Finite Group Databasebeta

← #32158495

Subgroups — #32158495

Order 18176.

5682 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556174C211yesmaximal, characteristic
2C2×#17986481C211yesmaximal, characteristic, complemented
3C2×C4×#11765866C211yesmaximal, characteristic, complemented
4#22591181C211yesmaximal, characteristic, complemented
5#22591178C211yesmaximal, characteristic, complemented
6#22591178C211yesmaximal, characteristic, complemented
7C22⋊C4×D284C213yesmaximal, complemented
8#22591161C213yesmaximal, complemented
9#22591161C213yesmaximal, complemented
10#22591160C213yesmaximal, complemented
11#22590929C213yesmaximal, complemented
12#22590919C213yesmaximal, complemented
13#22590826C213yesmaximal, complemented
14#390×D71C213yesmaximal, complemented
15C71×#2341C211yesmaximal, characteristic, complemented
16C2×#14556174—28no—
17C2×#14556174—28no—
18C2×#14556174C4116yescomplemented
19C22×#11765866C2211yescharacteristic
20C22×#11765866C2211yescharacteristic
21C22×#11765865C2213yes—
22C23×D284C2213yes—
23C22×D4×D71C2213yes—
24C22×D4×D71C2213yes—
25#17986481—28no—
26C4×#11765866—28no—
27C2×Q8×Dic71C2211yescharacteristic, complemented
28C2×Q8×Dic71C2211yescharacteristic, complemented
29C2×C4×D284C2213yescomplemented
30C2×C4×D284C2213yescomplemented
31C2×#14556090C2213yescomplemented
32C2×#14556090C2213yescomplemented
33C2×#14556086C2213yescomplemented
34C2×#14556085C2213yescomplemented
35C2×C4⋊C4×D71C2213yescomplemented
36C2×C22⋊C4×D71C2216yescomplemented
37C2×C22⋊C4×D71C2216yescomplemented
38C2×C42×D71C2213yescomplemented
39#17985903C2211yescharacteristic, complemented
40#17985903C2213yescomplemented
41#17985902C2213yescomplemented
42#17985902C2213yescomplemented
43#17985901C2213yescomplemented
44#17985901C2213yescomplemented
45#17985900C2213yescomplemented
46#17985900C2213yescomplemented
47#17985899C2213yescomplemented
48#17985899C2216yescomplemented
49#17985899C2213yescomplemented
50#17985877C2213yescomplemented
51#17985877C2213yescomplemented
52#17985877C2216yescomplemented
53#17985875C2213yescomplemented
54#17985875C2213yescomplemented
55#17985875C2216yescomplemented
56#17985859C2213yescomplemented
57#17985856C2213yescomplemented
58#17985856C2213yescomplemented
59#17985854C2216yescomplemented
60#17985854C2216yescomplemented
61C4×(C2×D71)⋊C4C2213yescomplemented
62C4×(C2×D71)⋊C4C2213yescomplemented
63C4×C22⋊Dic71C2213yescomplemented
64C22×#41×C71C2211yescharacteristic
65C2×C4×Q8×C71C2211yescharacteristic, complemented
66C2×C4×Q8×C71C2211yescharacteristic, complemented
67#390×C71C2213yescomplemented
68#390×C71C2213yescomplemented
69#380×C71C2213yescomplemented
70C4×C22⋊C4×C71C2213yescomplemented
71C24×D71C2316yes—
72#14556174—2128no—
73C2×#11765866—24no—
74C2×#11765866—24no—
75C2×#11765866C2×C418yes—
76C2×#11765866C2×C418yescomplemented
