Finite Group Databasebeta

← C2×C4×#14556042 #31995099

Subgroups — C2×C4×#14556042 #31995099

Order 18176.

2242 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D71C211yesmaximal, characteristic
2C22×#14556042C212yesmaximal
3C2×C4×C22⋊Dic71C211yesmaximal, characteristic, complemented
4C4×#14556042C218yesmaximal, direct product factor
5C2×#17985765C212yesmaximal, complemented
6C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
7C23×C22⋊D71C2211yescharacteristic
8C23×C4×D71C411yescharacteristic, complemented
9C2×C4×C22⋊D71—21no—
10C2×C4×C22⋊D71—21no—
11C2×C4×C22⋊D71—22no—
12C2×C4×C22⋊D71—21no—
13C2×C4×C22⋊D71—21no—
14C2×C4×C22⋊D71—22no—
15C2×C4×C22⋊D71C414yescomplemented
16C2×C4×C22⋊D71C2214yes—
17C22×Dic71⋊C4C411yescharacteristic, complemented
18C22×C22⋊Dic71C2212yes—
19C22×C22⋊Dic71C2211yescharacteristic
20C22×(C2×D71)⋊C4C411yescharacteristic, complemented
21C22×C4×Dic71—21no—
22C22×C4×Dic71C411yescharacteristic, complemented
23C2×#14556042C4116yesdirect product factor
24C2×#14556042C2218yes—
25C4×C22⋊Dic71—22no—
26C4×C22⋊Dic71C2214yescomplemented
27C2×C71⋊#95—21no—
28#17985765C2218yescomplemented
29C24×C4×C71C2211yescharacteristic
30C22×C22⋊C4×C71C2212yes—
31C22×C42×C71—21no—
32C4×C22⋊C4×C71—22no—
33C4×C22⋊C4×C71C2214yescomplemented
34C2×#95×C71—21no—
35C24×D71C2×C411yescharacteristic
36C22×C22⋊D71—21no—
37C22×C22⋊D71—21no—
38C22×C22⋊D71—21no—
39C22×C22⋊D71—21no—
40C22×C22⋊D71—24no—
41C22×C22⋊D71C2×C418yes—
42C22×C22⋊D71C2×C412yes—
43C22×C22⋊D71C2312yes—
44C23×Dic71—22no—
45C23×Dic71C2×C411yescharacteristic
46C23×Dic71C2×C411yescharacteristic
47C23×Dic71C2×C411yescharacteristic
48C22×C4×D71—21no—
49C22×C4×D71—22no—
50C22×C4×D71—21no—
51C22×C4×D71—44no—
52C22×C4×D71C2×C414yescomplemented
53C4×C22⋊D71—24no—
54C4×C22⋊D71—24no—
55C4×C22⋊D71—24no—
56C4×C22⋊D71—24no—
57C4×C22⋊D71—24no—
58C4×C22⋊D71—24no—
59C4×C22⋊D71—24no—
60C4×C22⋊D71—24no—
61C2×Dic71⋊C4—21no—
62C2×Dic71⋊C4—21no—
63C2×Dic71⋊C4—22no—
64C2×Dic71⋊C4C2×C414yescomplemented
65C2×C22⋊Dic71—22no—
66C2×C22⋊Dic71—21no—
67C2×C22⋊Dic71—21no—
68C2×C22⋊Dic71—21no—
69C2×C22⋊Dic71—21no—
70C2×C22⋊Dic71—24no—
71C2×C22⋊Dic71C2×C412yes—
72C2×C22⋊Dic71C2×C418yescomplemented
73C2×C22⋊Dic71C2312yes—
74C2×C22⋊Dic71C2314yes—
75C2×(C2×D71)⋊C4—21no—
76C2×(C2×D71)⋊C4—21no—
77C2×(C2×D71)⋊C4—22no—
78C2×(C2×D71)⋊C4C2×C414yescomplemented
79C2×C4×Dic71—21no—
80C2×C4×Dic71—22no—
81C2×C4×Dic71—21no—
82C2×C4×Dic71—24no—
83C2×C4×Dic71—44no—
84C2×C4×Dic71C2×C414yescomplemented
85#14556042C2×C4132yesdirect product factor
86C71⋊#95—24no—
87C25×C71C2311yescharacteristic
88C23×C4×C71—22no—
89C23×C4×C71—44no—
90C23×C4×C71C2×C411yescharacteristic
91C23×C4×C71C2×C411yescharacteristic
92C23×C4×C71C2×C412yes—
93C23×C4×C71D411yescharacteristic
94C23×C4×C71D411yescharacteristic
