Finite Group Databasebeta

← C2×#22602131 #32905920

Subgroups — C2×#22602131 #32905920

Order 18176.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556176C211yesmaximal, characteristic, complemented
2C22×#14556174C211yesmaximal, characteristic, complemented
3#22602131C2132yesmaximal, direct product factor
4C2×#17986661C211yesmaximal, characteristic, complemented
5C2×#17986660C211yesmaximal, characteristic, complemented
6C2×#17986656C211yesmaximal, characteristic, complemented
7C2×#17986646C213yesmaximal, complemented
8C2×#17986645C213yesmaximal, complemented
9C2×#17986642C213yesmaximal, complemented
10C2×#17986640C213yesmaximal, complemented
11C2×#17986572C213yesmaximal, complemented
12C2×#17986565C213yesmaximal, complemented
13C2×#17986546C213yesmaximal, complemented
14C2×#124×D71C213yesmaximal, complemented
15C2×C4×#11765866C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C2×#14556176—216no—
18C2×#14556176C22116yescomplemented
19C2×#14556174—216no—
20C2×#14556174C22116yescomplemented
21C22×#11765866C2211yescharacteristic
22C22×#11765866C2211yescharacteristic
23C22×#11765866C2213yescomplemented
24C22×#11765865C2213yes—
25C22×#11765865C2213yescomplemented
26C22×#11765865C2213yescomplemented
27C22×Q8×D71C2211yescharacteristic, complemented
28C22×Q8×D71C2213yescomplemented
29C23×D284C2213yes—
30C22×D4×D71C2213yes—
31C22×D4×D71C2213yes—
32#17986661C22116yescomplemented
33#17986660C22116yescomplemented
34#17986656C22116yescomplemented
35#17986646C22148yescomplemented
36#17986645C22148yescomplemented
37#17986642C22148yescomplemented
38#17986640C22148yescomplemented
39#17986572C22148yescomplemented
40#17986565C22148yescomplemented
41#17986546C22148yescomplemented
42C2×#14556127C2213yescomplemented
43C2×#14556124C2213yescomplemented
44C2×#14556117C2213yescomplemented
45C2×#14556116C2213yescomplemented
46C2×#14556115C2213yescomplemented
47C2×#14556114C2213yescomplemented
48C2×#14556114C2216yescomplemented
49C2×#14556114C2211yescharacteristic, complemented
50#124×D71C22148yescomplemented
51C2×#14556113C2216yescomplemented
52C2×#14556110C2216yescomplemented
53C2×#14556108C2213yescomplemented
54C2×#14556107C2213yescomplemented
55C2×#14556104C2213yescomplemented
56C2×#14556103C2213yescomplemented
57C2×#14556103C2213yescomplemented
58C2×#14556102C2213yescomplemented
59C2×#14556101C2213yescomplemented
60C2×#14556101C2213yescomplemented
61C2×#14556099C2213yescomplemented
62C2×#14556099C2213yescomplemented
63C2×#14556098C2216yescomplemented
64C2×#14556096C2216yescomplemented
65C4×#11765866C22116yescomplemented
66C2×Q8×Dic71C2211yescharacteristic, complemented
67C2×C4×D284C2213yescomplemented
68C2×C4×D284C2213yescomplemented
69C2×#14556090C2213yescomplemented
70C2×C4×C22⋊D71C2213yescomplemented
71C2×C4×C22⋊D71C2213yescomplemented
72C2×#14556086C2213yescomplemented
73C2×C22⋊C4×D71C2216yescomplemented
74C2×C22⋊C4×D71C2216yescomplemented