77C2×#11765866D418yes—
78C2×#11765866D418yes—
79C2×#11765865—212no—
80C2×#11765865—212no—
81C2×#11765865C2×C4124yescomplemented
82C22×Dic142C2311yescharacteristic
83C22×D284—212no—
84C22×D284—212no—
85C22×D284C2×C4124yescomplemented
86C22×D284C2313yes—
87C22×D284C2313yes—
88C22×D284C2313yes—
89C22×C22⋊D71C2313yes—
90C22×C22⋊D71C2313yes—
91C2×D4×D71—212no—
92C2×D4×D71—212no—
93C2×D4×D71—212no—
94C2×D4×D71—212no—
95C2×D4×D71C2×C4124yescomplemented
96C2×D4×D71C2×C4124yescomplemented
97C22×C4×D71C2313yes—
98C22×C4×D71C2313yes—
99C22×C4×D71C2313yes—
100C22×C4×D71C2316yes—
101C22×C4×D71C2313yes—
102Q8×Dic71—24no—
103Q8×Dic71—24no—
104C4×D284—212no—
105C4×D284—212no—
106#14556090—212no—
107#14556090—212no—
108#14556086—212no—
109#14556085—212no—
110C2×C4⋊Dic71C2313yes—
111C2×C4⋊Dic71C2313yes—
112C2×Dic71⋊C4C2313yes—
113C2×Dic71⋊C4C2311yescharacteristic
114C4⋊C4×D71—212no—
115C2×C22⋊Dic71C2313yes—
116C2×C22⋊Dic71C2313yes—
117C2×C22⋊Dic71C2316yes—
118C2×(C2×D71)⋊C4C2313yes—
119C2×(C2×D71)⋊C4C2313yes—
120C2×(C2×D71)⋊C4C2313yes—
121C2×(C2×D71)⋊C4C2313yes—
122C2×(C2×D71)⋊C4C2316yes—
123C2×(C2×D71)⋊C4C2313yes—
124C2×(C2×D71)⋊C4C2313yes—
125C2×(C2×D71)⋊C4C2316yes—
126C2×(C2×D71)⋊C4C2316yes—
127C22⋊C4×D71—412no—
128C22⋊C4×D71—412no—
129C2×C4×Dic71C2313yes—
130C2×C4×Dic71C2313yes—
131C2×C4×Dic71C2311yescharacteristic
132C2×C4×Dic71C2313yes—
133C42×D71—212no—
134C71⋊#95C2311yescharacteristic
135C71⋊#95C2313yes—
136C71⋊#95C2311yescharacteristic
137C71⋊#95C2311yescharacteristic
138C71⋊#95C2313yes—
139C71⋊#95C2313yes—
140C2×#41×C71—24no—
141C2×#41×C71—24no—
142C2×#41×C71C2×C418yescomplemented
143C22×Q8×C71C2311yescharacteristic
144C22×D4×C71C2313yes—
145C23×C4×C71C2313yes—
146C4×Q8×C71—24no—
147C4×Q8×C71—24no—
148C2×C4⋊C4×C71C2313yes—
149C2×C4⋊C4×C71C2313yes—
150C2×C22⋊C4×C71C2313yes—
151C2×C22⋊C4×C71C2313yes—
152C2×C22⋊C4×C71C2316yes—
153C2×C42×C71C2313yes—
154C2×C42×C71C2313yes—
155#95×C71C2311yescharacteristic
156#95×C71C2313yes—
157C23×D71—212no—
158C23×D71—212no—
159C23×D71—46no—
160C23×D71—46no—
161C23×D71—46no—
162C23×D71—46no—
163C23×D71C22×C4124yes—
164C23×D71C2413yes—
165C23×D71C2413yes—
166#11765866—232no—
167#11765866C22⋊C4164yescomplemented
168#11765865—296no—
169C2×Dic142—22no—
170C2×Dic142—22no—
171C2×Dic142C22×C414yes—
172C2×D284—26no—
173C2×D284—26no—
174C2×D284—26no—
175C2×D284—26no—
176C2×D284—296no—
177C2×D284C22×C4112yes—
178C2×D284C22×C4112yes—
179C2×D284C22×C4112yes—
180C2×D284C2×D4112yes—
181C2×D284C2×D4112yes—
182C2×C22⋊D71—26no—
183C2×C22⋊D71—26no—
184C2×C22⋊D71—26no—
185C2×C22⋊D71—26no—
186C2×C22⋊D71C22×C4112yes—
187C2×C22⋊D71C22×C4112yes—
188D4×D71—296no—
189D4×D71—296no—
190C22×Dic71C2413yes—
191C22×Dic71C2413yes—
192C22×Dic71C2411yescharacteristic
193C22×Dic71C2411yescharacteristic
194C22×Dic71C2411yescharacteristic
