Finite Group Databasebeta

← C4×#17986247 #32004085

Subgroups — C4×#17986247 #32004085

Order 18176.

1086 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986247C211yesmaximal, characteristic
2C2×C4×#11765852C211yesmaximal, characteristic, complemented
3C2×C4×#11765849C211yesmaximal, characteristic, complemented
4C4×#14556102C211yesmaximal, characteristic
5#22589224C211yesmaximal, characteristic, complemented
6#22589075C211yesmaximal, characteristic, complemented
7#22589036C211yesmaximal, characteristic, complemented
8#22589033C211yesmaximal, characteristic, complemented
9#22588776C211yesmaximal, characteristic
10#22588774C211yesmaximal, characteristic, complemented
11#22588371C211yesmaximal, characteristic, complemented
12C4×#14556061C211yesmaximal, characteristic, complemented
13C4×#14556052C211yesmaximal, characteristic, complemented
14C4×#14556048C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
16C22×#11765852C2211yescharacteristic
17C22×#11765849C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C2×#14556102C2211yescharacteristic
20C2×C4×D284C2211yescharacteristic
21C2×C4×C22⋊D71—21no—
22#17986247C418yesdirect product factor
23C4×#11765852—24no—
24C2×#14556061C2211yescharacteristic
25C2×#14556061C2211yescharacteristic
26C2×#14556059C2211yescharacteristic
27C2×#14556052C2211yescharacteristic
28C2×#14556052C2211yescharacteristic
29C2×#14556052C2211yescharacteristic
30C2×#14556048C2211yescharacteristic
31C2×#14556048C2211yescharacteristic
32C2×#14556048C2211yescharacteristic
33C4×#11765849—24no—
34C2×#14556039C2211yescharacteristic
35C2×#14556039C2211yescharacteristic
36C2×C4×C71⋊C8C2211yescharacteristic
37C2×C4×C71⋊C8C2211yescharacteristic
38#17985901C2211yescharacteristic
39#17985897C2211yescharacteristic
40#17985890—21no—
41#17985878—21no—
42#17985859C2211yescharacteristic
43C4×C4⋊Dic71C2211yescharacteristic
44C4×(C2×D71)⋊C4—21no—
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#17985761C2211yescharacteristic
50#17985761C2211yescharacteristic
51C2×C22⋊Q8×C71C2211yescharacteristic
52C2×C4×Q8×C71C2211yescharacteristic
53C22×C42×C71C2211yescharacteristic
54#391×C71C2211yescharacteristic
55#389×C71C2211yescharacteristic
56#387×C71—21no—
57#385×C71—21no—
58#380×C71C2211yescharacteristic
59C4×C4⋊C4×C71—21no—
60C4×C4⋊C4×C71C2211yescharacteristic
61C4×C22⋊C4×C71—21no—
62C22×D284C2311yescharacteristic
63C22×C22⋊D71—21no—
64C22×C4×D71—21no—
65C2×#11765852—22no—
66C2×#11765852—22no—
67C2×#11765852C2×C414yescomplemented
68C2×#11765849—22no—
69C2×#11765849—22no—
70C2×#11765849—22no—
71C2×#11765849—22no—
72C2×#11765849—22no—
73C2×#11765849C2×C414yescomplemented
74C22×C71⋊C8C2311yescharacteristic
75C22×C71⋊C8C2311yescharacteristic
76C22×C71⋊C8C2311yescharacteristic
77C22×C71⋊C8C2311yescharacteristic
78#14556102—22no—
79#14556102C2×C414yes—
80C4×D284—22no—
81C4×D284—22no—
82C4×C22⋊D71—44no—
83C2×C4⋊Dic71C2311yescharacteristic
84C2×C4⋊Dic71C2311yescharacteristic
85C2×C4⋊Dic71C2311yescharacteristic
86C2×Dic71⋊C4—21no—
87C2×C22⋊Dic71—21no—
88C2×(C2×D71)⋊C4—21no—
89C2×(C2×D71)⋊C4—21no—
90C2×(C2×D71)⋊C4—21no—
91C2×(C2×D71)⋊C4—21no—
92C2×C4×Dic71—21no—
93#14556061—22no—
94#14556061C2×C414yescomplemented
95#14556059—22no—
96#14556052—22no—