75C2×C42×D71C2213yescomplemented
76C22×#41×C71C2211yescharacteristic
77C23×Q8×C71C2211yescharacteristic, complemented
78#548×C71C22116yescomplemented
79C2×#124×C71C2213yescomplemented
80C2×C22⋊Q8×C71C2213yescomplemented
81C2×#121×C71C2213yescomplemented
82C2×C4×Q8×C71C2211yescharacteristic, complemented
83C2×C4×D4×C71C2213yescomplemented
84C24×D71C2316yes—
85#14556176—2128no—
86#14556174—2128no—
87C2×#11765866—224no—
88C2×#11765866—28no—
89C2×#11765866D4116yescomplemented
90C2×#11765866C2318yes—
91C2×#11765866C2318yes—
92C2×#11765866C23124yescomplemented
93C2×#11765865—224no—
94C2×#11765865—224no—
95C2×#11765865—224no—
96C2×#11765865C23124yes—
97C2×#11765865C23124yescomplemented
98C2×#11765865C23124yescomplemented
99C22×Dic142C2313yes—
100C22×Dic142C2313yes—
101C22×Dic142C2311yescharacteristic
102C2×Q8×D71—224no—
103C2×Q8×D71—28no—
104C2×Q8×D71C23124yescomplemented
105C2×Q8×D71C2318yescomplemented
106C22×D284—224no—
107C22×D284C2313yes—
108C22×D284C2313yes—
109C22×D284C23124yes—
110C22×D284C2313yes—
111C22×D284C2313yes—
112C22×D284C2313yes—
113C22×C22⋊D71C2313yes—
114C22×C22⋊D71C2313yes—
115C22×C22⋊D71C2313yes—
116C22×C22⋊D71C2311yescharacteristic
117C22×C22⋊D71C2313yes—
118C22×C22⋊D71C2313yes—
119C2×D4×D71—224no—
120C2×D4×D71—224no—
121C2×D4×D71C23124yes—
122C2×D4×D71C23124yes—
123C22×C4×D71C2313yes—
124C22×C4×D71C2316yes—
125C22×C4×D71C2313yes—
126C22×C4×D71C2313yes—
127C22×C4×D71C2313yes—
128C22×C4×D71C2313yes—
129#14556127C23124yescomplemented
130#14556124C23124yescomplemented
131#14556117C23124yescomplemented
132#14556116C23124yescomplemented
133#14556115C23124yescomplemented
134#14556114C23148yescomplemented
135#14556114C23124yescomplemented
136#14556114C2318yescomplemented
137#14556113C23148yescomplemented
138#14556110C23148yescomplemented
139#14556108C23124yescomplemented
140#14556107C23124yescomplemented
141#14556104C23124yescomplemented
142#14556103C23124yescomplemented
143#14556103C23124yescomplemented
144#14556102C23124yescomplemented
145#14556101C23124yescomplemented
146#14556101C23124yescomplemented
147#14556099C23124yescomplemented
148#14556099C23124yescomplemented
149#14556098C23148yescomplemented
150#14556096C23148yescomplemented
151Q8×Dic71C2318yescomplemented
152C4×D284C23124yescomplemented
153C4×D284C23124yescomplemented
154#14556090C23124yescomplemented
155C4×C22⋊D71C23124yescomplemented
156C4×C22⋊D71C23124yescomplemented
157#14556086C23124yescomplemented
158C2×C4⋊Dic71C2313yes—
159C2×C4⋊Dic71C2313yes—
160C2×Dic71⋊C4C2313yes—
161C2×Dic71⋊C4C2313yes—
162C2×C22⋊Dic71C2313yes—
163C2×C22⋊Dic71C2316yes—
164C2×C22⋊Dic71C2311yescharacteristic
165C2×(C2×D71)⋊C4C2313yes—
166C2×(C2×D71)⋊C4C2313yes—
167C2×(C2×D71)⋊C4C2316yes—
168C2×(C2×D71)⋊C4C2316yes—
169C2×(C2×D71)⋊C4C2316yes—
170C2×(C2×D71)⋊C4C2311yescharacteristic
171C2×(C2×D71)⋊C4C2311yescharacteristic
172C22⋊C4×D71C23148yescomplemented
173C22⋊C4×D71C23148yescomplemented
