Finite Group Databasebeta

← C4×#17985899 #31918636

Subgroups — C4×#17985899 #31918636

Order 18176.

2894 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D71C211yesmaximal, characteristic
2C2×#17985899C212yesmaximal
3C2×C4×Dic71⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic71C211yesmaximal, characteristic, complemented
7C2×C42×Dic71C211yesmaximal, characteristic, complemented
8#22586577C212yesmaximal, complemented
9#22586576C212yesmaximal, complemented
10Dic71⋊#95C212yesmaximal, complemented
11C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
12C23×C22⋊D71C2211yescharacteristic
13C23×C4×D71C2211yescharacteristic
14C2×C4×C22⋊D71—24no—
15C2×C4×C22⋊D71—24no—
16C2×C4×C22⋊D71C418yescomplemented
17C22×Dic71⋊C4C2211yescharacteristic
18C22×Dic71⋊C4C2212yes—
19C22×C22⋊Dic71C2211yescharacteristic
20C22×C22⋊Dic71C2212yes—
21C22×(C2×D71)⋊C4C2211yescharacteristic
22C22×(C2×D71)⋊C4C2212yes—
23C22×(C2×D71)⋊C4C2212yes—
24C22×C4×Dic71C2212yes—
25C22×C4×Dic71C2211yescharacteristic
26C22×C4×Dic71C2212yes—
27C22×C4×Dic71C2211yescharacteristic
28C22×C4×Dic71C2211yescharacteristic
29#17985899C4116yesdirect product factor
30C4×Dic71⋊C4—24no—
31C4×(C2×D71)⋊C4—24no—
32C4×(C2×D71)⋊C4—24no—
33C4×C22⋊Dic71—24no—
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2212yes—
36C2×C71⋊#95C2212yes—
37C2×C71⋊#95C2212yes—
38C42×Dic71—24no—
39C24×C4×C71C2211yescharacteristic
40C22×C22⋊C4×C71C2212yes—
41C22×C42×C71C2211yescharacteristic
42C22×C42×C71C2211yescharacteristic
43C4×C22⋊C4×C71—24no—
44C2×#95×C71C2212yes—
45C24×D71C2311yescharacteristic
46C22×C22⋊D71—22no—
47C22×C22⋊D71—22no—
48C22×C22⋊D71—24no—
49C22×C22⋊D71C2×C418yes—
50C22×C22⋊D71C2×C414yes—
51C23×Dic71C2311yescharacteristic
52C23×Dic71C2312yes—
53C23×Dic71C2311yescharacteristic
54C23×Dic71C2312yes—
55C23×Dic71C2311yescharacteristic
56C22×C4×D71—22no—
57C22×C4×D71—22no—
58C22×C4×D71—22no—
59C22×C4×D71—22no—
60C22×C4×D71—22no—
61C22×C4×D71—22no—
62C22×C4×D71C2×C414yes—
63C4×C22⋊D71—232no—
64C2×Dic71⋊C4—24no—
65C2×Dic71⋊C4—22no—
66C2×Dic71⋊C4—22no—
67C2×Dic71⋊C4—24no—
68C2×Dic71⋊C4C2×C414yes—
69C2×Dic71⋊C4C2×C418yescomplemented
70C2×C22⋊Dic71—24no—
71C2×C22⋊Dic71—22no—
72C2×C22⋊Dic71—22no—
73C2×C22⋊Dic71—24no—
74C2×C22⋊Dic71C2×C414yes—
75C2×C22⋊Dic71C2×C418yescomplemented
76C2×(C2×D71)⋊C4—24no—
77C2×(C2×D71)⋊C4—22no—
78C2×(C2×D71)⋊C4—22no—
79C2×(C2×D71)⋊C4—24no—
80C2×(C2×D71)⋊C4—24no—
81C2×(C2×D71)⋊C4—24no—
82C2×(C2×D71)⋊C4C2×C414yes—
83C2×(C2×D71)⋊C4C2×C418yescomplemented
84C2×(C2×D71)⋊C4C2×C418yescomplemented
85C2×C4×Dic71—24no—
86C2×C4×Dic71—24no—
87C2×C4×Dic71—24no—
88C2×C4×Dic71—24no—
89C2×C4×Dic71—22no—
