312yes—
226C2×C22⋊C4×C71C2312yes—
227C2×C22⋊C4×C71C2312yes—
228C2×C42×C71C2311yescharacteristic
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2311yescharacteristic
231C2×C42×C71C2311yescharacteristic
232C2×C42×C71C2318yes—
233C2×C42×C71C2312yes—
234C23×D71C2412yes—
235C23×D71C2412yes—
236#11765865—432no—
237#11765864—432no—
238C2×Dic142—28no—
239C2×Dic142—48no—
240C2×Dic142—44no—
241C2×Dic142—44no—
242C2×Dic142C2418yes—
243C2×Dic142C24116yes—
244C2×Dic142C2418yes—
245C2×Dic142C2418yes—
246Q8×D71—432no—
247C2×D284—24no—
248C2×D284—24no—
249C2×D284—44no—
250C2×D284—44no—
251C2×D284C2414yes—
252C2×D284C2414yes—
253C2×D284C2418yes—
254C2×D284C2418yes—
255C2×C22⋊D71—48no—
256C2×C22⋊D71—48no—
257C2×C22⋊D71—44no—
258C2×C22⋊D71—44no—
259C2×C22⋊D71C24116yes—
260C2×C22⋊D71C2418yes—
261C2×C22⋊D71C2418yes—
262C2×C22⋊D71C24116yes—
263C22×Dic71—48no—
264C22×Dic71C2412yes—
265C22×Dic71C2414yes—
266C22×Dic71C2412yes—
267C22×Dic71C2414yes—
268C22×Dic71C24116yes—
269C2×C4×D71—28no—
270C2×C4×D71—28no—
271C2×C4×D71—48no—
272C2×C4×D71—48no—
273C2×C4×D71C2418yes—
274C2×C4×D71C2418yes—
275C2×C4×D71C24116yes—
276C2×C4×D71C24116yes—
277C4⋊Dic71C2418yes—
278C4⋊Dic71C2414yes—
279C4⋊Dic71C2418yes—
280C4⋊Dic71C24116yes—
281C4⋊Dic71C24116yes—
282C4⋊Dic71C2418yes—
283C4⋊Dic71C2414yes—
284C4⋊Dic71C2418yes—
285C4⋊Dic71C2418yes—
286Dic71⋊C4C24116yes—
287Dic71⋊C4C24116yes—
288Dic71⋊C4C24116yes—
289Dic71⋊C4C24116yes—
290C22⋊Dic71C24116yes—
291C22⋊Dic71C24116yes—
292(C2×D71)⋊C4C2418yes—
293(C2×D71)⋊C4C24116yes—
294(C2×D71)⋊C4C24116yes—
295(C2×D71)⋊C4C2418yes—
296(C2×D71)⋊C4C24116yes—
297(C2×D71)⋊C4C24116yes—
298(C2×D71)⋊C4C2418yes—
299(C2×D71)⋊C4C2418yes—
300C4×Dic71C24116yes—
301C4×Dic71C24116yes—
302C24×C71C2412yes—
303C24×C71C2411yescharacteristic
304C2×Q8×C71—24no—
305C2×Q8×C71C2414yes—
306C2×D4×C71—24no—
307C2×D4×C71—44no—
308C2×D4×C71C2414yes—
309C2×D4×C71C2418yes—
310C22×C4×C71—24no—
311C22×C4×C71—24no—
312C22×C4×C71—28no—
313C22×C4×C71—42no—
314C22×C4×C71C2412yes—
315C22×C4×C71C2412yes—
316C22×C4×C71C2411yescharacteristic
317C22×C4×C71C2411yescharacteristic
318C22×C4×C71C2411yescharacteristic
319C22×C4×C71C2414yes—
320C22×C4×C71C2411yescharacteristic
321C22×C4×C71C2414yes—
322C22×C4×C71C2412yes—
323C22×C4×C71C2418yes—
324C22×C4×C71C2414yes—
325C22×C4×C71C2411yescharacteristic
326C22×C4×C71C2411yescharacteristic
327C4⋊C4×C71C2418yes—
328C4⋊C4×C71C2418yes—
329C4⋊C4×C71C2414yes—
330C4⋊C4×C71C2418yes—
331C4⋊C4×C71C2414yes—
332C4⋊C4×C71C2418yes—
333C22⋊C4×C71C2418yes—