174C2×C4×Dic71C2311yescharacteristic
175C2×C4×Dic71C2313yes—
176C2×C4×Dic71C2313yes—
177C42×D71C23124yescomplemented
178C2×#41×C71—28no—
179C2×#41×C71C2318yes—
180C22×Q8×C71—28no—
181C22×Q8×C71C2313yes—
182C22×Q8×C71C2311yescharacteristic
183C22×Q8×C71C2318yescomplemented
184C22×D4×C71C2313yes—
185C22×D4×C71C2313yes—
186C23×C4×C71C2313yes—
187C23×C4×C71C2313yes—
188#124×C71C23124yescomplemented
189C22⋊Q8×C71C23124yescomplemented
190#121×C71C23124yescomplemented
191C4×Q8×C71C2318yescomplemented
192C4×D4×C71C23124yescomplemented
193C2×C4⋊C4×C71C2313yes—
194C2×C4⋊C4×C71C2313yes—
195C2×C22⋊C4×C71C2311yescharacteristic
196C2×C22⋊C4×C71C2313yes—
197C2×C22⋊C4×C71C2316yes—
198C2×C42×C71C2313yes—
199C23×D71—224no—
200C23×D71—412no—
201C23×D71—412no—
202C23×D71C2411yescharacteristic
203C23×D71C2413yes—
204C23×D71C2413yes—
205C23×D71C24124yes—
206#11765866—232no—
207#11765866—296no—
208#11765866C2×D4164yescomplemented
209#11765865—296no—
210#11765865—296no—
211#11765865—296no—
212C2×Dic142—212no—
213C2×Dic142—212no—
214C2×Dic142—24no—
215C2×Dic142C24112yes—
216C2×Dic142C24112yes—
217C2×Dic142C2414yes—
218Q8×D71—232no—
219Q8×D71—296no—
220C2×D284—212no—
221C2×D284—212no—
222C2×D284—212no—
223C2×D284—296no—
224C2×D284—46no—
225C2×D284C2×D4124yes—
226C2×D284C24112yes—
227C2×D284C24112yes—
228C2×D284C24112yes—
229C2×D284C24112yes—
230C2×D284C24112yes—
231C2×C22⋊D71—212no—
232C2×C22⋊D71—212no—
233C2×C22⋊D71—212no—
234C2×C22⋊D71—24no—
235C2×C22⋊D71—46no—
236C2×C22⋊D71—46no—
237C2×C22⋊D71C24112yes—
238C2×C22⋊D71C24112yes—
239C2×C22⋊D71C24112yes—
240C2×C22⋊D71C2414yes—
241C2×C22⋊D71C24112yes—
242C2×C22⋊D71C24112yes—
243D4×D71—296no—
244D4×D71—296no—
245C22×Dic71C2411yescharacteristic
246C22×Dic71C2413yes—
247C22×Dic71C2411yescharacteristic
248C22×Dic71C2413yes—
249C22×Dic71C2411yescharacteristic
250C2×C4×D71—224no—
251C2×C4×D71—212no—
252C2×C4×D71—212no—
253C2×C4×D71—46no—
254C2×C4×D71—46no—
255C2×C4×D71C2×D4124yes—
256C2×C4×D71C24112yes—
257C2×C4×D71C24124yes—
258C2×C4×D71C24112yes—
259C2×C4×D71C24112yes—
260C2×C4×D71C24112yes—
261C2×C4×D71C24112yes—
262C4⋊Dic71C24112yes—
263C4⋊Dic71C24112yes—
264Dic71⋊C4C24112yes—
265Dic71⋊C4C24112yes—
266C22⋊Dic71C24112yes—
267C22⋊Dic71C24124yes—
268C22⋊Dic71C2414yes—
269(C2×D71)⋊C4C24112yes—
270(C2×D71)⋊C4C24112yes—
271(C2×D71)⋊C4C24124yes—
272(C2×D71)⋊C4C24124yes—
273(C2×D71)⋊C4C24124yes—
274(C2×D71)⋊C4C2414yes—
275(C2×D71)⋊C4C2414yes—
276C4×Dic71C2414yes—
277C4×Dic71C24112yes—
278C4×Dic71C24112yes—
279C24×C71C2411yescharacteristic
280C24×C71C2413yes—
281#41×C71—232no—
282C2×Q8×C71—232no—
283C2×Q8×C71—212no—
284C2×Q8×C71C2×D418yes—
285C2×Q8×C71C24112yes—
286C2×Q8×C71C2414yes—
287C2×D4×C71—212no—
288C2×D4×C71—46no—
289C2×D4×C71C24112yes—
290C2×D4×C71C24112yes—
291C22×C4×C71—212no—
292C22×C4×C71—212no—
293C22×C4×C71C2411yescharacteristic
294C22×C4×C71C2413yes—
295C22×C4×C71C2413yes—
296C22×C4×C71C2411yescharacteristic