195C22×Dic71C2411yescharacteristic
196C2×C4×D71—26no—
197C2×C4×D71—26no—
198C2×C4×D71—26no—
199C2×C4×D71—26no—
200C2×C4×D71—26no—
201C2×C4×D71—26no—
202C2×C4×D71—212no—
203C2×C4×D71—43no—
204C2×C4×D71—43no—
205C2×C4×D71—46no—
206C2×C4×D71—46no—
207C2×C4×D71C22×C4112yes—
208C2×C4×D71C22×C4112yes—
209C2×C4×D71C2×D4112yes—
210C2×C4×D71C2×D4112yes—
211C4⋊Dic71—26no—
212C4⋊Dic71—26no—
213Dic71⋊C4—26no—
214Dic71⋊C4—22no—
215C22⋊Dic71—26no—
216C22⋊Dic71—46no—
217C22⋊Dic71—43no—
218(C2×D71)⋊C4—26no—
219(C2×D71)⋊C4—26no—
220(C2×D71)⋊C4—212no—
221(C2×D71)⋊C4—26no—
222(C2×D71)⋊C4—26no—
223(C2×D71)⋊C4—46no—
224(C2×D71)⋊C4—46no—
225(C2×D71)⋊C4—43no—
226(C2×D71)⋊C4—43no—
227C4×Dic71—26no—
228C4×Dic71—26no—
229C4×Dic71—22no—
230C4×Dic71—26no—
231C24×C71C2413yes—
232#41×C71—232no—
233C2×Q8×C71C22×C414yes—
234C2×Q8×C71C2×D414yes—
235C2×Q8×C71C2×D414yes—
236C2×D4×C71—26no—
237C2×D4×C71—26no—
238C2×D4×C71C22×C4112yes—
239C22×C4×C71—26no—
240C22×C4×C71—26no—
241C22×C4×C71C22×C4112yes—
242C22×C4×C71C2413yes—
243C22×C4×C71C2413yes—
244C22×C4×C71C2411yescharacteristic
245C22×C4×C71C2411yescharacteristic
246C22×C4×C71C2411yescharacteristic
247C22×C4×C71C2413yes—
248C4⋊C4×C71—26no—
249C4⋊C4×C71—26no—
250C22⋊C4×C71—26no—
251C22⋊C4×C71—43no—
252C22⋊C4×C71—46no—
253C42×C71—26no—
254C42×C71—26no—
255C23×C71—23no—
256C23×C71—23no—
257C23×C71—23no—
258C23×C71—23no—
259C23×C71—23no—
260C23×C71—23no—
261C23×C71C23×C416yes—
262C23×C71C2511yescharacteristic
263C22×D71—23no—
264C22×D71—23no—
265C22×D71—23no—
266C22×D71—23no—
267C22×D71—23no—
268C22×D71—23no—
269C22×D71—23no—
270C22×D71—23no—
271C22×D71—23no—
272C22×D71—23no—
273C22×D71—248no—
274C22×D71—424no—
275C22×D71—424no—
276C22×D71—812no—
277C22×D71—812no—
278C22×D71—812no—
279C22×D71—812no—
280C22×D71C23×C416yes—
281C22×D71C23×C416yes—
282C22×D71C22×D416yes—
283C22×D71C22×D416yes—
284Q8×C71C2×C22⋊C4116yescomplemented
285D4×C71—224no—
286C2×C4×C71—21no—
287C2×C4×C71—21no—
288C2×C4×C71—21no—
289C2×C4×C71—21no—
290C2×C4×C71—224no—
291C2×C4×C71—21no—
292C2×C4×C71—23no—
293C2×C4×C71—23no—
294C2×C4×C71—23no—
295C2×C4×C71—23no—
296C2×C4×C71—23no—
297C2×C4×C71—21no—
298C2×C4×C71—23no—
299C2×C4×C71—21no—
300C2×C4×C71C23×C412yes—
301C2×C4×C71C23×C416yes—
302C2×C4×C71C22×D416yes—
303C2×C4×C71C22×D416yes—
304C2×C4×C71H(5,𝔽2)12yescomplemented
305C22⋊D71—224no—
306C22⋊D71—224no—
307C2×Dic71—21no—
308C2×Dic71—21no—
309C2×Dic71—21no—
310C2×Dic71—21no—
311C2×Dic71—21no—
312C2×Dic71—23no—
313C2×Dic71—23no—
314C2×Dic71—23no—
315C2×Dic71—23no—
316C2×Dic71—23no—
317C2×Dic71—21no—
318C2×Dic71—23no—
319C2×Dic71—21no—
320C2×Dic71C23×C412yes—
321C2×Dic71C23×C412yes—
322C2×Dic71C22×D412yes—
323C2×Dic71C22×D412yes—
324C2×Dic71H(5,𝔽2)12yescomplemented
325D284—224no—
326D284—224no—
327D284C2×C22⋊C4148yescomplemented
328C4×D71—224no—
329C4×D71—412no—