90C2×C4×Dic71—22no—
91C2×C4×Dic71—22no—
92C2×C4×Dic71—22no—
93C2×C4×Dic71—24no—
94C2×C4×Dic71—22no—
95C2×C4×Dic71C2×C414yes—
96C2×C4×Dic71C2×C418yescomplemented
97C2×C4×Dic71D414yes—
98C2×C4×Dic71D414yes—
99C2×C4×Dic71D414yescomplemented
100C71⋊#95—24no—
101C71⋊#95—24no—
102C71⋊#95—24no—
103C71⋊#95—24no—
104C25×C71C2311yescharacteristic
105C23×C4×C71—22no—
106C23×C4×C71—22no—
107C23×C4×C71—22no—
108C23×C4×C71—22no—
109C23×C4×C71—22no—
110C23×C4×C71—22no—
111C23×C4×C71C2×C414yes—
112C23×C4×C71C2312yes—
113C23×C4×C71C2311yescharacteristic
114C23×C4×C71C2312yes—
115C23×C4×C71C2311yescharacteristic
116C2×C22⋊C4×C71—24no—
117C2×C22⋊C4×C71—24no—
118C2×C22⋊C4×C71C2×C418yescomplemented
119C2×C42×C71—22no—
120C2×C42×C71—22no—
121C2×C42×C71—22no—
122C2×C42×C71—22no—
123C2×C42×C71—22no—
124C2×C42×C71D414yescomplemented
125#95×C71—24no—
126C23×D71—21no—
127C23×D71—21no—
128C23×D71—21no—
129C23×D71—21no—
130C23×D71—21no—
131C23×D71—21no—
132C23×D71—22no—
133C23×D71—22no—
134C23×D71—22no—
135C23×D71C22×C412yes—
136C23×D71C22×C414yes—
137C2×C22⋊D71—28no—
138C2×C22⋊D71—28no—
139C2×C22⋊D71—216no—
140C2×C22⋊D71—216no—
141C2×C22⋊D71C42116yescomplemented
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71—22no—
146C22×Dic71—22no—
147C22×Dic71—22no—
148C22×Dic71—21no—
149C22×Dic71—21no—
150C22×Dic71—21no—
151C22×Dic71—21no—
152C22×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—21no—
156C22×Dic71—21no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71C22×C412yes—
161C22×Dic71C22×C414yes—
162C22×Dic71C22×C412yes—
163C22×Dic71C22×C414yes—
164C22×Dic71C22×C412yes—
165C22×Dic71C22×C414yes—
166C22×Dic71C2×D412yes—
167C22×Dic71C2×D412yes—
168C22×Dic71C2×D414yes—
169C22×Dic71C2×D412yes—
170C22×Dic71C2×D412yes—
171C22×Dic71#4114yes—
172C22×Dic71#4114yes—
173C2×C4×D71—28no—
174C2×C4×D71—28no—
175C2×C4×D71—28no—
176C2×C4×D71—44no—
177C2×C4×D71—44no—
178C2×C4×D71—44no—
179C2×C4×D71—44no—
180Dic71⋊C4—28no—
181Dic71⋊C4—216no—
182C22⋊Dic71—28no—
183C22⋊Dic71—216no—
184(C2×D71)⋊C4—216no—
185(C2×D71)⋊C4—28no—
186(C2×D71)⋊C4—216no—
187C4×Dic71—216no—
188C4×Dic71—28no—
189C4×Dic71—216no—
190C4×Dic71—44no—
191C4×Dic71C22⋊C4116yescomplemented
192C24×C71—21no—
193C24×C71—21no—
194C24×C71—21no—
195C24×C71—21no—
196C24×C71—22no—
197C24×C71—22no—
198C24×C71—21no—
199C24×C71—21no—
200C24×C71—22no—
201C24×C71C22×C414yes—
202C24×C71C22×C412yes—
203C24×C71C2411yescharacteristic
204C22×C4×C71—22no—
205C22×C4×C71—22no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—21no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—21no—
213C22×C4×C71—21no—
214C22×C4×C71—21no—
215C22×C4×C71—22no—
216C22×C4×C71—21no—