297C22×C4×C71C24112yes—
298C22×C4×C71C24112yes—
299C22×C4×C71C2413yes—
300C4⋊C4×C71C24112yes—
301C4⋊C4×C71C24112yes—
302C22⋊C4×C71C2414yes—
303C22⋊C4×C71C24112yes—
304C22⋊C4×C71C24124yes—
305C42×C71C24112yes—
306C23×C71—22no—
307C23×C71—26no—
308C23×C71—22no—
309C23×C71—26no—
310C23×C71—22no—
311C23×C71—26no—
312C23×C71C2516yes—
313C23×C71C2512yes—
314C23×C71C2511yescharacteristic
315C22×D71—26no—
316C22×D71—26no—
317C22×D71—22no—
318C22×D71—26no—
319C22×D71—22no—
320C22×D71—26no—
321C22×D71—22no—
322C22×D71—26no—
323C22×D71—248no—
324C22×D71—424no—
325C22×D71—424no—
326C22×D71—848no—
327C22×D71C22×D4112yes—
328C22×D71C2516yes—
329C22×D71C2512yes—
330C22×D71C2516yes—
331Q8×C71—224no—
332Q8×C71C22×D4116yes—
333D4×C71—224no—
334D4×C71—412no—
335C2×C4×C71—22no—
336C2×C4×C71—26no—
337C2×C4×C71—26no—
338C2×C4×C71—22no—
339C2×C4×C71—224no—
340C2×C4×C71—224no—
341C2×C4×C71C22×D4112yes—
342C2×C4×C71C2512yes—
343C2×C4×C71C2516yes—
344C2×C4×C71C2516yes—
345C2×C4×C71C2512yes—
346C2×C4×C71C2516yes—
347C22⋊D71—224no—
348C22⋊D71—224no—
349C22⋊D71—224no—
350C22⋊D71—28no—
351C22⋊D71—412no—
352C22⋊D71—412no—
353C2×Dic71—22no—
354C2×Dic71—26no—
355C2×Dic71—22no—
356C2×Dic71—26no—
357C2×Dic71C22×D414yes—
358C2×Dic71C2512yes—
359C2×Dic71C2516yes—
360C2×Dic71C2516yes—
361C2×Dic71C2512yes—
362C2×Dic71C2512yes—
363D284—224no—
364D284—224no—
365D284—224no—
366D284—412no—
367D284C22×D4148yes—
368C4×D71—248no—
369C4×D71—224no—
370C4×D71—224no—
371C4×D71—412no—
372C4×D71—412no—
373C4×D71C22×D4148yes—
374Dic142—224no—
375Dic142—224no—
376Dic142—28no—
377C22×C71—22no—
378C22×C71—26no—
379C22×C71—22no—
380C22×C71—26no—
381C22×C71—22no—
382C22×C71—26no—
383C22×C71—412no—
384C22×C71—44no—
385C22×C71C23×D412yes—
386C22×C71#58512yes—
387C22×C71#58512yes—
388C22×C71C2611yescharacteristic
389C2×D71—26no—
390C2×D71—26no—
391C2×D71—224no—
392C2×D71—22no—
393C2×D71—26no—
394C2×D71—22no—
395C2×D71—26no—
396C2×D71—22no—
397C2×D71—26no—
398C2×D71—44no—
399C2×D71—412no—
400C2×D71—848no—
401C2×D71C23×D4112yes—
402C4×C71—26no—
403C4×C71—22no—
404C4×C71—22no—
405C4×C71—26no—
406C4×C71C23×D4112yes—
407Dic71—26no—
408Dic71—22no—
409Dic71—22no—
410Dic71—26no—
411Dic71C23×D414yes—
412C2×#3500—711nomaximal, Sylow
413C2×C71—46no—
414C2×C71—42no—
415C2×C71#350014yescomplemented
416C2×C71C24×D411yescharacteristic
417C2×C71C2×#58511yescharacteristic
418C2×C71C2×#58511yescharacteristic
419D71—212no—
420D71—42no—
421D71—46no—
422C22×2−1+4—711no—
423C22×H(5,𝔽2)—711no—
424#3500—7132no—
425C2×#548—711no—
426C2×#548—711no—
427C2×#548—711no—
428C2×#548D7111yescharacteristic, complemented
429C2×#546—713no—
430C2×#546—713no—
431C2×#546—713no—
432C2×#546—713no—
433C2×#536—713no—
434C2×#535—713no—
435C2×#532—713no—
436C22×#124—713no—
437C2×C4×#41—711no—
438C71C2×#350011yescharacteristic, complemented, Sylow
439C2×2−1+4—7116no—
440C2×2−1+4—14216no—
441C2×H(5,𝔽2)—7116no—
442C2×H(5,𝔽2)—14216no—
443C22×#41—711no—
