Finite Group Databasebeta

← C2×#22592189 #32165357

Subgroups — C2×#22592189 #32165357

Order 18176.

3614 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556126C211yesmaximal, characteristic, complemented
2C22×#14556106C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D71C211yesmaximal, characteristic
4#22592189C2116yesmaximal, direct product factor
5C2×#17985922C211yesmaximal, characteristic, complemented
6C2×#17985921C211yesmaximal, characteristic, complemented
7C2×#17985911C211yesmaximal, characteristic, complemented
8C2×#17985910C211yesmaximal, characteristic, complemented
9C2×#17985899C211yesmaximal, characteristic
10C2×#17985899C211yesmaximal, characteristic
11C2×#17985894C211yesmaximal, characteristic, complemented
12C2×#17985894C211yesmaximal, characteristic, complemented
13C2×#17985872C211yesmaximal, characteristic, complemented
14C2×#17985870C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556126—28no—
21C2×#14556126C2218yescomplemented
22C2×#14556106—28no—
23C2×#14556106C2218yescomplemented
24C2×C4×C22⋊D71—28no—
25C2×C4×C22⋊D71C2218yes—
26C22×C4⋊Dic71C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×C22⋊Dic71C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43C22×C4×Dic71C2211yescharacteristic
44C22×C4×Dic71C2211yescharacteristic
45#17985922C2218yescomplemented
46#17985921C2218yescomplemented
47#17985911C2218yescomplemented
48#17985910C2218yescomplemented
49#17985899C2218yes—
50#17985899C2218yes—
51#17985894C2218yescomplemented
52#17985894C2218yescomplemented
53#17985872C2218yescomplemented
54#17985870C2218yescomplemented
55C4⋊C4×Dic71C2218yescomplemented
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C23×Q8×C71C2211yescharacteristic
63C24×C4×C71C2211yescharacteristic
64C2×C22⋊Q8×C71—28no—
65C2×C22⋊Q8×C71C2218yescomplemented
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C4⋊C4×C71C2211yescharacteristic
68C22×C4⋊C4×C71C2211yescharacteristic
69C22×C22⋊C4×C71C2211yescharacteristic
70C22×C22⋊C4×C71C2211yescharacteristic
71C24×D71C2311yescharacteristic
72C22×Dic142—24no—
73C22×Dic142—24no—
74C22×Dic142—42no—
75C22×Dic142C2314yes—
76C22×C22⋊D71—24no—
77C22×C22⋊D71—24no—
78C22×C22⋊D71Q818yescomplemented
79C22×C22⋊D71C2314yes—
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C22×C4×D71—24no—
88C22×C4×D71—24no—
89C22×C4×D71—42no—
90C22×C4×D71C2314yes—
91#14556126—232no—
92#14556106—232no—
93C4×C22⋊D71—232no—
94C2×C4⋊Dic71—24no—
95C2×C4⋊Dic71C2314yes—
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4—24no—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4D418yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×C22⋊Dic71—24no—
111C2×C22⋊Dic71—24no—
112C2×C22⋊Dic71—42no—
113C2×C22⋊Dic71C2314yes—
114C2×C22⋊Dic71C2314yes—
115C2×C22⋊Dic71C2314yes—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4—24no—
120C2×(C2×D71)⋊C4—42no—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×C4×Dic71—24no—