95C23×C4×C71D411yescharacteristic
96C23×C4×C71D412yes—
97C23×C4×C71D411yescharacteristic
98C23×C4×C71D412yes—
99C23×C4×C71C2312yes—
100C2×C22⋊C4×C71—22no—
101C2×C22⋊C4×C71—24no—
102C2×C22⋊C4×C71C2×C418yescomplemented
103C2×C22⋊C4×C71C2314yes—
104C2×C42×C71—24no—
105C2×C42×C71—44no—
106#95×C71—24no—
107C23×D71—21no—
108C23×D71—21no—
109C23×D71—22no—
110C23×D71—42no—
111C23×D71—42no—
112C23×D71C4214yescomplemented
113C23×D71C22×C412yes—
114C2×C22⋊D71—22no—
115C2×C22⋊D71—22no—
116C2×C22⋊D71—24no—
117C2×C22⋊D71—28no—
118C2×C22⋊D71—28no—
119C2×C22⋊D71—28no—
120C2×C22⋊D71—28no—
121C2×C22⋊D71—22no—
122C2×C22⋊D71—22no—
123C2×C22⋊D71—24no—
124C2×C22⋊D71C4218yescomplemented
125C2×C22⋊D71C22×C418yes—
126C22×Dic71—21no—
127C22×Dic71—21no—
128C22×Dic71—22no—
129C22×Dic71—21no—
130C22×Dic71—21no—
131C22×Dic71—21no—
132C22×Dic71—21no—
133C22×Dic71—28no—
134C22×Dic71—24no—
135C22×Dic71—44no—
136C22×Dic71—44no—
137C22×Dic71—42no—
138C22×Dic71—42no—
139C22×Dic71C4214yescomplemented
140C22×Dic71C22×C412yes—
141C22×Dic71C22×C412yes—
142C22×Dic71C22×C412yes—
143C2×C4×D71—24no—
144C2×C4×D71—24no—
145C2×C4×D71—44no—
146C2×C4×D71—48no—
147C2×C4×D71—44no—
148C2×C4×D71—48no—
149Dic71⋊C4—24no—
150Dic71⋊C4—24no—
151C22⋊Dic71—22no—
152C22⋊Dic71—22no—
153C22⋊Dic71—28no—
154C22⋊Dic71—22no—
155C22⋊Dic71—22no—
156C22⋊Dic71—24no—
157C22⋊Dic71C22×C418yescomplemented
158(C2×D71)⋊C4—24no—
159(C2×D71)⋊C4—24no—
160C4×Dic71—24no—
161C4×Dic71—24no—
162C4×Dic71—48no—
163C24×C71—42no—
164C24×C71—42no—
165C24×C71C22×C411yescharacteristic
166C24×C71C22×C411yescharacteristic
167C24×C71C22×C414yes—
168C24×C71C2×D411yescharacteristic
169C24×C71C2×D411yescharacteristic
170C24×C71C2×D411yescharacteristic
171C24×C71C2×D411yescharacteristic
172C24×C71#4114yes—
173C24×C71C2411yescharacteristic
174C22×C4×C71—24no—
175C22×C4×C71—24no—
176C22×C4×C71—24no—
177C22×C4×C71—28no—
178C22×C4×C71—24no—
179C22×C4×C71—44no—
180C22×C4×C71—44no—
181C22×C4×C71—44no—
182C22×C4×C71—44no—
183C22×C4×C71—42no—
184C22×C4×C71—42no—
185C22×C4×C71—42no—
186C22×C4×C71—44no—
187C22×C4×C71—44no—
188C22×C4×C71C22⋊C411yescharacteristic
189C22×C4×C71C22⋊C412yes—
190C22×C4×C71C22⋊C411yescharacteristic
191C22×C4×C71C22⋊C411yescharacteristic
192C22×C4×C71C22⋊C412yes—
193C22×C4×C71C22⋊C412yes—
194C22×C4×C71C22⋊C412yes—
195C22×C4×C71C22⋊C412yes—
196C22×C4×C71C22⋊C412yes—
197C22×C4×C71C22⋊C411yescharacteristic
198C22×C4×C71C22×C412yes—
199C22×C4×C71C22×C412yes—
200C22×C4×C71C2×D412yes—
201C22×C4×C71C2×D412yes—
202C22×C4×C71C2×D412yes—
203C22×C4×C71C2×D412yes—
204C22⋊C4×C71—28no—
205C22⋊C4×C71—24no—
206C22⋊C4×C71C22×C418yescomplemented
207C42×C71—48no—
208C23×C71—22no—
209C23×C71—22no—
210C23×C71—22no—
211C23×C71—22no—
212C23×C71—22no—
213C23×C71—22no—
214C23×C71—41no—
215C23×C71—41no—
216C23×C71—41no—