444C22×#41—711no—
445C22×#41—713no—
446C22×#41—713no—
447C22×#41—713no—
448C22×#41—713no—
449C22×#41C2×D7111yescharacteristic
450C23×Q8—713no—
451C23×Q8—711no—
452C23×Q8C2×D7111yescharacteristic, complemented
453C23×D4—713no—
454C23×D4—713no—
455C23×D4—713no—
456#548—7116no—
457#548—7116no—
458#548—7116no—
459#548C2×D71116yescomplemented
460#546—7148no—
461#546—7148no—
462#546—7148no—
463#546—7148no—
464#536—7148no—
465#535—7148no—
466#532—7148no—
467C2×C4⋊Q8—713no—
468C2×#127—713no—
469C2×#124—713no—
470C2×#124—713no—
471C2×#124—7148no—
472C2×#124—713no—
473C2×#124—716no—
474C2×#124—711no—
475C2×#124—713no—
476C2×#124C2×D7113yescomplemented
477C2×#123—716no—
478C2×#123—716no—
479C2×C22⋊Q8—713no—
480C2×C22⋊Q8—713no—
481C2×C22⋊Q8—713no—
482C2×C22⋊Q8C2×D7113yescomplemented
483C2×#121—713no—
484C2×#121—713no—
485C2×#121—713no—
486C2×#121—713no—
487C2×#121—713no—
488C2×#121—713no—
489C2×#121—713no—
490C2×#121C2×D7113yescomplemented
491C2×#120—716no—
492C2×#120—716no—
493C4×#41—7116no—
494C2×C4×Q8—711no—
495C2×C4×Q8C2×D7111yescharacteristic, complemented
496C2×C4×D4—713no—
497C2×C4×D4—713no—
498C2×C4×D4—713no—
499C2×C4×D4—713no—
500C2×C4×D4—713no—
501C2×C4×D4C2×D7113yescomplemented
502C2×#117—713no—
503C22×C22⋊C4—716no—
504C22×C22⋊C4—716no—
505C22×C42—713no—
506C25—716no—
5072−1+4—142128no—
508H(5,𝔽2)—142128no—
509C2×#41—28no—
510C2×#41—7116no—
511C2×#41—718no—
512C2×#41—718no—
513C2×#41—7124no—
514C2×#41—7124no—
515C2×#41—7124no—
516C2×#41—7124no—
517C2×#41—14224no—
518C2×#41—14224no—
519C2×#41—14224no—
520C2×#41—14224no—
521C2×#41—1428no—
522C2×#41C22×D7118yes—
523C22×Q8—28no—
524C22×Q8—7124no—
525C22×Q8—718no—
526C22×Q8—713no—
527C22×Q8—713no—
528C22×Q8—711no—
529C22×Q8—14224no—
530C22×Q8—1428no—
531C22×Q8C22×D7113yes—
532C22×Q8C22×D7111yescharacteristic
533C22×Q8C22×D7118yescomplemented
534C22×D4—713no—
535C22×D4—713no—
536C22×D4—713no—
537C22×D4—713no—
538C22×D4—713no—
539C22×D4—711no—
540C22×D4—7124no—
541C22×D4—7124no—
542C22×D4—713no—
543C22×D4—713no—
544C22×D4—713no—
545C22×D4—713no—
546C22×D4—713no—
547C22×D4—7124no—
548C22×D4—14224no—
549C22×D4—14224no—
550C22×D4—14224no—
551C22×D4C22×D7113yes—
552C22×D4C22×D7113yes—
553C23×C4—713no—
554C23×C4—713no—
555C23×C4—713no—
556C23×C4—716no—
557C23×C4—713no—
558C23×C4—713no—
559C23×C4C22×D7113yes—
560C23×C4C22×D7113yes—
561C4⋊Q8—7124no—
562#127—7124no—
563#124—7124no—
564#124—7124no—
565#124—7124no—
566#124—7148no—
567#124—718no—
568#124—7124no—
569#124C22×D71124yescomplemented
570#123—7148no—
571#123—7148no—
572C22⋊Q8—7124no—
573C22⋊Q8—7124no—
574C22⋊Q8—7124no—
575C22⋊Q8C22×D71124yescomplemented
576#121—7124no—
577#121—7124no—
578#121—7124no—
579#121—7124no—
580#121—7124no—
581#121—7124no—
582#121—7124no—
583#121C22×D71124yescomplemented
584#120—7148no—
585#120—7148no—
586C4×Q8—718no—
587C4×Q8C22×D7118yescomplemented
588C4×D4—7124no—
589C4×D4—7124no—
590C4×D4—7124no—
591C4×D4—7124no—
