Finite Group Databasebeta

← C2×#22591019 #32156191

Subgroups — C2×#22591019 #32156191

Order 18176.

3198 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556105C211yesmaximal, characteristic
2C22×C4×Dic142C211yesmaximal, characteristic, complemented
3C22×#14556084C211yesmaximal, characteristic
4#22591019C2116yesmaximal, direct product factor
5C2×#17985903C211yesmaximal, characteristic, complemented
6C2×#17985896C211yesmaximal, characteristic, complemented
7C2×#17985895C211yesmaximal, characteristic, complemented
8C2×#17985894C211yesmaximal, characteristic, complemented
9C2×#17985892C211yesmaximal, characteristic
10C2×#17985887C211yesmaximal, characteristic
11C2×#17985887C211yesmaximal, characteristic
12C2×#17985884C211yesmaximal, characteristic, complemented
13C2×#17985883C211yesmaximal, characteristic, complemented
14C2×#17985857C211yesmaximal, characteristic
15C2×#17985850C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic
17C23×Dic142C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C2×#14556105C4116yescomplemented
20C2×#14556105C2218yes—
21C2×C4×Dic142—28no—
22C2×C4×Dic142C2218yescomplemented
23C2×#14556084—28no—
24C2×#14556084C2218yes—
25C22×C4⋊Dic71C2211yescharacteristic
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×Dic71⋊C4C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×C22⋊Dic71C2211yescharacteristic
37C22×C22⋊Dic71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39C22×C4×Dic71C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43#17985903C2218yescomplemented
44#17985896C2218yescomplemented
45#17985895C2218yescomplemented
46#17985894C2218yescomplemented
47#17985892C2218yes—
48#17985887C2218yes—
49#17985887C2218yes—
50#17985884C2218yescomplemented
51#17985883C2218yescomplemented
52#17985857C2218yes—
53#17985850C2218yescomplemented
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C42×C71C2211yescharacteristic
67#388×C71C2218yes—
68C2×#95×C71C2211yescharacteristic
69C2×#95×C71C2211yescharacteristic
70C22×Dic142—24no—
71C22×Dic142—24no—
72C22×Dic142C2×C418yes—
73C22×Dic142C2314yes—
74C23×Dic71—24no—
75C23×Dic71—24no—
76C23×Dic71C2×C418yes—
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2314yes—
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86#14556105C2×C4164yescomplemented
87C4×Dic142—232no—
88#14556084—232no—
89C2×C4⋊Dic71—24no—
90C2×C4⋊Dic71C2×C418yes—
91C2×C4⋊Dic71C2314yes—
92C2×C4⋊Dic71C2314yes—
93C2×Dic71⋊C4—24no—
94C2×Dic71⋊C4—24no—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—42no—
99C2×Dic71⋊C4C2×C418yes—
100C2×Dic71⋊C4C2×C418yes—
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×C22⋊Dic71—24no—
110C2×C22⋊Dic71—42no—
111C2×C22⋊Dic71C2×C418yes—
112C2×C22⋊Dic71C2314yes—
113C2×C22⋊Dic71C2314yes—
114C2×C22⋊Dic71C2314yes—
115C2×C4×Dic71—24no—
116C2×C4×Dic71—24no—
117C2×C4×Dic71—42no—
118C2×C4×Dic71—42no—
119C2×C4×Dic71D418yes—
120C2×C4×Dic71C2314yes—
121C2×C4×Dic71C2314yes—
122C2×C4×Dic71C2314yes—
123C2×C4×Dic71C2314yes—
124C2×C4×Dic71C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C25×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C2×C4⋊C4×C71—42no—
141C2×C4⋊C4×C71C2314yes—
142C2×C22⋊C4×C71—24no—
143C2×C22⋊C4×C71—42no—
144C2×C22⋊C4×C71C2×C418yes—
145C2×C22⋊C4×C71C2314yes—
146C2×C22⋊C4×C71C2314yes—
147C2×C22⋊C4×C71C2314yes—
148C2×C42×C71—24no—
149C2×C42×C71C2314yes—