330C4×D71—412no—
331C4×D71—812no—
332C4×D71C2×C22⋊C4148yescomplemented
333Dic142—28no—
334C22×C71—26no—
335C22×C71—26no—
336C22×C71—26no—
337C22×C71—43no—
338C22×C71—43no—
339C22×C71—43no—
340C22×C71—43no—
341C22×C71C24×C411yescharacteristic
342C22×C71C23×D411yescharacteristic
343C22×C71C23×D411yescharacteristic
344C22×C71C2×H(5,𝔽2)11yescharacteristic
345C22×C71C2×H(5,𝔽2)11yescharacteristic
346C22×C71#58511yescharacteristic
347C22×C71#58511yescharacteristic
348C2×D71—26no—
349C2×D71—26no—
350C2×D71—26no—
351C2×D71—26no—
352C2×D71—26no—
353C2×D71—26no—
354C2×D71—26no—
355C2×D71—26no—
356C2×D71—26no—
357C2×D71—43no—
358C2×D71—43no—
359C2×D71—43no—
360C2×D71—43no—
361C2×D71—848no—
362C2×D71C22×C22⋊C4112yes—
363C4×C71—22no—
364C4×C71—22no—
365C4×C71—43no—
366C4×C71—43no—
367C4×C71—41no—
368C4×C71C22×C22⋊C4112yes—
369Dic71—22no—
370Dic71—22no—
371Dic71—43no—
372Dic71—43no—
373Dic71—41no—
374Dic71C22×C22⋊C414yes—
375#34258—711nomaximal, Sylow
376C2×C71—46no—
377C2×C71C23×C22⋊C411yescharacteristic
378C2×C71C4×H(5,𝔽2)11yescharacteristic
379C2×C71C4×H(5,𝔽2)11yescharacteristic
380C2×C71#348811yescharacteristic
381C2×C71#348811yescharacteristic
382C2×C71#349811yescharacteristic
383C2×C71#350011yescharacteristic
384D71—212no—
385D71—46no—
386C22×H(5,𝔽2)—711no—
387C2×#520—711no—
388C2×C4×#41—711no—
389#2341—711no—
390#2341—711no—
391#2341—711no—
392#2341D7111yescharacteristic, complemented
393D4×C22⋊C4—713no—
394D4×C22⋊C4—713no—
395D4×C22⋊C4—713no—
396D4×C22⋊C4—713no—
397#2311—713no—
398#2309—713no—
399#2297—713no—
400C2×#390—713no—
401C71#3425811yescharacteristic, complemented, Sylow
402C2×H(5,𝔽2)—7116no—
403C2×H(5,𝔽2)—1428no—
404C2×H(5,𝔽2)—1428no—
405C22×#41—711no—
406C22×#41—711no—
407C22×#41—713no—
408C22×#41C2×D7111yescharacteristic
409C23×D4—713no—
410C23×D4—713no—
411C23×D4—713no—
412#520—1428no—
413C4×#41—1428no—
414C2×C4×Q8—711no—
415C2×C4×Q8—711no—
416C2×C4×Q8C2×D7111yescharacteristic, complemented
417C2×C4×Q8C2×D7111yescharacteristic, complemented
418C2×C4×D4—713no—
419C2×C4×D4—713no—
420C2×C4×D4—713no—
421C2×C4×D4—713no—
422C2×#117—713no—
423C2×#117—713no—
424C22×C4⋊C4—713no—
425C22×C22⋊C4—716no—
426C22×C22⋊C4—716no—
427C22×C42—713no—
428#391—713no—
429#391—711no—
430#390—713no—
431#390—713no—
432#390—713no—
433#390—713no—
434#390—713no—
435#390—716no—
436#390—713no—
437#390—713no—
438#390—713no—
439#390C2×D7113yescomplemented
440#390C2×D7113yescomplemented
441#386—716no—
442#386—713no—
443#386—713no—
444#386—716no—
445#386—713no—
446#386—713no—
447#380—713no—
448#380—713no—
449#380—713no—
450#380C2×D7113yescomplemented
451#379—716no—
452#379—716no—
453C4×C22⋊C4—713no—
454C4×C22⋊C4—713no—
455C4×C22⋊C4—713no—
456C4×C22⋊C4C2×D7113yescomplemented
457C25—716no—
458H(5,𝔽2)—142128no—
459C2×#41—24no—
460C2×#41—24no—
461C2×#41—718no—
