Finite Group Databasebeta

← C4×#17985870 #31918617

Subgroups — C4×#17985870 #31918617

Order 18176.

2782 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D71C211yesmaximal, characteristic
2C2×#17985870C212yesmaximal
3C2×C4×Dic71⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
5C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
6#22586572C212yesmaximal, complemented
7#22586571C212yesmaximal, complemented
8(C2×D71)⋊#95C212yesmaximal
9C4×C71⋊#95C211yesmaximal, characteristic, complemented
10C4×C71⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C71C211yesmaximal, characteristic, complemented
12C23×C4×D71C2212yes—
13C23×C4×D71C2211yescharacteristic
14C22×Dic71⋊C4C2212yes—
15C22×(C2×D71)⋊C4C2212yes—
16C22×(C2×D71)⋊C4C2211yescharacteristic
17C22×(C2×D71)⋊C4C2211yescharacteristic
18C22×C4×Dic71C2212yes—
19C22×C4×Dic71C2211yescharacteristic
20C22×C4×Dic71C2211yescharacteristic
21C22×C4×Dic71C2211yescharacteristic
22C2×C42×D71—24no—
23C2×C42×D71—24no—
24C2×C42×D71—24no—
25#17985870C4116yesdirect product factor
26C4×Dic71⋊C4—24no—
27C4×(C2×D71)⋊C4—24no—
28C4×(C2×D71)⋊C4C418yescomplemented
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2211yescharacteristic
36C2×C71⋊#95C2211yescharacteristic
37C22×C4⋊C4×C71C2212yes—
38C22×C42×C71C2211yescharacteristic
39C22×C42×C71C2211yescharacteristic
40C22×C42×C71C2211yescharacteristic
41C4×C4⋊C4×C71—24no—
42C2×#95×C71C2212yes—
43C24×D71C2311yescharacteristic
44C23×Dic71C2311yescharacteristic
45C23×Dic71C2312yes—
46C23×Dic71C2311yescharacteristic
47C23×Dic71C2311yescharacteristic
48C23×Dic71C2312yes—
49C22×C4×D71—24no—
50C22×C4×D71—24no—
51C22×C4×D71—24no—
52C22×C4×D71—24no—
53C22×C4×D71—22no—
54C22×C4×D71—24no—
55C22×C4×D71—22no—
56C22×C4×D71—24no—
57C22×C4×D71—22no—
58C22×C4×D71—22no—
59C22×C4×D71C2×C418yes—
60C22×C4×D71C2×C414yes—
61C22×C4×D71D414yes—
62C22×C4×D71Q814yes—
63C2×Dic71⋊C4—24no—
64C2×Dic71⋊C4—24no—
65C2×Dic71⋊C4C2×C418yescomplemented
66C2×(C2×D71)⋊C4—24no—
67C2×(C2×D71)⋊C4—24no—
68C2×(C2×D71)⋊C4—24no—
69C2×(C2×D71)⋊C4C2×C414yes—
70C2×(C2×D71)⋊C4C2×C418yes—
71C2×(C2×D71)⋊C4C2×C414yes—
72C2×(C2×D71)⋊C4C2×C418yes—
73C2×C4×Dic71—24no—
74C2×C4×Dic71—24no—
75C2×C4×Dic71—22no—
76C2×C4×Dic71—22no—
77C2×C4×Dic71—24no—
78C2×C4×Dic71—22no—
79C2×C4×Dic71—22no—
80C2×C4×Dic71—22no—
81C2×C4×Dic71—22no—
82C2×C4×Dic71—22no—
83C2×C4×Dic71C2×C414yescomplemented
84C2×C4×Dic71D414yes—
85C42×D71—232no—
86C71⋊#95—24no—
87C71⋊#95—24no—
88C71⋊#95—24no—
89C71⋊#95—24no—
90C71⋊#95C2×C414yescomplemented
91C71⋊#95C2×C414yescomplemented
92C71⋊#95C2×C418yescomplemented
93C71⋊#95C2×C418yescomplemented
94C23×C4×C71C2311yescharacteristic
95C23×C4×C71C2312yes—
96C23×C4×C71C2311yescharacteristic
97C23×C4×C71C2312yes—
98C23×C4×C71C2311yescharacteristic