150#95×C71C2314yes—
151#95×C71C2314yes—
152C2×Dic142—232no—
153C2×Dic142—28no—
154C2×Dic142—28no—
155C2×Dic142C22×C4116yes—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—232no—
165C22×Dic71—28no—
166C22×Dic71—28no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71C22×C414yes—
177C22×Dic71C22×C4116yes—
178C22×Dic71C22×C414yes—
179C22×Dic71C22×C414yes—
180C22×Dic71C22×C414yes—
181C22×Dic71C2×D414yes—
182C22×Dic71C2×D414yes—
183C22×Dic71#4114yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C4⋊Dic71—28no—
193C4⋊Dic71C22×C4116yes—
194Dic71⋊C4—28no—
195Dic71⋊C4—28no—
196Dic71⋊C4—28no—
197Dic71⋊C4—28no—
198Dic71⋊C4—28no—
199Dic71⋊C4—44no—
200Dic71⋊C4C22×C4116yes—
201Dic71⋊C4C22×C4116yes—
202C22⋊Dic71—28no—
203C22⋊Dic71—44no—
204C22⋊Dic71C22×C4116yes—
205C4×Dic71—28no—
206C4×Dic71—28no—
207C4×Dic71—44no—
208C4×Dic71—44no—
209C4×Dic71C2×D4116yes—
210C24×C71—22no—
211C24×C71—22no—
212C24×C71—22no—
213C24×C71—22no—
214C24×C71—22no—
215C24×C71—22no—
216C24×C71C22×C414yes—
217C24×C71C2412yes—
218C24×C71C2411yescharacteristic
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71C22×C414yes—
235C22×C4×C71C22×C414yes—
236C22×C4×C71C2×D414yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2412yes—
241C22×C4×C71C2412yes—
242C22×C4×C71C2412yes—
243C4⋊C4×C71—44no—
244C22⋊C4×C71—28no—
245C22⋊C4×C71—44no—
246C22⋊C4×C71C22×C4116yes—
247C42×C71—28no—
248C23×C71—28no—
249C23×C71—28no—
250C23×C71—28no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71—22no—
254C23×C71—22no—
255C23×C71—22no—
256C23×C71—22no—
257C23×C71—44no—
258C23×C71—44no—
259C23×C71—44no—
260C23×C71—44no—
261C23×C71C23×C414yes—
262C23×C71C23×C412yes—
263C23×C71C22×D412yes—
264C23×C71C2×#4112yes—
265C23×C71H(5,𝔽2)12yes—
266C23×C712−1+412yes—
267C23×C712−1+412yes—
268C23×C712−1+412yes—
269C23×C71C2511yescharacteristic
270C2×C4×C71—28no—
271C2×C4×C71—28no—
272C2×C4×C71—28no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—44no—
289C2×C4×C71—44no—
290C2×C4×C71—44no—
291C2×C4×C71C23×C414yes—
292C2×C4×C71C23×C414yes—
293C2×C4×C71C22×D414yes—
294C2×Dic71—28no—
295C2×Dic71—28no—
296C2×Dic71—28no—
297C2×Dic71—28no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—232no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—44no—
317C2×Dic71—44no—
318C2×Dic71—44no—
319C2×Dic71C4×D4116yes—
320C2×Dic71C23×C414yes—
321C2×Dic71C23×C414yes—
322C2×Dic71C23×C414yes—
323C2×Dic71C23×C414yes—
324C2×Dic71C22×D414yes—
325C2×Dic71C22×D414yes—
326C2×Dic71C2×#4114yes—
327Dic142—232no—
328C22×C71—24no—
329C22×C71—24no—
330C22×C71—24no—
331C22×C71—416no—
332C22×C71—42no—
333C22×C71—42no—
334C22×C71—42no—
335C22×C71—42no—
336C22×C71C2×C4×D414yes—
337C22×C71#51914yes—
338C22×C71#52014yes—
339C22×C71#53614yes—
340C22×C71#53714yes—
341C22×C71#54114yes—
342C22×C71#54214yes—
343C22×C71C24×C411yescharacteristic
344C22×C71C23×D411yescharacteristic
345C22×C71C22×#4111yescharacteristic
346C22×C71C2×H(5,𝔽2)11yescharacteristic
347C22×C71C2×2−1+411yescharacteristic
348C22×C71C2×2−1+411yescharacteristic
349C22×C71C2×2−1+411yescharacteristic
350C4×C71—24no—
351C4×C71—24no—
352C4×C71—24no—
353C4×C71—42no—
354C4×C71—42no—
355C4×C71—42no—
356Dic71—24no—
357Dic71—24no—
358Dic71—24no—
359Dic71—24no—
360Dic71—42no—
361Dic71—42no—
362Dic71—42no—
363Dic71C2×C4×D418yes—
364C2×#2323—711nomaximal, Sylow
365C2×C71—44no—
366C2×C71#232318yescomplemented