334C22⋊C4×C71C2418yes—
335C22⋊C4×C71C2418yes—
336C22⋊C4×C71C2418yes—
337C22⋊C4×C71C2418yes—
338C42×C71C2414yes—
339C42×C71C2414yes—
340C42×C71C2414yes—
341C42×C71C2414yes—
342C42×C71C2418yes—
343C23×C71—22no—
344C23×C71—24no—
345C23×C71—24no—
346C23×C71—22no—
347C23×C71—22no—
348C23×C71—24no—
349C23×C71C2514yes—
350C23×C71C2512yes—
351C23×C71C2511yescharacteristic
352C22×D71—24no—
353C22×D71—24no—
354C22×D71—24no—
355C22×D71—24no—
356C22×D71—24no—
357C22×D71—24no—
358C22×D71C2514yes—
359C22×D71C2514yes—
360Q8×C71—28no—
361D4×C71—28no—
362D4×C71—48no—
363C2×C4×C71—22no—
364C2×C4×C71—24no—
365C2×C4×C71—22no—
366C2×C4×C71—24no—
367C2×C4×C71—22no—
368C2×C4×C71—22no—
369C2×C4×C71—24no—
370C2×C4×C71—28no—
371C2×C4×C71—28no—
372C2×C4×C71—216no—
373C2×C4×C71—44no—
374C2×C4×C71H(5,𝔽2)14yes—
375C2×C4×C712−1+414yes—
376C2×C4×C71C2512yes—
377C2×C4×C71C2512yes—
378C2×C4×C71C2512yes—
379C2×C4×C71C2512yes—
380C2×C4×C71C2514yes—
381C2×C4×C71C2514yes—
382C2×C4×C71C2514yes—
383C2×C4×C71C2512yes—
384C2×C4×C71C2512yes—
385C22⋊D71—416no—
386C22⋊D71—416no—
387C22⋊D71—48no—
388C22⋊D71—48no—
389C2×Dic71—24no—
390C2×Dic71—24no—
391C2×Dic71—28no—
392C2×Dic71—28no—
393C2×Dic71—416no—
394C2×Dic71C2518yes—
395C2×Dic71C2514yes—
396C2×Dic71C2518yes—
397C2×Dic71C2514yes—
398D284—28no—
399D284—28no—
400D284—48no—
401D284—48no—
402C4×D71—216no—
403C4×D71—216no—
404C4×D71—416no—
405C4×D71—416no—
406Dic142—216no—
407Dic142—416no—
408Dic142—48no—
409Dic142—48no—
410C22×C71—24no—
411C22×C71—22no—
412C22×C71—24no—
413C22×C71—22no—
414C22×C71—24no—
415C22×C71—22no—
416C22×C71—44no—
417C22×C71—48no—
418C22×C71C2×H(5,𝔽2)12yes—
419C22×C71C2×2−1+412yes—
420C22×C71#58512yes—
421C22×C71C2611yescharacteristic
422C2×D71—24no—
423C2×D71—24no—
424C2×D71—24no—
425C2×D71—24no—
426C2×D71—24no—
427C2×D71—24no—
428C2×D71—48no—
429C2×D71—48no—
430C4×C71—24no—
431C4×C71—22no—
432C4×C71—22no—
433C4×C71—24no—
434C4×C71—22no—
435C4×C71—24no—
436C4×C71—22no—
437C4×C71C2×H(5,𝔽2)14yes—
438C4×C71C2×2−1+414yes—
439Dic71—28no—
440Dic71—24no—
441Dic71—24no—
442Dic71—28no—
443C2×#3547—711nomaximal, Sylow
444C2×C71—44no—
445C2×C71—42no—
446C2×C71#354714yescomplemented
447C2×C71C22×H(5,𝔽2)11yescharacteristic
448C2×C71C22×2−1+411yescharacteristic
449C2×C71C2×#58511yescharacteristic
450D71—44no—
451D71—44no—
452#3547—7132no—
453C2×#562—714no—
454C2×#555—712no—
455C2×#555—711no—
456C2×#554—711no—
457C2×#553—712no—
458C2×#552—712no—
459C2×D4×Q8—711no—
460C2×#548—712no—
461C2×#547—711no—