127C2×C4×Dic71—24no—
128C2×C4×Dic71—24no—
129C2×C4×Dic71C2314yes—
130C2×C4×Dic71C2314yes—
131C2×C4×Dic71C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C25×C71C2311yescharacteristic
139C22×Q8×C71—24no—
140C22×Q8×C71—24no—
141C22×Q8×C71—42no—
142C22×Q8×C71C2314yes—
143C23×C4×C71—24no—
144C23×C4×C71—24no—
145C23×C4×C71—42no—
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2314yes—
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C23×C4×C71C2311yescharacteristic
152C23×C4×C71C2311yescharacteristic
153C22⋊Q8×C71—232no—
154C2×C4⋊C4×C71—24no—
155C2×C4⋊C4×C71—24no—
156C2×C4⋊C4×C71D418yescomplemented
157C2×C4⋊C4×C71C2314yes—
158C2×C4⋊C4×C71C2314yes—
159C2×C4⋊C4×C71C2314yes—
160C2×C22⋊C4×C71—24no—
161C2×C22⋊C4×C71—24no—
162C2×C22⋊C4×C71C2314yes—
163C2×C22⋊C4×C71C2314yes—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71C2×Q814yes—
171C23×D71C2412yes—
172C2×Dic142—28no—
173C2×Dic142—28no—
174C2×Dic142—44no—
175C2×Dic142—416no—
176C2×C22⋊D71—232no—
177C2×C22⋊D71—28no—
178C2×C22⋊D71—28no—
179C2×C22⋊D71C2×Q8116yescomplemented
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—22no—
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71—22no—
187C22×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71—22no—
190C22×Dic71—22no—
191C22×Dic71—22no—
192C22×Dic71—22no—
193C22×Dic71—22no—
194C22×Dic71—22no—
195C22×Dic71—22no—
196C22×Dic71C2×D414yes—
197C22×Dic71C2×D414yes—
198C22×Dic71C2×Q814yes—
199C22×Dic71#4114yes—
200C22×Dic71#4114yes—
201C22×Dic71C2412yes—
202C22×Dic71C2412yes—
203C22×Dic71C2412yes—
204C22×Dic71C2412yes—
205C22×Dic71C2412yes—
206C22×Dic71C2412yes—
207C22×Dic71C2412yes—
208C2×C4×D71—28no—
209C2×C4×D71—28no—
210C2×C4×D71—44no—
211C2×C4×D71—416no—
212C4⋊Dic71—28no—
213Dic71⋊C4—28no—
214Dic71⋊C4—28no—
215Dic71⋊C4—28no—
216Dic71⋊C4—28no—
217Dic71⋊C4—28no—
218Dic71⋊C4—28no—
219Dic71⋊C4C2×D4116yes—
220C22⋊Dic71—28no—
221C22⋊Dic71—28no—
222C22⋊Dic71—44no—
223(C2×D71)⋊C4—28no—
224(C2×D71)⋊C4—28no—
225(C2×D71)⋊C4—28no—
226(C2×D71)⋊C4—28no—
227(C2×D71)⋊C4—44no—
228C4×Dic71—28no—
229C4×Dic71—28no—
230C4×Dic71—28no—
231C24×C71—22no—
232C24×C71—22no—
233C24×C71—22no—
234C24×C71—22no—
235C24×C71—22no—
236C24×C71—22no—
237C24×C71C2×Q814yes—
238C24×C71C2412yes—
239C24×C71C2411yescharacteristic
240C2×Q8×C71—28no—
241C2×Q8×C71—28no—
242C2×Q8×C71—44no—
243C2×Q8×C71—416no—
244C22×C4×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71—22no—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—22no—
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—22no—
257C22×C4×C71—22no—
258C22×C4×C71—28no—
259C22×C4×C71—28no—
260C22×C4×C71—44no—
261C22×C4×C71—416no—
262C22×C4×C71C2×D414yes—
263C22×C4×C71C2×D414yes—
264C22×C4×C71C2×D414yes—
265C22×C4×C71C2×D414yes—
266C22×C4×C71C2412yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2412yes—
269C22×C4×C71C2412yes—
270C22×C4×C71C2412yes—
271C22×C4×C71C2412yes—
272C4⋊C4×C71—28no—
273C4⋊C4×C71—28no—