367C2×C71C22×C4×D411yescharacteristic
368C2×C71C2×#51911yescharacteristic
369C2×C71C2×#52011yescharacteristic
370C2×C71C2×#53611yescharacteristic
371C2×C71C2×#53711yescharacteristic
372C2×C71C2×#54111yescharacteristic
373C2×C71C2×#54211yescharacteristic
374C22×C22⋊Q8—711no—
375C22×C4×Q8—711no—
376C22×#117—711no—
377#2323—7116no—
378C2×#391—711no—
379C2×#389—711no—
380C2×#389—711no—
381C2×#389—711no—
382C2×#388—711no—
383C2×#388—711no—
384C2×#388—711no—
385C2×#388D7111yescharacteristic
386C2×#387—711no—
387C2×#387—711no—
388C2×#380—711no—
389C2×C4×C4⋊C4—711no—
390C71C2×#232311yescharacteristic, complemented, Sylow
391C23×Q8—711no—
392C24×C4—711no—
393C2×C22⋊Q8—7116no—
394C2×C22⋊Q8—718no—
395C2×C4×Q8—718no—
396C2×C4×Q8—1428no—
397C2×#117—718no—
398C2×#117—1428no—
399C22×C4⋊C4—711no—
400C22×C4⋊C4—711no—
401C22×C4⋊C4—711no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4—711no—
405C22×C4⋊C4—711no—
406C22×C4⋊C4—711no—
407C22×C4⋊C4—711no—
408C22×C4⋊C4—711no—
409C22×C4⋊C4C2×D7111yescharacteristic
410C22×C22⋊C4—711no—
411C22×C22⋊C4—711no—
412C22×C22⋊C4—711no—
413C22×C22⋊C4C2×D7111yescharacteristic
414C22×C22⋊C4C2×D7111yescharacteristic
415C22×C22⋊C4C2×D7111yescharacteristic
416C22×C42—711no—
417C22×C42—711no—
418C22×C42—711no—
419C22×C42—711no—
420C22×C42—711no—
421C22×C42C2×D7111yescharacteristic
422#391—718no—
423#389—718no—
424#389—718no—
425#389—718no—
426#388—718no—
427#388—718no—
428#388—718no—
429#388C2×D7118yes—
430#387—718no—
431#387—718no—
432#380—718no—
433C4×C4⋊C4—718no—
434C2×#95—711no—
435C2×#95—711no—
436C2×#95—711no—
437C2×#95—711no—
438C2×#95—711no—
439C2×#95—711no—
440C2×#95—711no—
441C2×#95—711no—
442C2×#95C2×D7111yescharacteristic
443C2×#95C2×D7111yescharacteristic
444C25C22×D7111yescharacteristic
445C22×Q8—718no—
446C22×Q8—714no—
447C22×Q8—1424no—
448C22×Q8—1424no—
449C23×C4—711no—
450C23×C4—718no—
451C23×C4—714no—
452C23×C4—711no—
453C23×C4—711no—
454C23×C4—711no—
455C23×C4—711no—
456C23×C4—711no—
457C23×C4—711no—
458C23×C4—711no—
459C23×C4—1424no—
460C23×C4—1424no—
461C23×C4C22×D7111yescharacteristic
462C23×C4C22×D7111yescharacteristic
463C23×C4C22×D7111yescharacteristic
464C23×C4C22×D7111yescharacteristic
465C23×C4C22×D7111yescharacteristic
466C23×C4C22×D7111yescharacteristic
467C22⋊Q8—7164no—
468C4×Q8—14232no—
469#117—14232no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—2842no—
472C2×C4⋊C4—714no—
473C2×C4⋊C4—718no—
474C2×C4⋊C4—718no—
475C2×C4⋊C4—718no—
476C2×C4⋊C4—714no—
477C2×C4⋊C4—714no—
478C2×C4⋊C4—714no—
479C2×C4⋊C4—714no—
480C2×C4⋊C4—714no—
481C2×C4⋊C4—714no—
482C2×C4⋊C4—714no—
483C2×C4⋊C4—714no—
484C2×C4⋊C4—714no—
485C2×C4⋊C4—1424no—
486C2×C4⋊C4—1424no—
487C2×C4⋊C4—1424no—
488C2×C4⋊C4—1424no—
489C2×C4⋊C4—1424no—
490C2×C4⋊C4—1424no—
491C2×C4⋊C4C22×D7114yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—2842no—
495C2×C22⋊C4—714no—
496C2×C22⋊C4—718no—
497C2×C22⋊C4—714no—
498C2×C22⋊C4—714no—
499C2×C22⋊C4—1424no—
500C2×C22⋊C4C4×D7118yes—
501C2×C22⋊C4C22×D7114yes—
502C2×C22⋊C4C22×D7114yes—
503C2×C22⋊C4C22×D7114yes—
504C2×C42—24no—
505C2×C42—2842no—
506C2×C42—2842no—
507C2×C42—714no—
508C2×C42—714no—
509C2×C42—718no—
510C2×C42—714no—
511C2×C42—714no—
512C2×C42—714no—
513C2×C42—1424no—
514C2×C42—1424no—
515C2×C42C22×D7114yes—
516#95—714no—
517#95—714no—
518#95—714no—
519#95—714no—
520#95—714no—
521#95—714no—