217C23×C71—41no—
218C23×C71—41no—
219C23×C71—48no—
220C23×C71—41no—
221C23×C71—41no—
222C23×C71—48no—
223C23×C71—41no—
224C23×C71C2×C4212yes—
225C23×C71C2×C4212yes—
226C23×C71C2×C22⋊C411yescharacteristic
227C23×C71C2×C22⋊C411yescharacteristic
228C23×C71C2×C22⋊C411yescharacteristic
229C23×C71C2×C22⋊C411yescharacteristic
230C23×C71#11712yes—
231C23×C71#11712yes—
232C23×C71C4×D414yes—
233C23×C71C4×D414yes—
234C23×C71C4×D414yes—
235C23×C71C4×D414yes—
236C23×C71C23×C411yescharacteristic
237C23×C71C23×C412yes—
238C23×C71C22×D411yescharacteristic
239C23×C71C22×D411yescharacteristic
240C23×C71C2×#4112yes—
241C22×D71—22no—
242C22×D71—22no—
243C22×D71—24no—
244C22×D71—24no—
245C22×D71—42no—
246C22×D71—42no—
247C22×D71—48no—
248C22×D71—42no—
249C22×D71—42no—
250C22×D71—42no—
251C22×D71—48no—
252C22×D71—42no—
253C22×D71C2×C4214yescomplemented
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—24no—
258C2×C4×C71—24no—
259C2×C4×C71—24no—
260C2×C4×C71—24no—
261C2×C4×C71—24no—
262C2×C4×C71—24no—
263C2×C4×C71—28no—
264C2×C4×C71—42no—
265C2×C4×C71—42no—
266C2×C4×C71—42no—
267C2×C4×C71—42no—
268C2×C4×C71—42no—
269C2×C4×C71—42no—
270C2×C4×C71—44no—
271C2×C4×C71—44no—
272C2×C4×C71—416no—
273C2×C4×C71#9914yescomplemented
274C2×C4×C71C2×C22⋊C412yes—
275C2×C4×C71C2×C22⋊C412yes—
276C2×C4×C71C2×C22⋊C412yes—
277C2×C4×C71C2×C22⋊C412yes—
278C22⋊D71—28no—
279C22⋊D71—28no—
280C22⋊D71—28no—
281C22⋊D71—28no—
282C2×Dic71—22no—
283C2×Dic71—22no—
284C2×Dic71—24no—
285C2×Dic71—24no—
286C2×Dic71—22no—
287C2×Dic71—22no—
288C2×Dic71—28no—
289C2×Dic71—44no—
290C2×Dic71—42no—
291C2×Dic71—44no—
292C2×Dic71—416no—
293C2×Dic71—42no—
294C2×Dic71—42no—
295C2×Dic71—42no—
296C2×Dic71—42no—
297C2×Dic71—42no—
298C2×Dic71C2×C4214yescomplemented
299C4×D71—48no—
300C4×D71—48no—
301C22×C71—21no—
302C22×C71—21no—
303C22×C71—21no—
304C22×C71—21no—
305C22×C71—21no—
306C22×C71—21no—
307C22×C71—21no—
308C22×C71—21no—
309C22×C71—21no—
310C22×C71—21no—
311C22×C71—21no—
312C22×C71—21no—
313C22×C71—28no—
314C22×C71—28no—
315C22×C71—24no—
316C22×C71—24no—
317C22×C71—42no—
318C22×C71—42no—
319C22×C71—44no—
320C22×C71—44no—
321C22×C71—42no—
322C22×C71—42no—
323C22×C71C4×C22⋊C412yes—
324C22×C71C4×C22⋊C412yes—
325C22×C71C4×C22⋊C412yes—
326C22×C71C4×C22⋊C412yes—
327C22×C71C2×#9912yes—
328C22×C71#41012yes—
329C22×C71C22×C4211yescharacteristic
330C22×C71C22×C22⋊C411yescharacteristic
331C22×C71C2×#11711yescharacteristic
332C22×C71C2×C4×D412yes—
333C22×C71C2×C4×D412yes—
334C2×D71—24no—
335C2×D71—44no—
336C2×D71—48no—
337C2×D71—42no—
338C2×D71—42no—
339C2×D71—48no—
340C2×D71—44no—
341C4×C71—22no—
342C4×C71—22no—
343C4×C71—22no—
344C4×C71—48no—
345C4×C71C2×#9914yescomplemented
346Dic71—24no—
347Dic71—48no—
348Dic71—42no—
349Dic71—42no—
350C2×C4×#99—711nomaximal, Sylow
351C2×C71—22no—