592C4×D4—7124no—
593C4×D4C22×D71124yescomplemented
594#117—7124no—
595C2×C4⋊C4—713no—
596C2×C4⋊C4—713no—
597C2×C4⋊C4—713no—
598C2×C4⋊C4—713no—
599C2×C4⋊C4C22×D7113yes—
600C2×C4⋊C4C22×D7113yes—
601C2×C22⋊C4—713no—
602C2×C22⋊C4—716no—
603C2×C22⋊C4—711no—
604C2×C22⋊C4—713no—
605C2×C22⋊C4—713no—
606C2×C22⋊C4—716no—
607C2×C22⋊C4—716no—
608C2×C22⋊C4—716no—
609C2×C22⋊C4—711no—
610C2×C22⋊C4—711no—
611C2×C22⋊C4—7148no—
612C2×C22⋊C4—7148no—
613C2×C22⋊C4C22×D7113yes—
614C2×C22⋊C4C22×D7116yes—
615C2×C22⋊C4C22×D7111yescharacteristic
616C2×C42—713no—
617C2×C42—713no—
618C2×C42—711no—
619C2×C42—7124no—
620C2×C42C22×D7113yes—
621C24—28412no—
622C24—28412no—
623C24—7124no—
624C24—713no—
625C24—713no—
626C24—711no—
627C24—14224no—
628C24C23×D7113yes—
629C24C23×D7111yescharacteristic
630#41—232no—
631#41—7164no—
632#41—14296no—
633#41—14296no—
634#41—14296no—
635#41—14296no—
636#41—14232no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—7112no—
640C2×Q8—7112no—
641C2×Q8—714no—
642C2×Q8—14212no—
643C2×Q8—1424no—
644C2×Q8—14296no—
645C2×Q8—14232no—
646C2×Q8—14212no—
647C2×Q8D4×D7118yes—
648C2×Q8C23×D71112yes—
649C2×Q8C23×D7114yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—2846no—
653C2×D4—2846no—
654C2×D4—2846no—
655C2×D4—7112no—
656C2×D4—7112no—
657C2×D4—7112no—
658C2×D4—7112no—
659C2×D4—7112no—
660C2×D4—714no—
661C2×D4—7124no—
662C2×D4—7112no—
663C2×D4—7112no—
664C2×D4—7112no—
665C2×D4—7112no—
666C2×D4—7112no—
667C2×D4—14296no—
668C2×D4—14212no—
669C2×D4—14212no—
670C2×D4—14296no—
671C2×D4—14212no—
672C2×D4—1424no—
673C2×D4—14296no—
674C2×D4—14212no—
675C2×D4—14212no—
676C2×D4—14212no—
677C2×D4C23×D71112yes—
678C2×D4C23×D71112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—2846no—
682C22×C4—2846no—
683C22×C4—7112no—
684C22×C4—7112no—
685C22×C4—711no—
686C22×C4—7124no—
687C22×C4—7112no—
688C22×C4—711no—
689C22×C4—713no—
690C22×C4—713no—
691C22×C4—711no—
692C22×C4—7124no—
693C22×C4—7112no—
694C22×C4—7112no—
695C22×C4—14224no—
696C22×C4—14212no—
697C22×C4—14212no—
698C22×C4C23×D71112yes—
699C22×C4C23×D71112yes—
700C22×C4C23×D7111yescharacteristic
701C22×C4C23×D7113yes—
702C22×C4C23×D7113yes—
703C22×C4C23×D7111yescharacteristic
704C22×C4C23×D7113yes—
705C4⋊C4—7112no—
706C4⋊C4—7112no—
707C4⋊C4—7112no—
708C4⋊C4—7112no—
709C4⋊C4C23×D71112yes—
710C4⋊C4C23×D71112yes—
711C22⋊C4—7112no—
712C22⋊C4—7124no—
713C22⋊C4—714no—
714C22⋊C4—7112no—
715C22⋊C4—7112no—
716C22⋊C4—7124no—
717C22⋊C4—7124no—
718C22⋊C4—7124no—
719C22⋊C4—714no—
720C22⋊C4—714no—
721C22⋊C4C23×D71112yes—
722C22⋊C4C23×D71124yes—
723C22⋊C4C23×D7114yes—
724C42—714no—
725C42—7112no—
726C42—7112no—
727C42C23×D71112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—28424no—
735C23—28424no—
736C23—56848no—
737C23—7112no—
738C23—716no—
739C23—716no—
740C23—712no—
741C23—14248no—
742C23—1422no—
743C23—1426no—
744C23—1422no—
745C23—1426no—
746C23—1422no—
747C23—1426no—
748C23—1426no—
749C23—1426no—