217C22×C4×C71—21no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—28no—
221C22×C4×C71—28no—
222C22×C4×C71—28no—
223C22×C4×C71—44no—
224C22×C4×C71—44no—
225C22×C4×C71—44no—
226C22×C4×C71—44no—
227C22×C4×C71C22×C414yes—
228C22×C4×C71C22×C412yes—
229C22×C4×C71C22×C414yes—
230C22×C4×C71C22×C412yes—
231C22×C4×C71C2×D412yes—
232C22×C4×C71C2×D412yes—
233C22×C4×C71C2×D412yes—
234C22×C4×C71C2×D414yes—
235C22×C4×C71C2×D412yes—
236C22×C4×C71#4112yes—
237C22×C4×C71#4114yes—
238C22×C4×C71#4112yes—
239C22⋊C4×C71—216no—
240C42×C71—28no—
241C42×C71—44no—
242C23×C71—22no—
243C23×C71—22no—
244C23×C71—24no—
245C23×C71—22no—
246C23×C71—22no—
247C23×C71—24no—
248C23×C71—24no—
249C23×C71—24no—
250C23×C71—24no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71—24no—
254C23×C71—41no—
255C23×C71—41no—
256C23×C71—42no—
257C23×C71—41no—
258C23×C71—42no—
259C23×C71—42no—
260C23×C71—41no—
261C23×C71—42no—
262C23×C71—42no—
263C23×C71—42no—
264C23×C71C2×C4214yes—
265C23×C71C23×C411yescharacteristic
266C23×C71C23×C412yes—
267C23×C71C22×D411yescharacteristic
268C23×C71C22×D411yescharacteristic
269C23×C71C22×D411yescharacteristic
270C23×C71C22×D411yescharacteristic
271C23×C71C2×#4112yes—
272C23×C71C2×#4112yes—
273C23×C71C2×#4111yescharacteristic
274C23×C71C2×#4111yescharacteristic
275C23×C71C2×#4112yes—
276C22×D71—22no—
277C22×D71—22no—
278C22×D71—24no—
279C22×D71—24no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—24no—
283C22×D71—24no—
284C22×D71—24no—
285C22×D71—22no—
286C22×D71—22no—
287C22×D71—24no—
288C22×D71—41no—
289C22×D71—41no—
290C22×D71—42no—
291C22×D71—41no—
292C22×D71—42no—
293C22×D71—42no—
294C22×D71—41no—
295C22×D71—42no—
296C22×D71—42no—
297C22×D71—42no—
298C22×D71C2×C4214yes—
299C2×C4×C71—24no—
300C2×C4×C71—24no—
301C2×C4×C71—24no—
302C2×C4×C71—24no—
303C2×C4×C71—24no—
304C2×C4×C71—24no—
305C2×C4×C71—22no—
306C2×C4×C71—24no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—24no—
310C2×C4×C71—24no—
311C2×C4×C71—41no—
312C2×C4×C71—41no—
313C2×C4×C71—41no—
314C2×C4×C71—42no—
315C2×C4×C71—41no—
316C2×C4×C71—42no—
317C2×C4×C71—42no—
318C2×C4×C71—42no—
319C2×C4×C71—416no—
320C2×C4×C71C2×C22⋊C414yes—
321C2×C4×C71C4×D414yes—
322C2×C4×C71C4×D414yes—
323C2×C4×C71C4×D418yescomplemented
324C2×C4×C71#12114yes—
325C2×C4×C71#12114yes—
326C2×C4×C71#12414yes—
327C2×C4×C71#12714yes—
328C22⋊D71—232no—
329C2×Dic71—24no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—24no—
333C2×Dic71—24no—
334C2×Dic71—24no—
335C2×Dic71—24no—
336C2×Dic71—24no—
337C2×Dic71—24no—
338C2×Dic71—24no—
339C2×Dic71—22no—
340C2×Dic71—24no—
341C2×Dic71—24no—
342C2×Dic71—24no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—41no—