274C4⋊C4×C71C2×D4116yescomplemented
275C22⋊C4×C71—28no—
276C22⋊C4×C71—28no—
277C23×C71—28no—
278C23×C71—28no—
279C23×C71—28no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—44no—
287C23×C71—44no—
288C23×C71—44no—
289C23×C71—44no—
290C23×C71C22×D412yes—
291C23×C71C22×D412yes—
292C23×C71C22×Q814yes—
293C23×C71C22×Q812yes—
294C23×C71C2×#4112yes—
295C23×C71C2×#4112yes—
296C23×C71H(5,𝔽2)12yes—
297C23×C712−1+412yes—
298C23×C71C2511yescharacteristic
299C22×D71—28no—
300C22×D71—28no—
301C22×D71—28no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—44no—
309C22×D71—44no—
310C22×D71—44no—
311C22×D71—44no—
312C22×D71C22×Q814yes—
313Q8×C71—416no—
314C2×C4×C71—28no—
315C2×C4×C71—28no—
316C2×C4×C71—28no—
317C2×C4×C71—28no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—416no—
333C2×C4×C71—44no—
334C2×C4×C71—44no—
335C2×C4×C71C22×D414yes—
336C2×C4×C71C22×D414yes—
337C2×C4×C71C22×D414yes—
338C2×C4×C71C22×D414yes—
339C22⋊D71—232no—
340C2×Dic71—28no—
341C2×Dic71—28no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—22no—
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—22no—
353C2×Dic71—22no—
354C2×Dic71—22no—
355C2×Dic71—22no—
356C2×Dic71—22no—
357C2×Dic71—22no—
358C2×Dic71—44no—
359C2×Dic71—44no—
360C2×Dic71—44no—
361C2×Dic71—44no—
362C2×Dic71C22⋊Q8116yescomplemented
363C2×Dic71C22×D414yes—
364C2×Dic71C22×D414yes—
365C2×Dic71C22×Q814yes—
366C2×Dic71C2×#4114yes—
367C2×Dic71C2×#4114yes—
368C4×D71—416no—
369Dic142—416no—
370C22×C71—24no—
371C22×C71—24no—
372C22×C71—24no—
373C22×C71—42no—
374C22×C71—42no—
375C22×C71—42no—
376C22×C71—42no—
377C22×C71—416no—
378C22×C71C2×C22⋊Q814yes—
379C22×C71#53214yes—
380C22×C71#54214yes—
381C22×C71D4214yes—
382C22×C71#54814yes—
383C22×C71D4×Q814yes—
384C22×C71#55414yes—
385C22×C71C23×D411yescharacteristic
386C22×C71C23×D411yescharacteristic
387C22×C71C23×Q811yescharacteristic
388C22×C71C22×#4111yescharacteristic
389C22×C71C22×#4111yescharacteristic
390C22×C71C2×H(5,𝔽2)11yescharacteristic
391C22×C71C2×2−1+411yescharacteristic
392C2×D71—24no—
393C2×D71—24no—
394C2×D71—24no—
395C2×D71—42no—
396C2×D71—42no—
397C2×D71—42no—
398C2×D71—42no—
399C2×D71—416no—
400C4×C71—24no—
401C4×C71—24no—
402C4×C71—24no—
403C4×C71—24no—
404C4×C71—42no—
405C4×C71—42no—
406Dic71—24no—
407Dic71—24no—
408Dic71—42no—
409Dic71—42no—
410Dic71—42no—
411Dic71—42no—
412Dic71C2×C22⋊Q818yescomplemented
413C2×#2452—711nomaximal, Sylow
414C2×C71—44no—
415C2×C71#245218yescomplemented
416C2×C71C22×C22⋊Q811yescharacteristic
417C2×C71C2×#53211yescharacteristic
418C2×C71C2×#54211yescharacteristic
419C2×C71C2×D4211yescharacteristic
420C2×C71C2×#54811yescharacteristic
421C2×C71C2×D4×Q811yescharacteristic
422C2×C71C2×#55411yescharacteristic
423D71—44no—
424C22×C4⋊Q8—711no—
425C22×C22⋊Q8—711no—
426C22×C22⋊Q8D7111yescharacteristic, complemented
427C22×C4×D4—711no—
428#2452—7116no—
429C2×#396—711no—
430C2×#396—711no—
431C2×#393—711no—
432C2×#393—711no—