97#14556052—22no—
98#14556052C2×C414yescomplemented
99#14556048—22no—
100#14556048—22no—
101#14556048C2×C414yescomplemented
102#14556039—22no—
103#14556039—22no—
104C4×C71⋊C8—22no—
105C4×C71⋊C8D414yescomplemented
106C71⋊#95—21no—
107C71⋊#95—21no—
108C71⋊#95—21no—
109C22×Q8×C71C2311yescharacteristic
110C23×C4×C71D411yescharacteristic
111C23×C4×C71D411yescharacteristic
112C23×C4×C71C2311yescharacteristic
113C22⋊Q8×C71—22no—
114C22⋊Q8×C71C2×C414yescomplemented
115C4×Q8×C71—22no—
116C4×Q8×C71—22no—
117C2×C4⋊C4×C71—21no—
118C2×C4⋊C4×C71—21no—
119C2×C4⋊C4×C71—21no—
120C2×C4⋊C4×C71C2311yescharacteristic
121C2×C4⋊C4×C71C2311yescharacteristic
122C2×C4⋊C4×C71C2311yescharacteristic
123C2×C22⋊C4×C71—21no—
124C2×C22⋊C4×C71—21no—
125C2×C42×C71—22no—
126C2×C42×C71—22no—
127C2×C42×C71—21no—
128C2×C42×C71—21no—
129C2×C42×C71D411yescharacteristic
130C2×C42×C71D411yescharacteristic
131C2×C42×C71C2311yescharacteristic
132C2×C42×C71C2311yescharacteristic
133#95×C71—21no—
134#95×C71—21no—
135#95×C71—21no—
136#95×C71—21no—
137#95×C71—21no—
138C23×D71—21no—
139C2×D284—21no—
140C2×D284—21no—
141C2×D284—21no—
142C2×D284—21no—
143C2×D284—21no—
144C2×D284C22×C412yes—
145C2×C22⋊D71—24no—
146C2×C22⋊D71—42no—
147C2×C22⋊D71—42no—
148C22×Dic71—21no—
149C22×Dic71—21no—
150C22×Dic71—21no—
151C2×C4×D71—42no—
152C2×C4×D71—42no—
153C2×C4×D71—42no—
154#11765852—28no—
155#11765849—28no—
156#11765849—28no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161C2×C71⋊C8—21no—
162C2×C71⋊C8—21no—
163C2×C71⋊C8C22×C412yes—
164C2×C71⋊C8C22×C412yes—
165C2×C71⋊C8C2×D412yes—
166C2×C71⋊C8C2×D412yes—
167C2×C71⋊C8#4112yes—
168C2×C71⋊C8#4112yes—
169C4⋊Dic71—21no—
170C4⋊Dic71—21no—
171C4⋊Dic71—21no—
172C4⋊Dic71—21no—
173C4⋊Dic71—21no—
174C4⋊Dic71C22×C412yes—
175Dic71⋊C4—42no—
176C22⋊Dic71—42no—
177(C2×D71)⋊C4—24no—
178(C2×D71)⋊C4—42no—
179(C2×D71)⋊C4—42no—
180(C2×D71)⋊C4—42no—
181C4×Dic71—42no—
182C24×C71C2×D411yescharacteristic
183C2×Q8×C71—21no—
184C2×Q8×C71—21no—
185C2×Q8×C71—21no—
186C2×Q8×C71—21no—
187C2×Q8×C71—21no—
188C2×Q8×C71C22×C412yes—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—22no—
196C22×C4×C71—22no—
197C22×C4×C71—22no—
198C22×C4×C71—22no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—41no—
202C22×C4×C71—41no—
203C22×C4×C71C22×C412yes—
204C22×C4×C71C2×D411yescharacteristic
205C22×C4×C71C2×D411yescharacteristic
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D411yescharacteristic
209C22×C4×C71#4112yes—
210C22×C4×C71C2411yescharacteristic
211C4⋊C4×C71—24no—
212C4⋊C4×C71—21no—
213C4⋊C4×C71—21no—
214C4⋊C4×C71—21no—
215C4⋊C4×C71—21no—
216C4⋊C4×C71—21no—
217C4⋊C4×C71—42no—
218C4⋊C4×C71—42no—
219C4⋊C4×C71C22×C412yes—
220C22⋊C4×C71—24no—
221C22⋊C4×C71—42no—
222C42×C71—22no—
223C42×C71—22no—
224C42×C71—21no—
225C42×C71—21no—
226C42×C71—42no—
227C42×C71—42no—
228C42×C71C2×D412yes—
229C42×C71#4112yes—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71—21no—
233C23×C71—21no—
234C23×C71—21no—
235C23×C71—21no—
236C23×C71C4×D412yes—
237C23×C71C22×D411yescharacteristic
238C22×D71—22no—
239C22×D71—41no—
240C22×D71—41no—
241C22×D71—41no—
242C22×D71—41no—
243C22×D71—41no—
244C22×D71—41no—
245Q8×C71—22no—
246Q8×C71—22no—
247Q8×C71—41no—
248Q8×C71—41no—
249C2×C4×C71—21no—