352C2×C71—22no—
353C2×C71—21no—
354C2×C71—22no—
355C2×C71—21no—
356C2×C71—22no—
357C2×C71—22no—
358C2×C71C4×#9914yescomplemented
359C2×C71C2×C4×C22⋊C411yescharacteristic
360C2×C71C22×#9911yescharacteristic
361C2×C71C2×#41011yescharacteristic
362D71—44no—
363C22×C4×D4—711no—
364C22×#99—712no—
365C2×C4×C22⋊C4—711no—
366C2×C4×C22⋊C4D7111yescharacteristic, complemented
367C4×#99—718no—
368C2×#342—712no—
369C71C2×C4×#9911yescharacteristic, complemented, Sylow
370C23×D4—711no—
371C24×C4—711no—
372C24×C4C2×D7111yescharacteristic
373C2×C4×D4—714no—
374C2×C4×D4—714no—
375C2×C4×D4—1421no—
376C2×C4×D4—1422no—
377C2×C4×D4—1421no—
378C2×C4×D4—1421no—
379C2×C4×D4—1422no—
380C2×C4×D4—1421no—
381C22×C4⋊C4—711no—
382C22×C22⋊C4—712no—
383C22×C22⋊C4—711no—
384C22×C22⋊C4—711no—
385C22×C22⋊C4C2×D7112yes—
386C22×C42—21no—
387C22×C42—711no—
388C22×C42—1421no—
389C2×#99—7116no—
390C2×#99—718no—
391C4×C22⋊C4—22no—
392C4×C22⋊C4—714no—
393C4×C22⋊C4—1422no—
394C4×C22⋊C4C2×D7114yescomplemented
395C2×#95—21no—
396C2×#95—1421no—
397#342—718no—
398C25—711no—
399C25C22×D7111yescharacteristic
400C22×D4—712no—
401C22×D4—718no—
402C22×D4—712no—
403C22×D4—1421no—
404C22×D4—1421no—
405C22×D4—1421no—
406C22×D4—1421no—
407C22×D4—1424no—
408C23×C4—22no—
409C23×C4—44no—
410C23×C4—2844no—
411C23×C4—711no—
412C23×C4—711no—
413C23×C4—714no—
414C23×C4—711no—
415C23×C4—1422no—
416C23×C4—1421no—
417C23×C4—1422no—
418C23×C4—1421no—
419C23×C4C4×D7111yescharacteristic
420C23×C4C4×D7111yescharacteristic
421C23×C4C4×D7112yes—
422C23×C4D28411yescharacteristic
423C23×C4D28411yescharacteristic
424C23×C4D28412yes—
425C23×C4C22⋊D7111yescharacteristic
426C23×C4C22⋊D7111yescharacteristic
427C23×C4C22⋊D7112yes—
428C23×C4C22×D7112yes—
429C4×D4—1424no—
430C4×D4—1424no—
431C4×D4—1424no—
432C4×D4—1424no—
433C4×D4—1424no—
434C4×D4—1424no—
435C4×D4—1424no—
436C4×D4—1424no—
437C2×C4⋊C4—714no—
438C2×C4⋊C4—1421no—
439C2×C4⋊C4—1421no—
440C2×C4⋊C4—1422no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—718no—
444C2×C22⋊C4—714no—
445C2×C22⋊C4—712no—
446C2×C22⋊C4—712no—
447C2×C22⋊C4—714no—
448C2×C22⋊C4—1421no—
449C2×C22⋊C4—1421no—
450C2×C22⋊C4—1421no—
451C2×C22⋊C4—1421no—
452C2×C22⋊C4—1422no—
453C2×C22⋊C4—1424no—
454C2×C22⋊C4—1421no—
455C2×C22⋊C4—1421no—
456C2×C22⋊C4—1422no—
457C2×C22⋊C4C4×D7118yescomplemented
458C2×C22⋊C4C22×D7114yes—
459C2×C42—24no—
460C2×C42—44no—
461C2×C42—2844no—
462C2×C42—714no—
463C2×C42—1424no—
464C2×C42—1421no—
465C2×C42—1422no—
466C2×C42—1421no—
467#99—7132no—
468#95—24no—
469#95—1424no—
470C24—42no—
471C24—42no—
472C24—2842no—
473C24—2842no—
474C24—712no—
475C24—714no—
476C24—1421no—
477C24—1421no—
478C24—1422no—
479C24C2×C4×D7111yescharacteristic
480C24C2×C4×D7111yescharacteristic
481C24C2×C4×D7114yes—
482C24C2×C22⋊D7111yescharacteristic