433C2×#390—711no—
434C2×#390—711no—
435C2×#389—711no—
436C2×#389—711no—
437C2×#385—711no—
438C2×#385—711no—
439C2×C4×C4⋊C4—711no—
440C71C2×#245211yescharacteristic, complemented, Sylow
441C23×Q8—711no—
442C23×Q8C2×D7111yescharacteristic
443C23×D4—711no—
444C24×C4—711no—
445C24×C4C2×D7111yescharacteristic
446C2×C4⋊Q8—718no—
447C2×C4⋊Q8—1428no—
448C2×C22⋊Q8—28no—
449C2×C22⋊Q8—718no—
450C2×C22⋊Q8—1428no—
451C2×C22⋊Q8C2×D7118yescomplemented
452C2×C4×D4—718no—
453C2×C4×D4—1428no—
454C22×C4⋊C4—711no—
455C22×C4⋊C4—711no—
456C22×C4⋊C4—711no—
457C22×C4⋊C4—711no—
458C22×C4⋊C4—711no—
459C22×C4⋊C4—711no—
460C22×C4⋊C4—711no—
461C22×C4⋊C4—711no—
462C22×C4⋊C4C2×D7111yescharacteristic
463C22×C4⋊C4C2×D7111yescharacteristic
464C22×C4⋊C4C2×D7111yescharacteristic
465C22×C22⋊C4—711no—
466C22×C22⋊C4—711no—
467C22×C22⋊C4—711no—
468C22×C22⋊C4—711no—
469C22×C22⋊C4—711no—
470C22×C22⋊C4—711no—
471C22×C22⋊C4—711no—
472C22×C22⋊C4—711no—
473C22×C22⋊C4C2×D7111yescharacteristic
474C22×C22⋊C4C2×D7111yescharacteristic
475C22×C42—711no—
476C22×C42—711no—
477C22×C42—711no—
478#396—718no—
479#396—718no—
480#393—718no—
481#393—718no—
482#390—718no—
483#390—718no—
484#389—718no—
485#389—718no—
486#385—718no—
487#385—718no—
488C4×C4⋊C4—718no—
489C2×#95—711no—
490C2×#95—711no—
491C2×#95—711no—
492C2×#95—711no—
493C2×#95—711no—
494C2×#95—711no—
495C25—711no—
496C25C22×D7111yescharacteristic
497C22×Q8—24no—
498C22×Q8—24no—
499C22×Q8—42no—
500C22×Q8—2842no—
501C22×Q8—714no—
502C22×Q8—1424no—
503C22×Q8—1424no—
504C22×Q8C22×D7114yes—
505C22×D4—718no—
506C22×D4—714no—
507C22×D4—1424no—
508C22×D4—1424no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—42no—
512C23×C4—2842no—
513C23×C4—714no—
514C23×C4—711no—
515C23×C4—711no—
516C23×C4—711no—
517C23×C4—711no—
518C23×C4—711no—
519C23×C4—711no—
520C23×C4—711no—
521C23×C4—1424no—
522C23×C4—1424no—
523C23×C4C22×D7111yescharacteristic
524C23×C4C22×D7111yescharacteristic
525C23×C4C22×D7114yes—
526C23×C4C22×D7111yescharacteristic
527C23×C4C22×D7111yescharacteristic
528C23×C4C22×D7111yescharacteristic
529C23×C4C22×D7111yescharacteristic
530C4⋊Q8—14232no—
531C22⋊Q8—232no—
532C22⋊Q8—14232no—
533C4×D4—14232no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—718no—
537C2×C4⋊C4—714no—
538C2×C4⋊C4—714no—
539C2×C4⋊C4—714no—
540C2×C4⋊C4—714no—
541C2×C4⋊C4—714no—
542C2×C4⋊C4—714no—
543C2×C4⋊C4—714no—
544C2×C4⋊C4—714no—
545C2×C4⋊C4—1424no—
546C2×C4⋊C4—1424no—
547C2×C4⋊C4—1424no—
548C2×C4⋊C4—1424no—
549C2×C4⋊C4—1424no—
550C2×C4⋊C4—1424no—
551C2×C4⋊C4—1424no—
552C2×C4⋊C4C22⋊D7118yescomplemented
553C2×C4⋊C4C22×D7114yes—
554C2×C4⋊C4C22×D7114yes—
555C2×C4⋊C4C22×D7114yes—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—2842no—
559C2×C22⋊C4—2842no—
560C2×C22⋊C4—714no—
561C2×C22⋊C4—714no—
562C2×C22⋊C4—714no—
563C2×C22⋊C4—714no—
564C2×C22⋊C4—714no—
565C2×C22⋊C4—714no—
566C2×C22⋊C4—714no—
567C2×C22⋊C4—714no—
568C2×C22⋊C4—1424no—
569C2×C22⋊C4—1424no—
570C2×C22⋊C4—1424no—