346C2×Dic71—41no—
347C2×Dic71—41no—
348C2×Dic71—42no—
349C2×Dic71—41no—
350C2×Dic71—42no—
351C2×Dic71—42no—
352C2×Dic71—42no—
353C2×Dic71C2×C4214yes—
354C2×Dic71C2×C22⋊C414yes—
355C2×Dic71C2×C22⋊C414yes—
356C2×Dic71#11714yes—
357C2×Dic71C4×D418yes—
358C2×Dic71C4×D418yes—
359C2×Dic71C4×D418yescomplemented
360C4×D71—416no—
361C22×C71—24no—
362C22×C71—24no—
363C22×C71—24no—
364C22×C71—44no—
365C22×C71—42no—
366C22×C71—42no—
367C22×C71—42no—
368C22×C71—42no—
369C22×C71—44no—
370C22×C71—44no—
371C22×C71—44no—
372C22×C71C22×C4211yescharacteristic
373C22×C71C22×C22⋊C411yescharacteristic
374C22×C71C2×#11711yescharacteristic
375C22×C71C2×C4×D412yes—
376C22×C71C2×C4×D412yes—
377C22×C71C2×C4×D412yes—
378C22×C71C2×C4×D411yescharacteristic
379C22×C71C2×C4×D412yes—
380C22×C71C2×C4×D411yescharacteristic
381C22×C71C4×#4112yes—
382C22×C71C4×#4111yescharacteristic
383C22×C71C4×#4111yescharacteristic
384C22×C71C4×#4112yes—
385C22×C71C2×#12111yescharacteristic
386C22×C71C2×#12111yescharacteristic
387C22×C71#52512yes—
388C22×C71C2×#12411yescharacteristic
389C22×C71#52912yes—
390C22×C71#52912yes—
391C22×C71C2×#12711yescharacteristic
392C22×C71#53212yes—
393C22×C71#53212yes—
394C22×C71#53212yes—
395C2×D71—24no—
396C2×D71—24no—
397C2×D71—24no—
398C2×D71—44no—
399C2×D71—42no—
400C2×D71—42no—
401C2×D71—42no—
402C2×D71—42no—
403C2×D71—44no—
404C2×D71—44no—
405C2×D71—44no—
406C4×C71—28no—
407C4×C71—44no—
408C4×C71—42no—
409C4×C71#39018yescomplemented
410Dic71—24no—
411Dic71—28no—
412Dic71—44no—
413Dic71—42no—
414Dic71C4×C22⋊C418yescomplemented
415C4×#390—711nomaximal, Sylow
416C2×C71—44no—
417C2×C71C2×C4×C22⋊C411yescharacteristic
418C2×C71C42×D411yescharacteristic
419C2×C71C42×D411yescharacteristic
420C2×C71C2×#39011yescharacteristic
421C2×C71#229311yescharacteristic
422C2×C71#229311yescharacteristic
423C2×C71#229711yescharacteristic
424C2×C71C4×#12112yes—
425C2×C71C4×#12112yes—
426C2×C71C4×#12412yes—
427C2×C71C4×#12712yes—
428D71—44no—
429C22×C4×D4—711no—
430C2×#390—712no—
431C2×C4×C4⋊C4—711no—
432C2×C4×C22⋊C4—711no—
433C2×C4×C22⋊C4—711no—
434C2×C4×C22⋊C4—711no—
435C2×C4×C22⋊C4D7111yescharacteristic, complemented
436C2×C43—711no—
437#1437—712no—
438#1437—712no—
439C4⋊#95—712no—
440C71C4×#39011yescharacteristic, complemented, Sylow
441C23×D4—711no—
442C24×C4—711no—
443C24×C4C2×D7111yescharacteristic
444C2×C4×D4—718no—
445C2×C4×D4—1424no—
446C2×C4×D4—1424no—
447C22×C4⋊C4—711no—
448C22×C4⋊C4—712no—
449C22×C22⋊C4—711no—
450C22×C22⋊C4—712no—
451C22×C22⋊C4—711no—
452C22×C22⋊C4—712no—
453C22×C22⋊C4—712no—
454C22×C22⋊C4C2×D7112yes—
455C22×C42—711no—
456C22×C42—712no—