250C2×C4×C71—21no—
251C2×C4×C71—21no—
252C2×C4×C71—21no—
253C2×C4×C71—22no—
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—22no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—44no—
266C2×C4×C71—41no—
267C2×C4×C71—41no—
268C2×C4×C71—41no—
269C2×C4×C71—41no—
270C2×C4×C71—44no—
271C2×C4×C71—41no—
272C2×C4×C71—41no—
273C2×C4×C71—41no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71—41no—
277C2×C4×C71C4×D412yes—
278C2×C4×C71#12112yes—
279C2×C4×C71#12112yes—
280C2×C4×C71AGL(1,ℤ/8)12yes—
281C2×C4×C71#13712yes—
282C2×C4×C71C23×C411yescharacteristic
283C2×C4×C71C22×D411yescharacteristic
284C2×C4×C71C2×#4111yescharacteristic
285C2×C4×C71C2×#4111yescharacteristic
286C2×C4×C71C2×#4111yescharacteristic
287C2×C4×C71C2×#4111yescharacteristic
288C22⋊D71—48no—
289C2×Dic71—22no—
290C2×Dic71—41no—
291C2×Dic71—41no—
292C2×Dic71—41no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—41no—
297C2×Dic71—41no—
298D284—22no—
299D284—22no—
300D284—41no—
301D284—41no—
302C4×D71—84no—
303C71⋊C8—22no—
304C71⋊C8—22no—
305C71⋊C8—22no—
306C71⋊C8C4×D414yescomplemented
307C22×C71—22no—
308C22×C71—22no—
309C22×C71—22no—
310C22×C71—41no—
311C22×C71—41no—
312C22×C71—41no—
313C22×C71—41no—
314C22×C71C2×C4×D411yescharacteristic
315C22×C71C2×#12111yescharacteristic
316C22×C71#53211yescharacteristic
317C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C71C2×#13711yescharacteristic
319C22×C71#57511yescharacteristic
320C22×C71#57511yescharacteristic
321C2×D71—42no—
322C2×D71—42no—
323C2×D71—42no—
324C2×D71—81no—
325C2×D71—81no—
326C2×D71—81no—
327C2×D71—81no—
328C4×C71—22no—
329C4×C71—22no—
330C4×C71—42no—
331C4×C71—41no—
332C4×C71—41no—
333C4×C71—42no—
334C4×C71—81no—
335C4×C71—81no—
336C4×C71#46814yescomplemented
337C4×C71C2×C4×D411yescharacteristic
338C4×C71C4×#4111yescharacteristic
339C4×C71#52511yescharacteristic
340C4×C71#52911yescharacteristic
341Dic71—42no—
342Dic71—81no—
343Dic71—81no—
344C4×#468—711nomaximal, Sylow
345C2×C71—42no—
346C2×C71C4×#12111yescharacteristic
347C2×C71C4×AGL(1,ℤ/8)11yescharacteristic
348C2×C71C4×#13711yescharacteristic
349C2×C71C2×#46811yescharacteristic
350C2×C71#305411yescharacteristic
351C2×C71#317111yescharacteristic
352C2×C71#317211yescharacteristic
353D71—82no—
354C2×#468—711no—
355C2×C4×SD16—711no—
356C2×C4×M16—711no—
357C4×C22⋊Q8D7111yescharacteristic, complemented
358C4×#121—711no—
359#1973—711no—
360#1943—711no—
361#1936—711no—
362#1935—711no—
363#1895—711no—
364#1894—711no—
365#1809—711no—
366C4×#107—711no—
367C4×#103—711no—
368C4×#102—711no—
369C71C4×#46811yescharacteristic, complemented, Sylow
370C22×SD16—711no—
371C22×M16—711no—
372C22×M16—711no—
373C2×C22⋊Q8C2×D7111yescharacteristic
374C2×#121—711no—
375C2×C4×Q8C2×D7111yescharacteristic
376C2×C4×D4—711no—
377C2×C4×D4—1421no—
378C22×C42C2×D7111yescharacteristic
379#468—718no—
380C4×SD16—1424no—
381C2×#107—711no—
382C2×#107—711no—
383C2×#106—711no—
384C2×#103—711no—
385C2×#103—711no—
386C2×#103—711no—
387C2×#102—711no—
388C2×#102—711no—
389C2×#102—711no—
390C4×M16—1424no—
391C2×#97—711no—
392C2×#97—711no—
393C2×C4×C8—711no—
394C2×C4×C8—711no—
395#391C2×D7111yescharacteristic
396#390—711no—
397#389—711no—
398#389C2×D7111yescharacteristic
399#388—1421no—