99C2×C4⋊C4×C71—24no—
100C2×C4⋊C4×C71—24no—
101C2×C4⋊C4×C71C2×C418yescomplemented
102C2×C42×C71—22no—
103C2×C42×C71—22no—
104C2×C42×C71—22no—
105C2×C42×C71—22no—
106C2×C42×C71—22no—
107C2×C42×C71—22no—
108C2×C42×C71—22no—
109C2×C42×C71C2×C414yescomplemented
110C2×C42×C71D414yes—
111#95×C71—24no—
112C23×D71—21no—
113C23×D71—21no—
114C23×D71—22no—
115C23×D71—21no—
116C23×D71—22no—
117C23×D71—21no—
118C23×D71C22×C412yes—
119C23×D71C22×C414yes—
120C23×D71C2×D412yes—
121C23×D71C2×Q812yes—
122C23×D71#4114yes—
123C22×Dic71—21no—
124C22×Dic71—22no—
125C22×Dic71—21no—
126C22×Dic71—22no—
127C22×Dic71—21no—
128C22×Dic71—22no—
129C22×Dic71—21no—
130C22×Dic71—22no—
131C22×Dic71—21no—
132C22×Dic71—21no—
133C22×Dic71—22no—
134C22×Dic71—21no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71—22no—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—21no—
141C22×Dic71—22no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71C22×C414yes—
145C22×Dic71C22×C412yes—
146C22×Dic71C22×C412yes—
147C22×Dic71C22×C414yes—
148C22×Dic71C22×C412yes—
149C22×Dic71C22×C414yes—
150C22×Dic71C2×D412yes—
151C22×Dic71C2×D414yes—
152C22×Dic71C2×Q812yes—
153C22×Dic71#4114yes—
154C2×C4×D71—216no—
155C2×C4×D71—216no—
156C2×C4×D71—216no—
157C2×C4×D71—216no—
158C2×C4×D71—216no—
159C2×C4×D71—216no—
160C2×C4×D71—28no—
161C2×C4×D71—28no—
162C2×C4×D71—28no—
163C2×C4×D71—28no—
164C2×C4×D71—28no—
165C2×C4×D71—28no—
166C2×C4×D71—216no—
167C2×C4×D71C4⋊C4116yescomplemented
168Dic71⋊C4—216no—
169(C2×D71)⋊C4—28no—
170(C2×D71)⋊C4—216no—
171(C2×D71)⋊C4C42116yescomplemented
172C4×Dic71—216no—
173C4×Dic71—28no—
174C4×Dic71—28no—
175C4×Dic71—44no—
176C24×C71C2411yescharacteristic
177C22×C4×C71—22no—
178C22×C4×C71—22no—
179C22×C4×C71—21no—
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—21no—
183C22×C4×C71—22no—
184C22×C4×C71—21no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—22no—
188C22×C4×C71—21no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—22no—
194C22×C4×C71C22×C412yes—
195C22×C4×C71C22×C414yes—
196C22×C4×C71C22×C412yes—
197C22×C4×C71C22×C414yes—
198C22×C4×C71C22×C414yes—
199C22×C4×C71C22×C412yes—
200C22×C4×C71C2×D412yes—
201C22×C4×C71C2×D412yes—
202C22×C4×C71C2×D414yes—
203C22×C4×C71C2×D412yes—
204C22×C4×C71C2×Q812yes—
205C22×C4×C71#4114yes—
206C22×C4×C71#4112yes—
207C22×C4×C71#4112yes—
208C4⋊C4×C71—216no—
209C42×C71—28no—
210C42×C71—28no—
211C42×C71—44no—
212C23×C71C23×C411yescharacteristic
213C23×C71C23×C412yes—
214C23×C71C22×D411yescharacteristic
215C23×C71C22×D411yescharacteristic
216C23×C71C22×D411yescharacteristic
217C23×C71C22×Q811yescharacteristic
218C23×C71C2×#4112yes—
219C23×C71C2×#4112yes—
220C23×C71C2×#4111yescharacteristic
221C23×C71C2×#4112yes—
222C23×C71C2×#4111yescharacteristic
223C22×D71—24no—