457C22×C42—711no—
458C22×C42—712no—
459C22×C42—711no—
460C22×C42C2×D7111yescharacteristic
461C22×C42C2×D7111yescharacteristic
462#390—7116no—
463C4×C4⋊C4—1424no—
464C4×C22⋊C4—24no—
465C4×C22⋊C4—1424no—
466C4×C22⋊C4—1424no—
467C4×C22⋊C4—1424no—
468C2×#95—712no—
469C2×#95—712no—
470C2×#95—712no—
471C2×#95—712no—
472C2×#95C2×D7112yes—
473C43—1424no—
474C25—711no—
475C25C22×D7111yescharacteristic
476C22×D4—714no—
477C22×D4—718no—
478C22×D4—1422no—
479C22×D4—1422no—
480C22×D4—1424no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—22no—
487C23×C4—711no—
488C23×C4—711no—
489C23×C4—712no—
490C23×C4—712no—
491C23×C4—711no—
492C23×C4—714no—
493C23×C4—1422no—
494C23×C4—1422no—
495C23×C4—1422no—
496C23×C4—1422no—
497C23×C4—1422no—
498C23×C4—1422no—
499C23×C4C4×D7114yes—
500C23×C4C22×D7112yes—
501C23×C4C22×D7111yescharacteristic
502C23×C4C22×D7112yes—
503C23×C4C22×D7111yescharacteristic
504C4×D4—14232no—
505C2×C4⋊C4—714no—
506C2×C4⋊C4—718no—
507C2×C4⋊C4—1422no—
508C2×C4⋊C4—1422no—
509C2×C4⋊C4—1424no—
510C2×C4⋊C4—1424no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—714no—
514C2×C22⋊C4—718no—
515C2×C22⋊C4—714no—
516C2×C22⋊C4—718no—
517C2×C22⋊C4—718no—
518C2×C22⋊C4—1422no—
519C2×C22⋊C4—1422no—
520C2×C22⋊C4—1424no—
521C2×C22⋊C4—1424no—
522C2×C22⋊C4—1422no—
523C2×C22⋊C4—1422no—
524C2×C22⋊C4—1424no—
525C2×C22⋊C4—1424no—
526C2×C22⋊C4—1424no—
527C2×C22⋊C4—1424no—
528C2×C22⋊C4C4×D7118yescomplemented
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—714no—
535C2×C42—714no—
536C2×C42—714no—
537C2×C42—718no—
538C2×C42—714no—
539C2×C42—1422no—
540C2×C42—1422no—
541C2×C42—1422no—
542C2×C42—1424no—
543C2×C42—1424no—
544C2×C42—1424no—
545C2×C42—1424no—
546C2×C42—1422no—
547C2×C42—1424no—
548C2×C42—1422no—
549C2×C42C22⋊D7114yescomplemented
550#95—24no—
551#95—1424no—
552#95—1424no—
553#95—1424no—
554#95—1424no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—22no—
560C24—22no—
561C24—21no—
562C24—22no—
563C24—21no—
564C24—714no—
565C24—712no—
566C24—1421no—
567C24—1421no—
568C24—1421no—
569C24—1421no—
570C24—1422no—
571C24—1422no—
572C24—1421no—
573C24—1422no—
574C24—1421no—
575C24C2×C4×D7114yes—
576C24C2×C4×D7112yes—
577C24C23×D7111yescharacteristic
578C2×D4—7116no—
579C2×D4—1428no—
580C2×D4—1428no—
581C2×D4—14216no—
582C2×D4—14216no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—2844no—
607C22×C4—2844no—
608C22×C4—2844no—
609C22×C4—2844no—
610C22×C4—712no—
611C22×C4—714no—
612C22×C4—712no—
613C22×C4—712no—
614C22×C4—714no—
615C22×C4—712no—
616C22×C4—714no—
617C22×C4—712no—
618C22×C4—714no—
619C22×C4—712no—
620C22×C4—714no—
621C22×C4—714no—
622C22×C4—712no—
623C22×C4—1421no—