462C2×#544—712no—
463C2×#542—714no—
464C2×#540—712no—
465C2×#537—712no—
466C2×#536—712no—
467C2×#533—711no—
468C2×#532—711no—
469C2×#529D7111yescharacteristic, complemented
470C71C2×#354711yescharacteristic, complemented, Sylow
471C22×#41—712no—
472C22×#41—712no—
473C23×Q8—712no—
474#562—7164no—
475#555—7132no—
476#555—7116no—
477#554—7116no—
478#553—7132no—
479#552—7132no—
480D4×Q8—7116no—
481#548—7132no—
482#547—7116no—
483#544—7132no—
484#542—7164no—
485#540—7132no—
486#537—7132no—
487#536—7132no—
488#533—7116no—
489#532—7116no—
490C2×C4⋊Q8—714no—
491C2×C4⋊Q8—711no—
492C2×C4⋊Q8—711no—
493C2×C4⋊Q8—711no—
494C2×C4⋊Q8—712no—
495C2×#127—711no—
496#529C2×D71116yescomplemented
497C2×#126—714no—
498C2×#126C2×D7112yes—
499C2×#125—714no—
500C2×#125—712no—
501C2×#125—712no—
502C2×#125C2×D7111yescharacteristic
503C2×#124—714no—
504C2×#124—714no—
505C2×#124—714no—
506C2×#124—712no—
507C2×#124C2×D7111yescharacteristic
508C2×#123—714no—
509C2×#123—714no—
510C2×#123—714no—
511C2×#123—714no—
512C2×#123C2×D7112yes—
513C2×C22⋊Q8—712no—
514C2×C22⋊Q8—712no—
515C2×C22⋊Q8—712no—
516C2×C22⋊Q8—712no—
517C2×C22⋊Q8—712no—
518C2×C22⋊Q8—714no—
519C2×C22⋊Q8—714no—
520C2×C22⋊Q8—714no—
521C2×C22⋊Q8—714no—
522C2×C22⋊Q8C2×D7111yescharacteristic
523C2×#121—712no—
524C2×#121—714no—
525C2×#121—714no—
526C2×#121—711no—
527C2×#121—711no—
528C2×#121—712no—
529C2×#121—712no—
530C2×#121—712no—
531C2×#121—714no—
532C2×#121—714no—
533C2×#121C2×D7111yescharacteristic
534C2×C4×Q8—712no—
535C2×C4×Q8—712no—
536C2×C4×Q8C2×D7111yescharacteristic
537C2×C4×D4—714no—
538C2×C4×D4—711no—
539C2×C4×D4—712no—
540C2×C4×D4—711no—
541C2×C4×D4—712no—
542C2×C4×D4—712no—
543C2×C4×D4C2×D7111yescharacteristic
544C2×C4×D4C2×D7112yes—
545C2×#117—712no—
546C2×#117—712no—
547C2×#117—712no—
548C2×#117—714no—
549C2×#117C2×D7112yes—
550C22×C4⋊C4—712no—
551C22×C4⋊C4—712no—
552C22×C42C2×D7111yescharacteristic
553C2×#41—2848no—
554C2×#41—2848no—
555C2×#41—7116no—
556C2×#41—7116no—
557C22×Q8—2848no—
558C22×Q8—7116no—
559C22×Q8—712no—
560C22×Q8—714no—
561C22×Q8—712no—
562C22×Q8—712no—
563C22×Q8C22×D7111yescharacteristic
564C22×D4—714no—
565C22×D4—712no—
566C22×D4—714no—
567C22×D4—712no—
568C22×D4—712no—
569C22×D4—712no—
570C22×D4—711no—
571C22×D4—711no—
572C22×D4C22×D7111yescharacteristic
573C22×D4C22×D7112yes—
574C23×C4—714no—
575C23×C4—714no—
576C23×C4—714no—
577C23×C4—712no—
578C23×C4—712no—
579C23×C4C22×D7112yes—
580C23×C4C22×D7111yescharacteristic
581C23×C4C22×D7111yescharacteristic
582C23×C4C22×D7111yescharacteristic