571C2×C22⋊C4—1424no—
572C2×C22⋊C4—1424no—
573C2×C22⋊C4—1424no—
574C2×C22⋊C4C22×D7114yes—
575C2×C22⋊C4C22×D7114yes—
576C2×C42—714no—
577C2×C42—714no—
578C2×C42—714no—
579C2×C42—1424no—
580C2×C42—1424no—
581C2×C42—1424no—
582#95—714no—
583#95—714no—
584#95—714no—
585#95—714no—
586#95—714no—
587#95—714no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—714no—
595C24—712no—
596C24—1422no—
597C24—1422no—
598C24—1422no—
599C24—1422no—
600C24—1422no—
601C24—1422no—
602C24Q8×D7114yes—
603C24C23×D7112yes—
604C24C23×D7111yescharacteristic
605C2×Q8—28no—
606C2×Q8—28no—
607C2×Q8—44no—
608C2×Q8—416no—
609C2×Q8—28416no—
610C2×Q8—2844no—
611C2×Q8—1428no—
612C2×Q8—1428no—
613C2×D4—7116no—
614C2×D4—1428no—
615C2×D4—1428no—
616C2×D4—14232no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—44no—
634C22×C4—416no—
635C22×C4—28416no—
636C22×C4—2844no—
637C22×C4—714no—
638C22×C4—714no—
639C22×C4—714no—
640C22×C4—712no—
641C22×C4—714no—
642C22×C4—714no—
643C22×C4—712no—
644C22×C4—712no—
645C22×C4—712no—
646C22×C4—712no—
647C22×C4—712no—
648C22×C4—712no—
649C22×C4—1428no—
650C22×C4—1422no—
651C22×C4—1422no—
652C22×C4—1422no—
653C22×C4—1422no—
654C22×C4—1422no—
655C22×C4—1422no—
656C22×C4—1422no—
657C22×C4—1422no—
658C22×C4—1422no—
659C22×C4—1422no—
660C22×C4—1422no—
661C22×C4—1422no—
662C22×C4—1428no—
663C22×C4—1422no—
664C22×C4—1422no—
665C22×C4—1422no—
666C22×C4—1422no—
667C22×C4D4×D7114yes—
668C22×C4C2×C22⋊D7114yes—
669C22×C4C2×C22⋊D7114yes—
670C22×C4C2×C22⋊D7114yes—
671C22×C4C23×D7112yes—
672C22×C4C23×D7112yes—
673C22×C4C23×D7112yes—
674C22×C4C23×D7112yes—
675C22×C4C23×D7112yes—
676C22×C4C23×D7112yes—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—7116no—
680C4⋊C4—1428no—
681C4⋊C4—1428no—
682C4⋊C4—1428no—
683C4⋊C4—1428no—
684C4⋊C4—1428no—
685C4⋊C4—1428no—
686C4⋊C4—1428no—
687C4⋊C4C2×C22⋊D71116yescomplemented
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—2844no—
691C22⋊C4—2844no—
692C22⋊C4—1428no—
693C22⋊C4—1428no—
694C22⋊C4—1428no—
695C22⋊C4—1428no—
696C22⋊C4—1428no—
697C22⋊C4—1428no—
698C42—1428no—
699C42—1428no—
700C42—1428no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—2844no—
715C23—2844no—
716C23—2844no—
717C23—2844no—
718C23—714no—
719C23—1422no—
720C23—1422no—
721C23—1422no—
722C23—1422no—
723C23—1422no—
724C23—1422no—
725C23—1428no—
726C23—1428no—
727C23—1428no—
728C23C2×D4×D7112yes—
729C23C22×C22⋊D7112yes—
730C23C2×Q8×D7114yes—
731C23C2×Q8×D7112yes—
732C23#41×D7112yes—
733C23#41×D7112yes—
734C23#1455617312yes—
735C23#1455617612yes—
736C23C24×D7111yescharacteristic
737Q8—416no—
738Q8—28416no—
739D4—14232no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—416no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—28416no—
762C2×C4—2844no—
763C2×C4—2844no—
764C2×C4—2844no—
765C2×C4—2844no—
766C2×C4—714no—
767C2×C4—714no—
768C2×C4—714no—
769C2×C4—7116no—
770C2×C4—714no—
771C2×C4—714no—
772C2×C4—1422no—
773C2×C4—1422no—
774C2×C4—1422no—