624C22×C4—1422no—
625C22×C4—1422no—
626C22×C4—1421no—
627C22×C4—1421no—
628C22×C4—1421no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4—1421no—
633C22×C4—1422no—
634C22×C4—1421no—
635C22×C4—1428no—
636C22×C4—1428no—
637C22×C4—1428no—
638C22×C4—1422no—
639C22×C4—1422no—
640C22×C4—1422no—
641C22×C4—1422no—
642C22×C4—1422no—
643C22×C4—1422no—
644C22×C4C2×C4×D7114yes—
645C22×C4C2×C4×D7112yes—
646C22×C4C2×C4×D7114yes—
647C22×C4C2×C4×D7112yes—
648C22×C4D4×D7112yes—
649C22×C4D4×D7112yes—
650C22×C4D4×D7112yes—
651C22×C4C2×C22⋊D7114yes—
652C22×C4C2×C22⋊D7112yes—
653C22×C4#1176586412yes—
654C22×C4#1176586514yes—
655C22×C4#1176586512yes—
656C4⋊C4—14216no—
657C4⋊C4—1428no—
658C22⋊C4—216no—
659C22⋊C4—14216no—
660C22⋊C4—1428no—
661C22⋊C4—14216no—
662C22⋊C4—1428no—
663C22⋊C4—14216no—
664C42—28no—
665C42—44no—
666C42—2844no—
667C42—7116no—
668C42—14216no—
669C42—14216no—
670C42—1428no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—2841no—
694C23—2841no—
695C23—2842no—
696C23—2841no—
697C23—2842no—
698C23—2842no—
699C23—2841no—
700C23—2842no—
701C23—2842no—
702C23—2842no—
703C23—714no—
704C23—1422no—
705C23—1422no—
706C23—1424no—
707C23—1424no—
708C23—1424no—
709C23—1422no—
710C23—1424no—
711C23—1422no—
712C23—1424no—
713C23—1422no—
714C23—1422no—
715C23—1424no—
716C23C42×D7114yes—
717C23C22×C4×D7111yescharacteristic
718C23C22×C4×D7112yes—
719C23C2×D4×D7111yescharacteristic
720C23C2×D4×D7111yescharacteristic
721C23C2×D4×D7111yescharacteristic
722C23C22×C22⋊D7111yescharacteristic
723C23#41×D7112yes—
724C23#41×D7112yes—
725C23C2×#1176586411yescharacteristic
726C23C2×#1176586511yescharacteristic
727C23C2×#1176586512yes—
728D4—14232no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—416no—
750C2×C4—2841no—
751C2×C4—2841no—
752C2×C4—2841no—
753C2×C4—2842no—
754C2×C4—2841no—
755C2×C4—2842no—
756C2×C4—2842no—
757C2×C4—2842no—
758C2×C4—28416no—
759C2×C4—714no—
760C2×C4—714no—
761C2×C4—714no—
762C2×C4—718no—
763C2×C4—718no—
764C2×C4—714no—
765C2×C4—718no—
766C2×C4—1422no—
767C2×C4—1424no—
768C2×C4—1424no—
769C2×C4—1422no—
770C2×C4—1424no—
771C2×C4—1422no—
772C2×C4—1424no—
773C2×C4—1422no—
774C2×C4—1422no—
775C2×C4—1424no—
776C2×C4—1424no—
777C2×C4—1424no—
778C2×C4—1424no—
779C2×C4—1424no—
780C2×C4—1424no—
781C2×C4—1424no—
782C2×C4C22⋊C4×D7114yes—
783C2×C4(C22⋊D71)⋊C414yes—
784C2×C4C4×C22⋊D7114yes—
785C2×C4C4×C22⋊D7118yescomplemented
786C2×C4#1455610014yes—
787C2×C4#1455610114yes—
788C2×C4#1455611414yes—
789C2×C4#1455612414yes—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—2842no—
802C22—2842no—
803C22—2842no—
804C22—2842no—
805C22—2844no—
806C22—2844no—
807C22—2844no—