583C4⋊Q8—7132no—
584C4⋊Q8—718no—
585C4⋊Q8—718no—
586C4⋊Q8—718no—
587C4⋊Q8—7116no—
588#127—718no—
589#126—7132no—
590#126C22×D71116yes—
591#125—7132no—
592#125—7116no—
593#125—7116no—
594#125C22×D7118yes—
595#124—7132no—
596#124—7132no—
597#124—7132no—
598#124—7116no—
599#124C22×D7118yes—
600#123—7132no—
601#123—7132no—
602#123—7132no—
603#123—7132no—
604#123C22×D71116yes—
605C22⋊Q8—7116no—
606C22⋊Q8—7116no—
607C22⋊Q8—7116no—
608C22⋊Q8—7116no—
609C22⋊Q8—7116no—
610C22⋊Q8—7132no—
611C22⋊Q8—7132no—
612C22⋊Q8—7132no—
613C22⋊Q8—7132no—
614C22⋊Q8C22×D7118yes—
615#121—7116no—
616#121—7132no—
617#121—7132no—
618#121—718no—
619#121—718no—
620#121—7116no—
621#121—7116no—
622#121—7116no—
623#121—7132no—
624#121—7132no—
625#121C22×D7118yes—
626C4×Q8—7116no—
627C4×Q8—7116no—
628C4×Q8C22×D7118yes—
629C4×D4—7132no—
630C4×D4—718no—
631C4×D4—7116no—
632C4×D4—718no—
633C4×D4—7116no—
634C4×D4—7116no—
635C4×D4C22×D7118yes—
636C4×D4C22×D71116yes—
637#117—7116no—
638#117—7116no—
639#117—7116no—
640#117—7132no—
641#117C22×D71116yes—
642C2×C4⋊C4—711no—
643C2×C4⋊C4—712no—
644C2×C4⋊C4—712no—
645C2×C4⋊C4—714no—
646C2×C4⋊C4—714no—
647C2×C4⋊C4—7116no—
648C2×C4⋊C4—712no—
649C2×C4⋊C4—711no—
650C2×C4⋊C4—714no—
651C2×C4⋊C4—712no—
652C2×C4⋊C4—714no—
653C2×C4⋊C4—714no—
654C2×C4⋊C4—714no—
655C2×C4⋊C4—712no—
656C2×C4⋊C4—7116no—
657C2×C4⋊C4C22×D7111yescharacteristic
658C2×C4⋊C4C22×D7111yescharacteristic
659C2×C4⋊C4C22×D7112yes—
660C2×C4⋊C4C22×D7112yes—
661C2×C4⋊C4C22×D7112yes—
662C2×C4⋊C4C22×D7112yes—
663C2×C22⋊C4—714no—
664C2×C22⋊C4—714no—
665C2×C22⋊C4—712no—
666C2×C22⋊C4—714no—
667C2×C22⋊C4—714no—
668C2×C22⋊C4—712no—
669C2×C22⋊C4—714no—
670C2×C22⋊C4—712no—
671C2×C22⋊C4—714no—
672C2×C22⋊C4—712no—
673C2×C22⋊C4C22×D7112yes—
674C2×C22⋊C4C22×D7112yes—
675C2×C22⋊C4C22×D7112yes—
676C2×C22⋊C4C22×D7112yes—
677C2×C22⋊C4C22×D7112yes—
678C2×C42—714no—
679C2×C42—714no—
680C2×C42C22×D7111yescharacteristic
681C2×C42C22×D7112yes—
682C2×C42C22×D7111yescharacteristic
683C2×C42C22×D7111yescharacteristic
684C2×C42C22×D7111yescharacteristic
685C2×C42C22×D7118yes—
686C24—712no—
687C24—712no—
688C24C23×D7111yescharacteristic
689C24C23×D7112yes—
690#41—28432no—
691#41—28432no—
692C2×Q8—24no—
693C2×Q8—2848no—
694C2×Q8—2844no—
695C2×Q8—2844no—
696C2×Q8—28432no—
697C2×Q8—718no—
698C2×Q8—7116no—
699C2×Q8—718no—
700C2×Q8—718no—
701C2×Q8—1428no—
702C2×Q8C23×D7114yes—
703C2×D4—24no—
704C2×D4—44no—
705C2×D4—2844no—
706C2×D4—2844no—
707C2×D4—2848no—
708C2×D4—2844no—
709C2×D4—2848no—