224C22×D71—22no—
225C22×D71—24no—
226C22×D71—22no—
227C22×D71—22no—
228C22×D71—22no—
229C22×D71—24no—
230C22×D71—24no—
231C22×D71—22no—
232C22×D71—22no—
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—24no—
236C22×D71—24no—
237C22×D71—24no—
238C22×D71—24no—
239C22×D71—24no—
240C22×D71—24no—
241C22×D71C2×C4214yes—
242C22×D71C2×C4⋊C414yes—
243C22×D71#11714yes—
244C22×D71C4×D418yes—
245C22×D71C4×Q818yes—
246C2×C4×C71—22no—
247C2×C4×C71—24no—
248C2×C4×C71—24no—
249C2×C4×C71—24no—
250C2×C4×C71—22no—
251C2×C4×C71—24no—
252C2×C4×C71—24no—
253C2×C4×C71—24no—
254C2×C4×C71—24no—
255C2×C4×C71—24no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—24no—
259C2×C4×C71—24no—
260C2×C4×C71—24no—
261C2×C4×C71—22no—
262C2×C4×C71—42no—
263C2×C4×C71—42no—
264C2×C4×C71—42no—
265C2×C4×C71—42no—
266C2×C4×C71—42no—
267C2×C4×C71—42no—
268C2×C4×C71C2×C4214yescomplemented
269C2×C4×C71C2×C4⋊C414yes—
270C2×C4×C71C4×D418yes—
271C2×C4×C71C4×D414yes—
272C2×C4×C71C4×D414yes—
273C2×C4×C71#12014yes—
274C2×C4×C71C22⋊Q814yes—
275C2×C4×C71C22⋊Q814yes—
276C2×C4×C71#12314yes—
277C2×Dic71—22no—
278C2×Dic71—24no—
279C2×Dic71—24no—
280C2×Dic71—22no—
281C2×Dic71—24no—
282C2×Dic71—22no—
283C2×Dic71—22no—
284C2×Dic71—24no—
285C2×Dic71—22no—
286C2×Dic71—24no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—24no—
291C2×Dic71—24no—
292C2×Dic71—24no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—24no—
296C2×Dic71—22no—
297C2×Dic71—24no—
298C2×Dic71—24no—
299C2×Dic71—42no—
300C2×Dic71—42no—
301C2×Dic71—42no—
302C2×Dic71—42no—
303C2×Dic71—42no—
304C2×Dic71—42no—
305C2×Dic71C2×C4214yescomplemented
306C2×Dic71C2×C4⋊C414yes—
307C2×Dic71C4×D418yes—
308C4×D71—264no—
309C4×D71—232no—
310C22×C71C22×C4211yescharacteristic
311C22×C71C22×C4⋊C411yescharacteristic
312C22×C71C2×#11711yescharacteristic
313C22×C71C2×C4×D412yes—
314C22×C71C2×C4×D412yes—
315C22×C71C2×C4×D411yescharacteristic
316C22×C71C2×C4×D412yes—
317C22×C71C2×C4×D411yescharacteristic
318C22×C71C2×C4×Q812yes—
319C22×C71C4×#4111yescharacteristic
320C22×C71C4×#4111yescharacteristic
321C22×C71C4×#4112yes—
322C22×C71C4×#4112yes—
323C22×C71C2×#12011yescharacteristic
324C22×C71C2×C22⋊Q811yescharacteristic
325C22×C71C2×C22⋊Q811yescharacteristic
326C22×C71C2×#12311yescharacteristic
327C22×C71#52512yes—
328C22×C71#52512yes—
329C22×C71#52512yes—
330C22×C71#52912yes—
331C22×C71#52912yes—
332C22×C71#53312yes—
333C2×D71—24no—
334C2×D71—24no—
335C2×D71—24no—
336C2×D71—24no—
337C2×D71—24no—
338C2×D71—24no—
339C2×D71—28no—
340C2×D71—28no—
341C2×D71—28no—
342C2×D71—28no—
343C2×D71C4×C4⋊C418yescomplemented
344C4×C71—24no—
345C4×C71—28no—
346C4×C71—42no—
347C4×C71—44no—
348C4×C71#38518yescomplemented
349Dic71—24no—
350Dic71—24no—
351Dic71—28no—
352Dic71—42no—
353Dic71—44no—