400#387—21no—
401#386—1421no—
402#385—21no—
403#380—711no—
404#380C2×D7111yescharacteristic
405C4×C4⋊C4—21no—
406C4×C4⋊C4—711no—
407C4×C4⋊C4C2×D7111yescharacteristic
408C4×C22⋊C4—21no—
409C4×C22⋊C4—1421no—
410#340—711no—
411#340—711no—
412#340—711no—
413#340—711no—
414#340—711no—
415#340—711no—
416C22×Q8C22×D7111yescharacteristic
417C22×D4—711no—
418C22×D4—1421no—
419C23×C4—1421no—
420C23×C4C22⋊D7111yescharacteristic
421C23×C4C22⋊D7111yescharacteristic
422C23×C4C22×D7111yescharacteristic
423C2×SD16—714no—
424C2×SD16—1422no—
425C2×SD16—1422no—
426C2×M16—714no—
427C2×M16—1422no—
428C2×M16—1422no—
429C2×M16—1422no—
430C2×M16—1422no—
431C2×M16—1422no—
432C22×C8—711no—
433C22×C8—711no—
434C22×C8—711no—
435C22×C8—711no—
436C22⋊Q8—22no—
437C22⋊Q8C4×D7114yescomplemented
438#121—714no—
439#121—1422no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×D4—2844no—
443C4×D4—1422no—
444C4×D4—1422no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—711no—
449C2×C4⋊C4—711no—
450C2×C4⋊C4—711no—
451C2×C4⋊C4—1421no—
452C2×C4⋊C4C22×D7111yescharacteristic
453C2×C4⋊C4C22×D7111yescharacteristic
454C2×C4⋊C4C22×D7111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—1421no—
458C2×C22⋊C4—1421no—
459C2×C22⋊C4—1421no—
460C2×C22⋊C4—1421no—
461C2×C22⋊C4—1421no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—1421no—
467C2×C42C22⋊D7111yescharacteristic
468C2×C42C22⋊D7111yescharacteristic
469C2×C42C22×D7111yescharacteristic
470C2×C42C22×D7111yescharacteristic
471#107—714no—
472#107—1422no—
473#106—1422no—
474#103—714no—
475#103—1422no—
476#103—1422no—
477#102—714no—
478#102—1422no—
479#102—1422no—
480#97—1422no—
481#97—1422no—
482C4×C8—714no—
483C4×C8—1422no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—1421no—
490#95—1421no—
491#95—1421no—
492C24—1421no—
493C24C2×C22⋊D7111yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D7112yes—
500C2×D4—2842no—
501C2×D4—2842no—
502C2×D4—712no—
503C2×D4—1424no—
504C2×D4—1421no—
505C2×D4—1421no—
506C2×D4—1421no—
507C2×D4—1421no—
508C2×D4—1421no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—2842no—
524C22×C4—2842no—
525C22×C4—2842no—
526C22×C4—1421no—
527C22×C4—1421no—
528C22×C4—1421no—
529C22×C4C2×C4×D7112yes—
530C22×C4C2×C22⋊D7111yescharacteristic
531C22×C4C2×C22⋊D7111yescharacteristic
532C22×C4C2×C22⋊D7111yescharacteristic
533C22×C4C2×C22⋊D7111yescharacteristic
534C22×C4C2×C22⋊D7111yescharacteristic
535C22×C4#1176586512yes—
536C22×C4C23×D7111yescharacteristic
537SD16—1428no—
538M16—1428no—
539M16—1428no—
540C2×C8—712no—
541C2×C8—712no—
542C2×C8—712no—
543C2×C8—712no—
544C2×C8—712no—
545C2×C8—712no—
546C2×C8—1421no—
547C2×C8—1421no—
548C2×C8—1421no—
549C2×C8—1421no—
550C2×C8—1421no—
551C2×C8—1421no—
552C4⋊C4—21no—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—2842no—
561C4⋊C4—712no—
562C4⋊C4—1421no—
563C4⋊C4—1421no—
564C4⋊C4—1421no—
565C4⋊C4—1421no—
566C4⋊C4—1421no—
567C4⋊C4C2×C4×D7112yes—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—2842no—
571C22⋊C4—2842no—
572C22⋊C4—2842no—
573C22⋊C4—2842no—
574C22⋊C4—1424no—
575C42—21no—
576C42—21no—
577C42—22no—
578C42—22no—
579C42—42no—
580C42—42no—
581C42—2842no—
582C42D4×D7112yes—
583C42#1176586412yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—2841no—