710C2×D4—2844no—
711C2×D4—7116no—
712C2×D4—718no—
713C2×D4—7116no—
714C2×D4—718no—
715C2×D4—718no—
716C2×D4—718no—
717C2×D4—714no—
718C2×D4—714no—
719C2×D4—1424no—
720C2×D4—1424no—
721C2×D4C23×D7114yes—
722C2×D4C23×D7118yes—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—42no—
727C22×C4—2848no—
728C22×C4—2848no—
729C22×C4—2848no—
730C22×C4—7116no—
731C22×C4—7116no—
732C22×C4—7116no—
733C22×C4—714no—
734C22×C4—712no—
735C22×C4—714no—
736C22×C4—712no—
737C22×C4—718no—
738C22×C4—718no—
739C22×C4—1428no—
740C22×C4—1428no—
741C22×C4C23×D7114yes—
742C22×C4C23×D7114yes—
743C22×C4C23×D7118yes—
744C22×C4C23×D7111yescharacteristic
745C22×C4C23×D7112yes—
746C22×C4C23×D7111yescharacteristic
747C22×C4C23×D7111yescharacteristic
748C22×C4C23×D7111yescharacteristic
749C22×C4C23×D7112yes—
750C22×C4C23×D7112yes—
751C22×C4C23×D7114yes—
752C22×C4C23×D7111yescharacteristic
753C22×C4C23×D7111yescharacteristic
754C4⋊C4—7116no—
755C4⋊C4—7116no—
756C4⋊C4—7116no—
757C4⋊C4—7116no—
758C4⋊C4—714no—
759C4⋊C4—718no—
760C4⋊C4—718no—
761C4⋊C4—7116no—
762C4⋊C4—718no—
763C4⋊C4—714no—
764C4⋊C4—7116no—
765C4⋊C4—718no—
766C4⋊C4—718no—
767C4⋊C4C23×D7114yes—
768C4⋊C4C23×D7114yes—
769C4⋊C4C23×D7118yes—
770C4⋊C4C23×D7118yes—
771C4⋊C4C23×D7118yes—
772C4⋊C4C23×D7118yes—
773C22⋊C4—7116no—
774C22⋊C4—7116no—
775C22⋊C4—718no—
776C22⋊C4—7116no—
777C22⋊C4—7116no—
778C22⋊C4—718no—
779C22⋊C4—7116no—
780C22⋊C4—718no—
781C22⋊C4—7116no—
782C22⋊C4—718no—
783C22⋊C4C23×D7118yes—
784C22⋊C4C23×D7118yes—
785C22⋊C4C23×D7118yes—
786C22⋊C4C23×D7118yes—
787C22⋊C4C23×D7118yes—
788C42—7116no—
789C42—7116no—
790C42C23×D7114yes—
791C42C23×D7114yes—
792C42C23×D7114yes—
793C42C23×D7114yes—
794C42C23×D7118yes—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—714no—
802C23—714no—
803C23—1424no—
804C23—1424no—
805C23—1424no—
806C23—1424no—
807C23—1424no—
808C23—1424no—
809C23C24×D7112yes—
810C23C24×D7114yes—
811C23C24×D7111yescharacteristic
812Q8—28no—
813Q8—28416no—
814Q8—2848no—
815Q8—2848no—
816Q8—14216no—
817D4—28no—
818D4—48no—
819D4—2848no—
820D4—2848no—
821D4—2848no—
822D4—28416no—
823D4—2848no—
824D4—28416no—
825D4—1428no—
826D4—1428no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—216no—
837C2×C4—44no—
838C2×C4—28416no—
839C2×C4—28416no—
840C2×C4—28416no—
841C2×C4—718no—
842C2×C4—714no—
843C2×C4—718no—
844C2×C4—714no—
845C2×C4—1424no—
846C2×C4—1428no—
847C2×C4—1424no—
848C2×C4—1428no—
849C2×C4—14216no—
850C2×C4—14216no—
851C2×C4#1455617414yes—
852C2×C4#1455617514yes—
853C2×C4C24×D7112yes—