462C2×#41—718no—
463C2×#41—718no—
464C2×#41—718no—
465C2×#41—7124no—
466C2×#41—14212no—
467C2×#41—14212no—
468C2×#41—1424no—
469C2×#41—1424no—
470C2×#41C4×D7118yescomplemented
471C22×Q8—711no—
472C22×Q8C22×D7111yescharacteristic
473C22×D4—713no—
474C22×D4—713no—
475C22×D4—7124no—
476C22×D4—7124no—
477C22×D4—7124no—
478C22×D4—713no—
479C22×D4—713no—
480C22×D4—713no—
481C22×D4—14212no—
482C22×D4—14212no—
483C22×D4—14212no—
484C22×D4—14212no—
485C22×D4—14212no—
486C22×D4—14212no—
487C22×D4C22×D7113yes—
488C23×C4—716no—
489C23×C4—713no—
490C23×C4—713no—
491C23×C4—713no—
492C23×C4—713no—
493C23×C4C22×D7113yes—
494C4×Q8—24no—
495C4×Q8—24no—
496C4×Q8—1424no—
497C4×Q8—1424no—
498C4×D4—14212no—
499C4×D4—14212no—
500C4×D4—14212no—
501C4×D4—14212no—
502#117—14212no—
503#117—14212no—
504C2×C4⋊C4—713no—
505C2×C4⋊C4—713no—
506C2×C4⋊C4—711no—
507C2×C4⋊C4—713no—
508C2×C4⋊C4—14212no—
509C2×C4⋊C4C22×D7113yes—
510C2×C4⋊C4C22×D7113yes—
511C2×C22⋊C4—28412no—
512C2×C22⋊C4—28412no—
513C2×C22⋊C4—716no—
514C2×C22⋊C4—713no—
515C2×C22⋊C4—716no—
516C2×C22⋊C4—716no—
517C2×C22⋊C4—713no—
518C2×C22⋊C4—713no—
519C2×C22⋊C4—713no—
520C2×C22⋊C4—713no—
521C2×C22⋊C4—713no—
522C2×C22⋊C4—713no—
523C2×C22⋊C4—716no—
524C2×C22⋊C4—713no—
525C2×C22⋊C4C22×D7113yes—
526C2×C22⋊C4C22×D7116yes—
527C2×C22⋊C4C22×D7113yes—
528C2×C42—713no—
529C2×C42—713no—
530C2×C42—713no—
531C2×C42—711no—
532C2×C42—14212no—
533C2×C42C22×D7113yes—
534C2×C42C22×D7113yes—
535#95—711no—
536#95—711no—
537#95—711no—
538#95—713no—
539#95—713no—
540#95—713no—
541#95C22×D7111yescharacteristic
542#95C22×D7113yes—
543C24—2846no—
544C24—2846no—
545C24—2846no—
546C24—2846no—
547C24—7124no—
548C24—713no—
549C24—713no—
550C24—14212no—
551C24—14212no—
552C24C23×D7113yes—
553#41—232no—
554#41—7164no—
555#41—14296no—
556#41—14232no—
557C2×Q8—714no—
558C2×Q8—1422no—
559C2×Q8—1422no—
560C2×Q8C2×C4×D7114yes—
561C2×Q8D4×D7114yes—
562C2×Q8D4×D7114yes—
563C2×D4—26no—
564C2×D4—26no—
565C2×D4—7112no—
566C2×D4—7112no—
567C2×D4—7112no—
568C2×D4—7112no—
569C2×D4—7112no—
570C2×D4—7112no—
571C2×D4—7112no—
572C2×D4—14296no—
573C2×D4—1426no—
574C2×D4—1426no—
575C2×D4—14296no—
576C2×D4—1426no—
577C2×D4—1426no—
578C2×D4—14296no—
579C2×D4—1426no—
580C2×D4—1426no—
581C2×D4—1426no—
582C2×D4—1426no—
583C2×D4C2×C4×D71112yes—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—2843no—
587C22×C4—2843no—
588C22×C4—2846no—
589C22×C4—2846no—
590C22×C4—711no—
591C22×C4—7112no—
592C22×C4—7112no—
593C22×C4—7112no—
594C22×C4—711no—
595C22×C4—711no—
596C22×C4—7112no—
597C22×C4—711no—
598C22×C4—713no—
599C22×C4—713no—
600C22×C4—1426no—
601C22×C4—1426no—
602C22×C4—1426no—
603C22×C4—14212no—
604C22×C4—1426no—
605C22×C4—1426no—
606C22×C4—1426no—
607C22×C4C2×C4×D71112yes—
608C22×C4C23×D7113yes—
609C22×C4C23×D7111yescharacteristic
610C22×C4C23×D7113yes—