750C23C24×D7116yes—
751C23C24×D7112yes—
752C23C24×D7111yescharacteristic
753Q8—224no—
754Q8—14224no—
755Q8—1428no—
756Q8—14224no—
757Q8C2×D4×D71116yes—
758D4—224no—
759D4—412no—
760D4—28412no—
761D4—28412no—
762D4—28412no—
763D4—7148no—
764D4—14224no—
765D4—14224no—
766D4—14224no—
767D4—1428no—
768D4—14224no—
769D4—14224no—
770D4—14224no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—28412no—
778C2×C4—28412no—
779C2×C4—714no—
780C2×C4—712no—
781C2×C4—7148no—
782C2×C4—712no—
783C2×C4—716no—
784C2×C4—716no—
785C2×C4—712no—
786C2×C4—14248no—
787C2×C4—1422no—
788C2×C4—1426no—
789C2×C4—1422no—
790C2×C4—1426no—
791C2×C4—14224no—
792C2×C4—14224no—
793C2×C4C2×D4×D71112yes—
794C2×C4C24×D7112yes—
795C2×C4C24×D7116yes—
796C2×C4C24×D7116yes—
797C2×C4C24×D7112yes—
798C2×C4C24×D7116yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—28412no—
808C22—2844no—
809C22—56848no—
810C22—7112no—
811C22—1422no—
812C22—1426no—
813C22—1422no—
814C22—1426no—
815C22—1422no—
816C22—1426no—
817C22—1426no—
818C22—1426no—
819C22—14224no—
820C22C22×D4×D7112yes—
821C22#1798683512yes—
822C22#1798683612yes—
823C22C25×D7111yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—714no—
829C4—1422no—
830C4—1426no—
831C4—1422no—
832C4—1426no—
833C4C22×D4×D71112yes—
834C2—46no—
835C2—42no—
836C2—2846no—
837C2—2842no—
838C2—14212no—
839C2#2260213114yesdirect product factor
840C2C23×D4×D7111yescharacteristic
841C2C2×#1798683511yescharacteristic
842C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#548×C71C2
socleC23×C71C25
hypercenterC2×#548D71
hypocenterC71C2×#3500
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14556176C2semidirect
2. C22×#14556174C2semidirect
3. #22602131C2direct (N × H)
4. C2×#17986661C2semidirect
5. C2×#17986660C2semidirect
6. C2×#17986656C2semidirect
7. C2×#17986646C2semidirect
8. C2×#17986645C2semidirect
9. C2×#17986642C2semidirect
10. C2×#17986640C2semidirect
11. C2×#17986572C2semidirect
12. C2×#17986565C2semidirect
13. C2×#17986546C2semidirect
14. C2×#124×D71C2semidirect
15. C2×C4×#11765866C2semidirect
16. C2×#548×C71C2semidirect
18. C2×#14556176C22semidirect
20. C2×#14556174C22semidirect
23. C22×#11765866C22semidirect
25. C22×#11765865C22semidirect
26. C22×#11765865C22semidirect
27. C22×Q8×D71C22semidirect
28. C22×Q8×D71C22semidirect
32. #17986661C22semidirect
33. #17986660C22semidirect
34. #17986656C22semidirect
35. #17986646C22semidirect
36. #17986645C22semidirect
37. #17986642C22semidirect
38. #17986640C22semidirect
39. #17986572C22semidirect
40. #17986565C22semidirect
41. #17986546C22semidirect
42. C2×#14556127C22semidirect
43. C2×#14556124C22semidirect
44. C2×#14556117C22semidirect
45. C2×#14556116C22semidirect
46. C2×#14556115C22semidirect
47. C2×#14556114C22semidirect
48. C2×#14556114C22semidirect
49. C2×#14556114C22semidirect
50. #124×D71C22semidirect
51. C2×#14556113C22semidirect
52. C2×#14556110C22semidirect