591C23—2841no—
592C23—2841no—
593C23—2841no—
594C23—2841no—
595C23—2841no—
596C23—1422no—
597C23C4×C22⋊D7112yes—
598C23C22×C22⋊D7111yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—2848no—
604D4—2841no—
605D4—2841no—
606D4—1422no—
607D4—1422no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—44no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—44no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—2841no—
637C2×C4—2841no—
638C2×C4—2841no—
639C2×C4—2841no—
640C2×C4—2841no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—2841no—
644C2×C4—5684no—
645C2×C4—1422no—
646C2×C4C4×C22⋊D7112yes—
647C2×C4#1455610012yes—
648C2×C4#1455610012yes—
649C2×C4#1455615312yes—
650C2×C4#1455615912yes—
651C2×C4C22×C4×D7111yescharacteristic
652C2×C4C2×D4×D7111yescharacteristic
653C2×C4#41×D7111yescharacteristic
654C2×C4#41×D7111yescharacteristic
655C2×C4C2×#1176586411yescharacteristic
656C2×C4C2×#1176586511yescharacteristic
657C8—714no—
658C8—1422no—
659C8—1422no—
660C8—1422no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—2842no—
669C22—2842no—
670C22—2842no—
671C22—5681no—
672C22—5681no—
673C22—5681no—
674C22—5681no—
675C22C2×C4×C22⋊D7111yescharacteristic
676C22C2×#1455610011yescharacteristic
677C22#1798654511yescharacteristic
678C22C2×#1455615311yescharacteristic
679C22C2×#1455615911yescharacteristic
680C22#1798679711yescharacteristic
681C22#1798679711yescharacteristic
682C4—22no—
683C4—22no—
684C4—42no—
685C4—41no—
686C4—41no—
687C4—42no—
688C4—81no—
689C4—81no—
690C4—2842no—
691C4—5681no—
692C4—5681no—
693C4#1798624714yesdirect product factor
694C4C4×D4×D7111yescharacteristic
695C4C4×#1176586411yescharacteristic
696C4#1798650811yescharacteristic
697C4#1798652911yescharacteristic
698C2—42no—
699C2—5682no—
700C2C4×#1455610011yescharacteristic
701C2C4×#1455615311yescharacteristic
702C2C4×#1455615911yescharacteristic
703C2C2×#1798624711yescharacteristic
704C2#2259794611yescharacteristic
705C2#2259893611yescharacteristic
706C2#2259894011yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC4×C22⋊Q8×C71C2
socleC23×C71C22×D4
prime radicalC2×#14556102C22
cosocleC22×C4×C71C24
hypercenterC4×C22⋊Q8D71
hypocenterC71C4×#468
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11765852C2semidirect
3. C2×C4×#11765849C2semidirect
5. #22589224C2semidirect
6. #22589075C2semidirect
7. #22589036C2semidirect
8. #22589033C2semidirect
10. #22588774C2semidirect
11. #22588371C2semidirect
12. C4×#14556061C2semidirect
13. C4×#14556052C2semidirect
14. C4×#14556048C2semidirect
15. C4×C22⋊Q8×C71C2semidirect
22. #17986247C4direct (N × H)
67. C2×#11765852C2×C4semidirect
73. C2×#11765849C2×C4semidirect
94. #14556061C2×C4semidirect
98. #14556052C2×C4semidirect
101. #14556048C2×C4semidirect
105. C4×C71⋊C8D4semidirect
114. C22⋊Q8×C71C2×C4semidirect
306. C71⋊C8C4×D4semidirect
336. C4×C71#468semidirect
357. C4×C22⋊Q8D71semidirect
369. C71C4×#468semidirect
437. C22⋊Q8C4×D71semidirect
693. C4#17986247direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179862472
C2×C4×#117658522
C2×C4×#117658492
C4×#145561022
#225892242
#225890752
#225890362
#225890332
#225887762
#225887742
#225883712
C4×#145560612
C4×#145560522
C4×#145560482
C4×C22⋊Q8×C712
C4×#46871