611C22×C4C23×D7111yescharacteristic
612C22×C4C23×D7111yescharacteristic
613C22×C4C23×D7113yes—
614C4⋊C4—26no—
615C4⋊C4—26no—
616C4⋊C4—1426no—
617C4⋊C4—1422no—
618C4⋊C4—1426no—
619C4⋊C4—1426no—
620C22⋊C4—26no—
621C22⋊C4—46no—
622C22⋊C4—43no—
623C22⋊C4—2846no—
624C22⋊C4—2846no—
625C22⋊C4—2843no—
626C22⋊C4—2843no—
627C22⋊C4—2846no—
628C22⋊C4—2843no—
629C22⋊C4—1426no—
630C22⋊C4—1426no—
631C22⋊C4—14212no—
632C22⋊C4—1426no—
633C22⋊C4—1426no—
634C22⋊C4—1426no—
635C42—26no—
636C42—26no—
637C42—1422no—
638C42—1426no—
639C42—1426no—
640C42—1426no—
641C23—23no—
642C23—23no—
643C23—23no—
644C23—23no—
645C23—23no—
646C23—23no—
647C23—28424no—
648C23—28424no—
649C23—56812no—
650C23—56812no—
651C23—56812no—
652C23—56812no—
653C23—716no—
654C23—716no—
655C23—716no—
656C23—716no—
657C23—14248no—
658C23—1423no—
659C23—1423no—
660C23—1423no—
661C23—1423no—
662C23—1423no—
663C23—1423no—
664C23—1423no—
665C23—1423no—
666C23—1423no—
667C23—1423no—
668C23C22×C4×D7116yes—
669C23C24×D7111yescharacteristic
670Q8—1428no—
671Q8C22⋊C4×D71116yescomplemented
672D4—224no—
673D4—7148no—
674D4—14224no—
675D4—14224no—
676D4—14224no—
677D4—14224no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—224no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—23no—
687C2×C4—23no—
688C2×C4—23no—
689C2×C4—21no—
690C2×C4—23no—
691C2×C4—21no—
692C2×C4—28412no—
693C2×C4—28412no—
694C2×C4—56812no—
695C2×C4—712no—
696C2×C4—712no—
697C2×C4—712no—
698C2×C4—7148no—
699C2×C4—712no—
700C2×C4—712no—
701C2×C4—1421no—
702C2×C4—1423no—
703C2×C4—1423no—
704C2×C4—1423no—
705C2×C4—1423no—
706C2×C4—1423no—
707C2×C4—1421no—
708C2×C4—1421no—
709C2×C4—1423no—
710C2×C4—1421no—
711C2×C4—1421no—
712C2×C4—1421no—
713C2×C4—1421no—
714C2×C4—14224no—
715C2×C4C22×C4×D7112yes—
716C2×C4C22×C4×D7116yes—
717C2×C4C2×D4×D7116yes—
718C2×C4C2×D4×D7116yes—
719C2×C4#1455617412yescomplemented
720C22—26no—
721C22—26no—
722C22—26no—
723C22—43no—
724C22—43no—
725C22—43no—
726C22—43no—
727C22—2843no—
728C22—2843no—
729C22—2843no—
730C22—2843no—
731C22—56848no—
732C22—7112no—
733C22—1426no—
734C22—1426no—
735C22—1426no—
736C22—1426no—
737C22—1426no—
738C22—1426no—
739C22—1426no—
740C22—1426no—
741C22—1426no—
742C22C23×C4×D7111yescharacteristic
743C22C22×D4×D7111yescharacteristic
744C22C22×D4×D7111yescharacteristic
745C22H(5,𝔽2)×D7111yescharacteristic
746C22C2×#1455617411yescharacteristic
747C22#1798683511yescharacteristic
748C22#1798683611yescharacteristic
749C4—22no—
750C4—22no—
751C4—43no—
752C4—43no—
753C4—41no—
754C4—2843no—
755C4—2843no—
756C4—2841no—
757C4—714no—
758C4—1422no—
759C4—1422no—
760C4C2×C22⋊C4×D71112yes—
761C2—46no—
762C2—2846no—
763C2—14212no—
764C2C22×C22⋊C4×D7111yescharacteristic
765C2#2260154611yescharacteristic
766C2C4×#1455617411yescharacteristic
767C2#2260200611yescharacteristic
768C2#2260200811yescharacteristic