483C24C2×C22⋊D7111yescharacteristic
484C24C2×D28411yescharacteristic
485C24C2×D28411yescharacteristic
486C24#1176586514yes—
487C24C23×D7111yescharacteristic
488C2×D4—718no—
489C2×D4—718no—
490C2×D4—1422no—
491C2×D4—1422no—
492C2×D4—1424no—
493C2×D4—1422no—
494C2×D4—1422no—
495C2×D4—1424no—
496C2×D4—1428no—
497C2×D4—1428no—
498C2×D4—1428no—
499C2×D4—1428no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—28no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—2844no—
515C22×C4—2848no—
516C22×C4—2848no—
517C22×C4—2844no—
518C22×C4—2844no—
519C22×C4—2844no—
520C22×C4—2842no—
521C22×C4—2842no—
522C22×C4—712no—
523C22×C4—712no—
524C22×C4—712no—
525C22×C4—714no—
526C22×C4—1424no—
527C22×C4—1421no—
528C22×C4—1421no—
529C22×C4—1421no—
530C22×C4—1421no—
531C22×C4—1428no—
532C22×C4—1424no—
533C22×C4—1424no—
534C22×C4—1421no—
535C22×C4—1421no—
536C22×C4—1422no—
537C22×C4(C2×D71)⋊C411yescharacteristic
538C22×C4(C2×D71)⋊C412yes—
539C22×C4(C2×D71)⋊C411yescharacteristic
540C22×C4(C2×D71)⋊C411yescharacteristic
541C22×C4(C2×D71)⋊C412yes—
542C22×C4(C2×D71)⋊C412yes—
543C22×C4(C2×D71)⋊C412yes—
544C22×C4(C2×D71)⋊C412yes—
545C22×C4(C2×D71)⋊C412yes—
546C22×C4(C2×D71)⋊C411yescharacteristic
547C22×C4C2×C4×D7112yes—
548C22×C4C2×C4×D7112yes—
549C22×C4C2×C22⋊D7112yes—
550C22×C4C2×C22⋊D7112yes—
551C22×C4C2×D28412yes—
552C22×C4C2×D28412yes—
553C4⋊C4—1424no—
554C4⋊C4—1424no—
555C22⋊C4—24no—
556C22⋊C4—28no—
557C22⋊C4—718no—
558C22⋊C4—1422no—
559C22⋊C4—1422no—
560C22⋊C4—1424no—
561C22⋊C4—1422no—
562C22⋊C4—1422no—
563C22⋊C4—1428no—
564C22⋊C4—1424no—
565C22⋊C4—1424no—
566C22⋊C4C2×C4×D7118yescomplemented
567C42—48no—
568C42—2848no—
569C42—1424no—
570C42—1424no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—48no—
583C23—41no—
584C23—41no—
585C23—48no—
586C23—41no—
587C23—2842no—
588C23—2842no—
589C23—2848no—
590C23—2842no—
591C23—2842no—
592C23—2848no—
593C23—2842no—
594C23—2842no—
595C23—714no—
596C23—1424no—
597C23—1424no—
598C23—1422no—
599C23—1422no—
600C23C42×D7112yes—
601C23C42×D7112yes—
602C23C2×(C2×D71)⋊C411yescharacteristic
603C23C2×(C2×D71)⋊C411yescharacteristic
604C23C2×(C2×D71)⋊C411yescharacteristic
605C23C2×(C2×D71)⋊C411yescharacteristic
606C23#1455608512yes—
607C23#1455608512yes—
608C23C4×C22⋊D7114yes—
609C23C4×C22⋊D7114yes—
610C23C4×D28414yes—
611C23C4×D28414yes—
612C23C22×C4×D7111yescharacteristic
613C23C22×C4×D7112yes—
614C23C22×C22⋊D7111yescharacteristic
615C23C22×D28411yescharacteristic
616C23C2×#1176586512yes—
617D4—1428no—
618D4—1428no—
619D4—1428no—
620D4—1428no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—416no—
640C2×C4—2848no—
641C2×C4—2844no—
642C2×C4—2842no—
643C2×C4—2844no—
644C2×C4—28416no—
645C2×C4—2842no—
646C2×C4—2842no—
647C2×C4—2842no—
648C2×C4—2848no—
649C2×C4—2842no—
650C2×C4—2842no—
651C2×C4—714no—