354C4×#385—711nomaximal, Sylow
355C2×C71C2×C4×C4⋊C411yescharacteristic
356C2×C71C42×D411yescharacteristic
357C2×C71C42×D411yescharacteristic
358C2×C71C2×#38511yescharacteristic
359C2×C71#229011yescharacteristic
360C2×C71#229011yescharacteristic
361C2×C71#229611yescharacteristic
362C2×C71C4×#12012yes—
363C2×C71C4×#12312yes—
364C2×C71C4×C22⋊Q812yes—
365C2×C71C4×C22⋊Q812yes—
366D71—28no—
367C23×C42—711no—
368C2×#385—712no—
369C2×C4×C4⋊C4—711no—
370C2×C4×C4⋊C4D7111yescharacteristic, complemented
371C2×C4×C22⋊C4—711no—
372C2×C4×C22⋊C4—711no—
373#1436—712no—
374#1436—712no—
375C22⋊#95—712no—
376C4×#95—711no—
377C4×#95—711no—
378C71C4×#38511yescharacteristic, complemented, Sylow
379C24×C4—711no—
380C24×C4—712no—
381C22×C4⋊C4—712no—
382C22×C4⋊C4C2×D7112yes—
383C22×C22⋊C4—711no—
384C22×C22⋊C4—711no—
385C22×C22⋊C4—712no—
386C22×C42—711no—
387C22×C42—711no—
388C22×C42—712no—
389C22×C42—711no—
390C22×C42—1424no—
391C22×C42—1424no—
392C22×C42—1424no—
393C22×C42C2×D7111yescharacteristic
394C22×C42C2×D7111yescharacteristic
395C22×C42C2×D7111yescharacteristic
396#385—7116no—
397C4×C4⋊C4—24no—
398C4×C4⋊C4—1424no—
399C4×C22⋊C4—718no—
400C4×C22⋊C4—1424no—
401C2×#95—712no—
402C2×#95—712no—
403C2×#95—711no—
404C2×#95—711no—
405C2×#95—712no—
406C2×#95—712no—
407C2×#95—712no—
408C2×#95—712no—
409C2×#95C2×D7112yes—
410C25—711no—
411C23×C4—711no—
412C23×C4—712no—
413C23×C4—711no—
414C23×C4—714no—
415C23×C4—714no—
416C23×C4—714no—
417C23×C4—712no—
418C23×C4—711no—
419C23×C4—718no—
420C23×C4—1424no—
421C23×C4—1424no—
422C23×C4—1424no—
423C23×C4—1424no—
424C23×C4—1422no—
425C23×C4—1424no—
426C23×C4—1422no—
427C23×C4—1424no—
428C23×C4—1422no—
429C23×C4—1422no—
430C23×C4C22×D7112yes—
431C23×C4C22×D7111yescharacteristic
432C23×C4C22×D7111yescharacteristic
433C23×C4C22×D7112yes—
434C23×C4C22×D7111yescharacteristic
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—718no—
438C2×C4⋊C4—1424no—
439C2×C4⋊C4—1424no—
440C2×C4⋊C4C4×D7118yescomplemented
441C2×C22⋊C4—714no—
442C2×C22⋊C4—718no—
443C2×C22⋊C4—714no—
444C2×C22⋊C4—718no—
445C2×C22⋊C4—1424no—
446C2×C22⋊C4—1424no—
447C2×C22⋊C4—1424no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—714no—
456C2×C42—714no—
457C2×C42—14232no—
458C2×C42—1422no—
459C2×C42—1422no—
460C2×C42—1422no—
461C2×C42—1424no—
462C2×C42—1424no—
463C2×C42—1422no—
464C2×C42—1422no—
465C2×C42—1424no—
466C2×C42—1422no—
467C2×C42—1422no—
468C2×C42C4×D7114yescomplemented
469C2×C42C22⋊D7114yes—
470#95—24no—
471#95—714no—
472#95—714no—
473#95—718no—
474#95—718no—
475#95—1424no—
476#95—1424no—
477#95—1424no—
478#95—1424no—
479C24—712no—
480C24—714no—
481C24—712no—
482C24—712no—
483C24—714no—
484C24—1421no—
485C24—1421no—
486C24—1422no—
487C24—1421no—
488C24—1422no—
489C24—1421no—
490C24C23×D7111yescharacteristic