769C2#2260211711yescharacteristic
770C2#2260213111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2341C2
socle, cosocleC23×C71C25
prime radicalC22×#14556174C2
hypercenter#2341D71
hypocenterC71#34258
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#17986481C2semidirect
3. C2×C4×#11765866C2semidirect
4. #22591181C2semidirect
5. #22591178C2semidirect
6. #22591178C2semidirect
7. C22⋊C4×D284C2semidirect
8. #22591161C2semidirect
9. #22591161C2semidirect
10. #22591160C2semidirect
11. #22590929C2semidirect
12. #22590919C2semidirect
13. #22590826C2semidirect
14. #390×D71C2semidirect
15. C71×#2341C2semidirect
18. C2×#14556174C4semidirect
27. C2×Q8×Dic71C22semidirect
28. C2×Q8×Dic71C22semidirect
29. C2×C4×D284C22semidirect
30. C2×C4×D284C22semidirect
31. C2×#14556090C22semidirect
32. C2×#14556090C22semidirect
33. C2×#14556086C22semidirect
34. C2×#14556085C22semidirect
35. C2×C4⋊C4×D71C22semidirect
36. C2×C22⋊C4×D71C22semidirect
37. C2×C22⋊C4×D71C22semidirect
38. C2×C42×D71C22semidirect
39. #17985903C22semidirect
40. #17985903C22semidirect
41. #17985902C22semidirect
42. #17985902C22semidirect
43. #17985901C22semidirect
44. #17985901C22semidirect
45. #17985900C22semidirect
46. #17985900C22semidirect
47. #17985899C22semidirect
48. #17985899C22semidirect
49. #17985899C22semidirect
50. #17985877C22semidirect
51. #17985877C22semidirect
52. #17985877C22semidirect
53. #17985875C22semidirect
54. #17985875C22semidirect
55. #17985875C22semidirect
56. #17985859C22semidirect
57. #17985856C22semidirect
58. #17985856C22semidirect
59. #17985854C22semidirect
60. #17985854C22semidirect
61. C4×(C2×D71)⋊C4C22semidirect
62. C4×(C2×D71)⋊C4C22semidirect
63. C4×C22⋊Dic71C22semidirect
65. C2×C4×Q8×C71C22semidirect
66. C2×C4×Q8×C71C22semidirect
67. #390×C71C22semidirect
68. #390×C71C22semidirect
69. #380×C71C22semidirect
70. C4×C22⋊C4×C71C22semidirect
76. C2×#11765866C2×C4semidirect
81. C2×#11765865C2×C4semidirect
85. C22×D284C2×C4semidirect
95. C2×D4×D71C2×C4semidirect
96. C2×D4×D71C2×C4semidirect
142. C2×#41×C71C2×C4semidirect
167. #11765866C22⋊C4semidirect
284. Q8×C71C2×C22⋊C4semidirect
304. C2×C4×C71H(5,𝔽2)semidirect
324. C2×Dic71H(5,𝔽2)semidirect
327. D284C2×C22⋊C4semidirect
332. C4×D71C2×C22⋊C4semidirect
392. #2341D71semidirect
401. C71#34258semidirect
416. C2×C4×Q8C2×D71semidirect
417. C2×C4×Q8C2×D71semidirect
439. #390C2×D71semidirect
440. #390C2×D71semidirect
450. #380C2×D71semidirect
456. C4×C22⋊C4C2×D71semidirect
470. C2×#41C4×D71semidirect
671. Q8C22⋊C4×D71semidirect
719. C2×C4#14556174semidirect

Maximal subgroups

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

subgroupindex
C22×#145561742
C2×#179864812
C2×C4×#117658662
#225911812
#225911782
C22⋊C4×D2842
#225911612
#225911602
#225909292
#225909192
#225908262
#390×D712
C71×#23412
#3425871