53. C2×#14556108C22semidirect
54. C2×#14556107C22semidirect
55. C2×#14556104C22semidirect
56. C2×#14556103C22semidirect
57. C2×#14556103C22semidirect
58. C2×#14556102C22semidirect
59. C2×#14556101C22semidirect
60. C2×#14556101C22semidirect
61. C2×#14556099C22semidirect
62. C2×#14556099C22semidirect
63. C2×#14556098C22semidirect
64. C2×#14556096C22semidirect
65. C4×#11765866C22semidirect
66. C2×Q8×Dic71C22semidirect
67. C2×C4×D284C22semidirect
68. C2×C4×D284C22semidirect
69. C2×#14556090C22semidirect
70. C2×C4×C22⋊D71C22semidirect
71. C2×C4×C22⋊D71C22semidirect
72. C2×#14556086C22semidirect
73. C2×C22⋊C4×D71C22semidirect
74. C2×C22⋊C4×D71C22semidirect
75. C2×C42×D71C22semidirect
77. C23×Q8×C71C22semidirect
78. #548×C71C22semidirect
79. C2×#124×C71C22semidirect
80. C2×C22⋊Q8×C71C22semidirect
81. C2×#121×C71C22semidirect
82. C2×C4×Q8×C71C22semidirect
83. C2×C4×D4×C71C22semidirect
89. C2×#11765866D4semidirect
92. C2×#11765866C23semidirect
97. C2×#11765865C23semidirect
98. C2×#11765865C23semidirect
104. C2×Q8×D71C23semidirect
105. C2×Q8×D71C23semidirect
129. #14556127C23semidirect
130. #14556124C23semidirect
131. #14556117C23semidirect
132. #14556116C23semidirect
133. #14556115C23semidirect
134. #14556114C23semidirect
135. #14556114C23semidirect
136. #14556114C23semidirect
137. #14556113C23semidirect
138. #14556110C23semidirect
139. #14556108C23semidirect
140. #14556107C23semidirect
141. #14556104C23semidirect
142. #14556103C23semidirect
143. #14556103C23semidirect
144. #14556102C23semidirect
145. #14556101C23semidirect
146. #14556101C23semidirect
147. #14556099C23semidirect
148. #14556099C23semidirect
149. #14556098C23semidirect
150. #14556096C23semidirect
151. Q8×Dic71C23semidirect
152. C4×D284C23semidirect
153. C4×D284C23semidirect
154. #14556090C23semidirect
155. C4×C22⋊D71C23semidirect
156. C4×C22⋊D71C23semidirect
157. #14556086C23semidirect
172. C22⋊C4×D71C23semidirect
173. C22⋊C4×D71C23semidirect
177. C42×D71C23semidirect
183. C22×Q8×C71C23semidirect
188. #124×C71C23semidirect
189. C22⋊Q8×C71C23semidirect
190. #121×C71C23semidirect
191. C4×Q8×C71C23semidirect
192. C4×D4×C71C23semidirect
208. #11765866C2×D4semidirect
415. C2×C71#3500semidirect
428. C2×#548D71semidirect
438. C71C2×#3500semidirect
452. C23×Q8C2×D71semidirect
459. #548C2×D71semidirect
476. C2×#124C2×D71semidirect
482. C2×C22⋊Q8C2×D71semidirect
490. C2×#121C2×D71semidirect
495. C2×C4×Q8C2×D71semidirect
501. C2×C4×D4C2×D71semidirect
533. C22×Q8C22×D71semidirect
569. #124C22×D71semidirect
575. C22⋊Q8C22×D71semidirect
583. #121C22×D71semidirect
587. C4×Q8C22×D71semidirect
593. C4×D4C22×D71semidirect
839. C2#22602131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561762
C22×#145561742
#226021312
C2×#179866612
C2×#179866602
C2×#179866562
C2×#179866462
C2×#179866452
C2×#179866422
C2×#179866402
C2×#179865722
C2×#179865652
C2×#179865462
C2×#124×D712
C2×C4×#117658662
C2×#548×C712
C2×#350071