775C2×C4—1422no—
776C2×C4—1422no—
777C2×C4—1422no—
778C2×C4—1422no—
779C2×C4—1422no—
780C2×C4—1422no—
781C2×C4—1422no—
782C2×C4—1422no—
783C2×C4—1422no—
784C2×C4—1422no—
785C2×C4—1422no—
786C2×C4—1422no—
787C2×C4—1422no—
788C2×C4—1428no—
789C2×C4—1428no—
790C2×C4C2×D4×D7114yes—
791C2×C4C22×C22⋊D7114yes—
792C2×C4C22×C22⋊D7114yes—
793C2×C4C22×C22⋊D7114yes—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—416no—
801C22—42no—
802C22—2842no—
803C22—2842no—
804C22—2842no—
805C22—28416no—
806C22—2842no—
807C22—1424no—
808C22—1424no—
809C22—1424no—
810C22C22⋊Q8×D7114yes—
811C22#1798654514yes—
812C22#1798661914yes—
813C22D4×C22⋊D7114yes—
814C22#1798665914yes—
815C22Q8×C22⋊D7114yes—
816C22#1798670314yes—
817C22C22×D4×D7111yescharacteristic
818C22C23×C22⋊D7111yescharacteristic
819C22C22×Q8×D7111yescharacteristic
820C22C2×#41×D7111yescharacteristic
821C22C2×#41×D7111yescharacteristic
822C22C2×#1455617311yescharacteristic
823C22C2×#1455617611yescharacteristic
824C4—24no—
825C4—24no—
826C4—24no—
827C4—24no—
828C4—42no—
829C4—42no—
830C4—2842no—
831C4—2842no—
832C4—2842no—
833C4—2842no—
834C4—718no—
835C4—1424no—
836C4—1424no—
837C2—44no—
838C2—2844no—
839C2#2259218918yesdirect product factor
840C2C2×C22⋊Q8×D7111yescharacteristic
841C2C2×#1798654511yescharacteristic
842C2C2×#1798661911yescharacteristic
843C2C2×D4×C22⋊D7111yescharacteristic
844C2C2×#1798665911yescharacteristic
845C2C2×Q8×C22⋊D7111yescharacteristic
846C2C2×#1798670311yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2452
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14556126C2semidirect
2. C22×#14556106C2semidirect
4. #22592189C2direct (N × H)
5. C2×#17985922C2semidirect
6. C2×#17985921C2semidirect
7. C2×#17985911C2semidirect
8. C2×#17985910C2semidirect
11. C2×#17985894C2semidirect
12. C2×#17985894C2semidirect
13. C2×#17985872C2semidirect
14. C2×#17985870C2semidirect
15. C2×C4⋊C4×Dic71C2semidirect
16. C22×C22⋊Q8×C71C2semidirect
21. C2×#14556126C22semidirect
23. C2×#14556106C22semidirect
45. #17985922C22semidirect
46. #17985921C22semidirect
47. #17985911C22semidirect
48. #17985910C22semidirect
51. #17985894C22semidirect
52. #17985894C22semidirect
53. #17985872C22semidirect
54. #17985870C22semidirect
55. C4⋊C4×Dic71C22semidirect
65. C2×C22⋊Q8×C71C22semidirect
78. C22×C22⋊D71Q8semidirect
156. C2×C4⋊C4×C71D4semidirect
179. C2×C22⋊D71C2×Q8semidirect
274. C4⋊C4×C71C2×D4semidirect
362. C2×Dic71C22⋊Q8semidirect
412. Dic71C2×C22⋊Q8semidirect
415. C2×C71#2452semidirect
426. C22×C22⋊Q8D71semidirect
440. C71C2×#2452semidirect
451. C2×C22⋊Q8C2×D71semidirect
552. C2×C4⋊C4C22⋊D71semidirect
687. C4⋊C4C2×C22⋊D71semidirect
839. C2#22592189direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561262
C22×#145561062
C22×C4×C22⋊D712
#225921892
C2×#179859222
C2×#179859212
C2×#179859112
C2×#179859102
C2×#179858992
C2×#179858942
C2×#179858722
C2×#179858702
C2×C4⋊C4×Dic712
C22×C22⋊Q8×C712
C2×#245271