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—712no—
509C22×C4—712no—
510C22×C4—714no—
511C22×C4—714no—
512C22×C4—712no—
513C22×C4—714no—
514C22×C4—712no—
515C22×C4—714no—
516C22×C4—7116no—
517C22×C4—714no—
518C22×C4—712no—
519C22×C4—14216no—
520C22×C4—14216no—
521C22×C4—14216no—
522C22×C4—14216no—
523C22×C4—14216no—
524C22×C4—14216no—
525C22×C4—1421no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1422no—
529C22×C4—1422no—
530C22×C4—1422no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—1422no—
534C22×C4—1421no—
535C22×C4—1422no—
536C22×C4—1421no—
537C22×C4—1421no—
538C22×C4—1421no—
539C22×C4—1422no—
540C22×C4—1422no—
541C22×C4—1422no—
542C22×C4—1421no—
543C22×C4—1422no—
544C22×C4—1421no—
545C22×C4—1421no—
546C22×C4—14216no—
547C22×C4—1428no—
548C22×C4—1428no—
549C22×C4—1428no—
550C22×C4—1428no—
551C22×C4—1428no—
552C22×C4—1428no—
553C22×C4C2×C4×D7112yes—
554C22×C4C2×C4×D7114yes—
555C22×C4C2×C4×D7112yes—
556C22×C4C2×C4×D7114yes—
557C22×C4C2×C4×D7114yes—
558C22×C4C2×C4×D7112yes—
559C22×C4D4×D7112yes—
560C22×C4D4×D7112yes—
561C22×C4C2×C22⋊D7114yes—
562C22×C4C2×C22⋊D7112yes—
563C22×C4Q8×D7112yes—
564C22×C4#1176586514yes—
565C22×C4#1176586512yes—
566C22×C4#1176586612yes—
567C4⋊C4—216no—
568C4⋊C4—14216no—
569C22⋊C4—7116no—
570C22⋊C4—1428no—
571C22⋊C4—14216no—
572C42—28no—
573C42—28no—
574C42—44no—
575C42—2844no—
576C42—14216no—
577C42—1428no—
578C42—1428no—
579C23—714no—
580C23—714no—
581C23—714no—
582C23—718no—
583C23—718no—
584C23—1424no—
585C23—1422no—
586C23—1424no—
587C23—1422no—
588C23—1422no—
589C23—1422no—
590C23—1424no—
591C23—1424no—
592C23—1422no—
593C23—1422no—
594C23—1422no—
595C23—1422no—
596C23—1424no—
597C23—1424no—
598C23—1424no—
599C23—1424no—
600C23—1424no—
601C23—1424no—
602C23C22×C4×D7111yescharacteristic
603C23C22×C4×D7112yes—
604C23C2×D4×D7111yescharacteristic
605C23C2×D4×D7111yescharacteristic
606C23C22×C22⋊D7111yescharacteristic
607C23C2×Q8×D7111yescharacteristic
608C23#41×D7112yes—
609C23#41×D7112yes—
610C23C2×#1176586511yescharacteristic
611C23C2×#1176586512yes—
612C23C2×#1176586611yescharacteristic
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—2842no—
636C2×C4—2842no—
637C2×C4—2842no—
638C2×C4—2842no—
639C2×C4—2842no—
640C2×C4—2842no—
641C2×C4—714no—
642C2×C4—714no—
643C2×C4—718no—
644C2×C4—14264no—
645C2×C4—1422no—
646C2×C4—1424no—
647C2×C4—1422no—
648C2×C4—1422no—
649C2×C4—1424no—
650C2×C4—1424no—
651C2×C4—1424no—
652C2×C4—1424no—
653C2×C4—1422no—
654C2×C4—1424no—
655C2×C4—1422no—
656C2×C4—1422no—
657C2×C4—1422no—
658C2×C4—1424no—
659C2×C4—1422no—
660C2×C4—1424no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1424no—
665C2×C4—1424no—
666C2×C4—1424no—
667C2×C4—14232no—
668C2×C4C42×D7114yescomplemented
669C2×C4C4⋊C4×D7114yes—