652C2×C4—1422no—
653C2×C4—1422no—
654C2×C4—1428no—
655C2×C4—1424no—
656C2×C4—1424no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4#1455604214yesdirect product factor
660C2×C4C2×(C2×D71)⋊C412yes—
661C2×C4C2×(C2×D71)⋊C412yes—
662C2×C4C2×(C2×D71)⋊C412yes—
663C2×C4C2×(C2×D71)⋊C412yes—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—44no—
685C22—44no—
686C22—2844no—
687C22—2848no—
688C22—2844no—
689C22—2842no—
690C22—2842no—
691C22—2848no—
692C22—1424no—
693C22C4×(C2×D71)⋊C412yes—
694C22C4×(C2×D71)⋊C412yes—
695C22C4×(C2×D71)⋊C412yes—
696C22C4×(C2×D71)⋊C412yes—
697C22C2×#1455604212yes—
698C22#1798597212yes—
699C22C2×C42×D7111yescharacteristic
700C22C22×(C2×D71)⋊C411yescharacteristic
701C22C2×#1455608511yescharacteristic
702C22C2×C4×C22⋊D7112yes—
703C22C2×C4×D28412yes—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—48no—
708C4—2848no—
709C4—2842no—
710C4—2842no—
711C4—1424no—
712C4C2×#1455604214yesdirect product factor
713C2—22no—
714C2—22no—
715C2—22no—
716C2—21no—
717C2—21no—
718C2—22no—
719C2—22no—
720C2—2844no—
721C2C4×#1455604214yesdirect product factor
722C2C2×C4×(C2×D71)⋊C411yescharacteristic
723C2C22×#1455604211yescharacteristic
724C2C2×#1798597211yescharacteristic
subgroupG/H
centerC22×C4(C2×D71)⋊C4
commutatorC22×C71C22×C42
FrattiniC24C23×D71
FittingC2×C4×C22⋊C4×C71C2
socleC23×C71C2×C22⋊C4
prime radicalC23×C22⋊D71C22
cosocleC24×C71C24
hypercenterC2×C4×C22⋊C4D71
hypocenterC71C2×C4×#99
LCSG ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic71C2semidirect
4. C4×#14556042C2direct (N × H)
5. C2×#17985765C2semidirect
6. C2×C4×C22⋊C4×C71C2semidirect
8. C23×C4×D71C4semidirect
15. C2×C4×C22⋊D71C4semidirect
17. C22×Dic71⋊C4C4semidirect
20. C22×(C2×D71)⋊C4C4semidirect
22. C22×C4×Dic71C4semidirect
23. C2×#14556042C4direct (N × H)
26. C4×C22⋊Dic71C22semidirect
28. #17985765C22semidirect
33. C4×C22⋊C4×C71C22semidirect
52. C22×C4×D71C2×C4semidirect
64. C2×Dic71⋊C4C2×C4semidirect
72. C2×C22⋊Dic71C2×C4semidirect
78. C2×(C2×D71)⋊C4C2×C4semidirect
84. C2×C4×Dic71C2×C4semidirect
85. #14556042C2×C4direct (N × H)
102. C2×C22⋊C4×C71C2×C4semidirect
112. C23×D71C42semidirect
124. C2×C22⋊D71C42semidirect
139. C22×Dic71C42semidirect
157. C22⋊Dic71C22×C4semidirect
206. C22⋊C4×C71C22×C4semidirect
253. C22×D71C2×C42semidirect
273. C2×C4×C71#99semidirect
298. C2×Dic71C2×C42semidirect
345. C4×C71C2×#99semidirect
358. C2×C71C4×#99semidirect
366. C2×C4×C22⋊C4D71semidirect
369. C71C2×C4×#99semidirect
394. C4×C22⋊C4C2×D71semidirect
457. C2×C22⋊C4C4×D71semidirect
566. C22⋊C4C2×C4×D71semidirect
659. C2×C4#14556042direct (N × H)
712. C4C2×#14556042direct (N × H)
721. C2C4×#14556042direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D712
C22×#145560422
C2×C4×C22⋊Dic712
C4×#145560422
C2×#179857652
C2×C4×C22⋊C4×C712
C2×C4×#9971