854C2×C4C24×D7114yes—
855C2×C4C24×D7112yes—
856C2×C4C24×D7112yes—
857C2×C4C24×D7112yes—
858C2×C4C24×D7114yes—
859C2×C4C24×D7114yes—
860C2×C4C24×D7112yes—
861C2×C4C24×D7112yes—
862C22—22no—
863C22—24no—
864C22—22no—
865C22—24no—
866C22—22no—
867C22—24no—
868C22—44no—
869C22—48no—
870C22—2848no—
871C22—2848no—
872C22—1424no—
873C22—1424no—
874C22—1424no—
875C22—1424no—
876C22—1424no—
877C22—1424no—
878C22C2×#1455617412yes—
879C22C2×#1455617512yes—
880C22#1798683512yes—
881C22C25×D7111yescharacteristic
882C4—22no—
883C4—24no—
884C4—22no—
885C4—24no—
886C4—22no—
887C4—22no—
888C4—24no—
889C4—1424no—
890C4—1428no—
891C4—1424no—
892C4—1428no—
893C4C2×#1455617414yes—
894C4C2×#1455617514yes—
895C2—42no—
896C2—44no—
897C2—2844no—
898C2—2844no—
899C2#2260273114yesdirect product factor
900C2C22×#1455617411yescharacteristic
901C2C22×#1455617511yescharacteristic
902C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#529×C71C2
socleC23×C71C25
hypercenterC2×#529D71
hypocenterC71C2×#3547
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22602731C2direct (N × H)
2. C2×#17986746C2semidirect
3. C2×#17986714C2semidirect
4. C2×#17986714C2semidirect
5. C2×#17986709C2semidirect
6. C2×#17986695C2semidirect
7. C2×#17986687C2semidirect
8. C2×Q8×D284C2semidirect
9. C2×#17986657C2semidirect
10. C2×#17986653C2semidirect
11. C2×#17986627C2semidirect
12. C2×#17986615C2semidirect
13. C2×#17986604C2semidirect
14. C2×#17986578C2semidirect
15. C2×#17986572C2semidirect
16. C2×#17986556C2semidirect
17. C2×#17986549C2semidirect
18. C2×#529×C71C2semidirect
22. #17986746C22semidirect
23. #17986714C22semidirect
24. #17986714C22semidirect
25. #17986709C22semidirect
26. #17986695C22semidirect
27. #17986687C22semidirect
28. Q8×D284C22semidirect
29. #17986657C22semidirect
30. #17986653C22semidirect
31. #17986627C22semidirect
32. #17986615C22semidirect
33. #17986604C22semidirect
34. #17986578C22semidirect
35. #17986572C22semidirect
36. #17986556C22semidirect
37. #17986549C22semidirect
89. #529×C71C22semidirect
446. C2×C71#3547semidirect
469. C2×#529D71semidirect
470. C71C2×#3547semidirect
496. #529C2×D71semidirect
899. C2#22602731direct (N × H)

Maximal subgroups

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

subgroupindex
#226027312
C2×#179867462
C2×#179867142
C2×#179867092
C2×#179866952
C2×#179866872
C2×Q8×D2842
C2×#179866572
C2×#179866532
C2×#179866272
C2×#179866152
C2×#179866042
C2×#179865782
C2×#179865722
C2×#179865562
C2×#179865492
C2×#529×C712
C2×#354771