670C2×C4C4×C22⋊D7118yes—
671C2×C4C4×C22⋊D7114yes—
672C2×C4#1455609014yes—
673C2×C4#1455609614yes—
674C2×C4#1455610414yes—
675C2×C4#1455610614yes—
676C2×C4#1455611314yes—
677C22—718no—
678C22—1424no—
679C22—1424no—
680C22—1424no—
681C22—1424no—
682C22—1428no—
683C22—1428no—
684C22—1428no—
685C22—1428no—
686C22—1424no—
687C22—1424no—
688C22C2×C42×D7111yescharacteristic
689C22C2×C4⋊C4×D7111yescharacteristic
690C22#117×D7111yescharacteristic
691C22C4×D4×D7112yes—
692C22C4×D4×D7112yes—
693C22C2×C4×C22⋊D7111yescharacteristic
694C22C2×C4×C22⋊D7112yes—
695C22C2×#1455609011yescharacteristic
696C22C4×Q8×D7112yes—
697C22#1798646711yescharacteristic
698C22C4×#1176586511yescharacteristic
699C22C4×#1176586512yes—
700C22C4×#1176586612yes—
701C22C2×#1455609611yescharacteristic
702C22C2×#1455610411yescharacteristic
703C22C2×#1455610611yescharacteristic
704C22C2×#1455611311yescharacteristic
705C22#1798650612yes—
706C22#1798650812yes—
707C22#1798650812yes—
708C22#1798652712yes—
709C22#1798653612yes—
710C22#1798655312yes—
711C4—28no—
712C4—24no—
713C4—42no—
714C4—44no—
715C4—2842no—
716C4—2844no—
717C4—1424no—
718C4—1428no—
719C4—1424no—
720C4#1798587018yesdirect product factor
721C2—1428no—
722C2C4×C4⋊C4×D7111yescharacteristic
723C2C4×#1455609011yescharacteristic
724C2C42×C22⋊D7111yescharacteristic
725C2C2×#1798587011yescharacteristic
726C2#2259077711yescharacteristic
727C2#2259078111yescharacteristic
728C2#2259082011yescharacteristic
729C2C4×#1455609612yes—
730C2C4×#1455611312yes—
731C2C4×#1455610412yes—
732C2C4×#1455610612yes—
subgroupG/H
centerC23×C4C22×D71
commutatorC22×C71C22×C42
FrattiniC24C23×D71
FittingC2×C4×C4⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×C4×C4⋊C4D71
hypocenterC71C4×#385
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic71⋊C4C2semidirect
6. #22586572C2semidirect
7. #22586571C2semidirect
9. C4×C71⋊#95C2semidirect
10. C4×C71⋊#95C2semidirect
11. C2×C4×C4⋊C4×C71C2semidirect
25. #17985870C4direct (N × H)
28. C4×(C2×D71)⋊C4C4semidirect
65. C2×Dic71⋊C4C2×C4semidirect
83. C2×C4×Dic71C2×C4semidirect
90. C71⋊#95C2×C4semidirect
91. C71⋊#95C2×C4semidirect
92. C71⋊#95C2×C4semidirect
93. C71⋊#95C2×C4semidirect
101. C2×C4⋊C4×C71C2×C4semidirect
109. C2×C42×C71C2×C4semidirect
167. C2×C4×D71C4⋊C4semidirect
171. (C2×D71)⋊C4C42semidirect
268. C2×C4×C71C2×C42semidirect
305. C2×Dic71C2×C42semidirect
343. C2×D71C4×C4⋊C4semidirect
348. C4×C71#385semidirect
370. C2×C4×C4⋊C4D71semidirect
378. C71C4×#385semidirect
440. C2×C4⋊C4C4×D71semidirect
468. C2×C42C4×D71semidirect
668. C2×C4C42×D71semidirect
720. C4#17985870direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C42×D712
C2×#179858702
C2×C4×Dic71⋊C42
C2×C4×(C2×D71)⋊C42
#225865722
#225865712
(C2×D71)⋊#952
C4×C71⋊#952
C2×C4×C4⋊C4×C712
C4×#38571