808C22—2844no—
809C22—1424no—
810C22—1424no—
811C22—1424no—
812C22C2×C42×D7111yescharacteristic
813C22C2×C22⋊C4×D7111yescharacteristic
814C22#117×D7111yescharacteristic
815C22C4×D4×D7112yes—
816C22C4×D4×D7112yes—
817C22C4×D4×D7112yes—
818C22C2×(C22⋊D71)⋊C411yescharacteristic
819C22C2×C4×C22⋊D7111yescharacteristic
820C22C2×C4×C22⋊D7112yes—
821C22C4×#1176586412yes—
822C22#1798646711yescharacteristic
823C22C4×#1176586511yescharacteristic
824C22C4×#1176586512yes—
825C22C2×#1455610011yescharacteristic
826C22C2×#1455610111yescharacteristic
827C22#1798650812yes—
828C22C2×#1455611411yescharacteristic
829C22#1798652712yes—
830C22#1798652912yes—
831C22C2×#1455612411yescharacteristic
832C22#1798654512yes—
833C22#1798654612yes—
834C22#1798654612yes—
835C4—28no—
836C4—42no—
837C4—44no—
838C4—2842no—
839C4—2844no—
840C4—718no—
841C4—1424no—
842C4—1428no—
843C4#1798589918yesdirect product factor
844C2—44no—
845C2—2844no—
846C2C4×C22⋊C4×D7111yescharacteristic
847C2C4×(C22⋊D71)⋊C411yescharacteristic
848C2C42×C22⋊D7111yescharacteristic
849C2C2×#1798589911yescharacteristic
850C2#2259079911yescharacteristic
851C2#2259080311yescharacteristic
852C2#2259082611yescharacteristic
853C2C4×#1455610012yes—
854C2C4×#1455610112yes—
855C2C4×#1455611412yes—
856C2C4×#1455612412yes—
subgroupG/H
centerC23×C4C22×D71
commutatorC22×C71C22×C42
FrattiniC24C23×D71
FittingC2×C4×C22⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC2×C4×C22⋊C4D71
hypocenterC71C4×#390
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic71⋊C4C2semidirect
4. C2×C4×(C2×D71)⋊C4C2semidirect
5. C2×C4×(C2×D71)⋊C4C2semidirect
6. C2×C4×C22⋊Dic71C2semidirect
7. C2×C42×Dic71C2semidirect
8. #22586577C2semidirect
9. #22586576C2semidirect
10. Dic71⋊#95C2semidirect
11. C2×C4×C22⋊C4×C71C2semidirect
16. C2×C4×C22⋊D71C4semidirect
29. #17985899C4direct (N × H)
69. C2×Dic71⋊C4C2×C4semidirect
75. C2×C22⋊Dic71C2×C4semidirect
83. C2×(C2×D71)⋊C4C2×C4semidirect
84. C2×(C2×D71)⋊C4C2×C4semidirect
96. C2×C4×Dic71C2×C4semidirect
99. C2×C4×Dic71D4semidirect
118. C2×C22⋊C4×C71C2×C4semidirect
124. C2×C42×C71D4semidirect
141. C2×C22⋊D71C42semidirect
191. C4×Dic71C22⋊C4semidirect
323. C2×C4×C71C4×D4semidirect
359. C2×Dic71C4×D4semidirect
409. C4×C71#390semidirect
414. Dic71C4×C22⋊C4semidirect
435. C2×C4×C22⋊C4D71semidirect
440. C71C4×#390semidirect
528. C2×C22⋊C4C4×D71semidirect
549. C2×C42C22⋊D71semidirect
785. C2×C4C4×C22⋊D71semidirect
843. C4#17985899direct (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
C2×#179858992
C2×C4×Dic71⋊C42
C2×C4×(C2×D71)⋊C42
C2×C4×C22⋊Dic712
C2×C42×Dic712
#225865772
#225865762
Dic71⋊#952
C2×C4×C22⋊C4×C712
C4×#39071