522#95—714no—
523#95—714no—
524#95C22×D7114yes—
525#95C22×D7114yes—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24C2×C4×D7114yes—
533C24C23×D7112yes—
534C24C23×D7111yescharacteristic
535C2×Q8—7116no—
536C2×Q8—1428no—
537C2×Q8—1428no—
538C2×Q8—14232no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—714no—
555C22×C4—714no—
556C22×C4—714no—
557C22×C4—712no—
558C22×C4—714no—
559C22×C4—714no—
560C22×C4—714no—
561C22×C4—7116no—
562C22×C4—714no—
563C22×C4—712no—
564C22×C4—712no—
565C22×C4—712no—
566C22×C4—712no—
567C22×C4—712no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—1422no—
571C22×C4—1422no—
572C22×C4—1422no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1428no—
580C22×C4—1428no—
581C22×C4—14232no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1422no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4—1422no—
589C22×C4—1422no—
590C22×C4C2×C4×D7114yes—
591C22×C4C2×C4×D7114yes—
592C22×C4D4×D7114yes—
593C22×C4C23×D7112yes—
594C22×C4C23×D7112yes—
595C22×C4C23×D7112yes—
596C22×C4C23×D7112yes—
597C22×C4C23×D7112yes—
598C22×C4C23×D7112yes—
599C4⋊C4—44no—
600C4⋊C4—2844no—
601C4⋊C4—7116no—
602C4⋊C4—7116no—
603C4⋊C4—7116no—
604C4⋊C4—1428no—
605C4⋊C4—1428no—
606C4⋊C4—1428no—
607C4⋊C4—1428no—
608C4⋊C4—1428no—
609C4⋊C4—1428no—
610C22⋊C4—28no—
611C22⋊C4—44no—
612C22⋊C4—2844no—
613C22⋊C4—7116no—
614C22⋊C4—1428no—
615C22⋊C4C2×C4×D71116yes—
616C42—28no—
617C42—2844no—
618C42—2844no—
619C42—7116no—
620C42—1428no—
621C42—1428no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23C22×C4×D7114yes—
636C23C22×C4×D7112yes—
637C23C2×D4×D7112yes—
638C23#41×D7112yes—
639C23#1455617312yes—
640C23#1455617512yes—
641C23#1455617512yes—
642C23#1455617512yes—
643C23C24×D7111yescharacteristic
644Q8—14232no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—28no—
653C2×C4—28no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—2844no—
667C2×C4—2844no—
668C2×C4—2844no—
669C2×C4—714no—
670C2×C4—714no—
671C2×C4—714no—
672C2×C4—7116no—
673C2×C4—714no—
674C2×C4—714no—
675C2×C4—714no—
676C2×C4—714no—
677C2×C4—1422no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4—14232no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1428no—
696C2×C4—1428no—
697C2×C4—1428no—
698C2×C4—1428no—
699C2×C4C22×C4×D7114yes—
700C2×C4C22×C4×D7114yes—
701C2×C4C2×D4×D7114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—416no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22C4×D4×D7114yes—
711C22#1798647614yes—
712C22#1798647814yes—
713C22#1798657114yes—
714C22#1798657814yes—
715C22#1798660614yes—
716C22#1798661314yes—
717C22C23×C4×D7111yescharacteristic
718C22C22×D4×D7111yescharacteristic
719C22C2×#41×D7111yescharacteristic
720C22C2×#1455617311yescharacteristic
721C22C2×#1455617511yescharacteristic
722C22C2×#1455617511yescharacteristic
723C22C2×#1455617511yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—2842no—
731C4—2842no—
732C4—2842no—
733C4—718no—
734C4—1424no—
735C4—1424no—
736C4—1424no—
737C4—1424no—
738C2—44no—
739C2#2259101918yesdirect product factor
740C2C2×C4×D4×D7111yescharacteristic
741C2C2×#1798647611yescharacteristic
742C2C2×#1798647811yescharacteristic
743C2C2×#1798657111yescharacteristic
744C2C2×#1798657811yescharacteristic
745C2C2×#1798660611yescharacteristic
746C2C2×#1798661311yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC25×C71C23
cosocleC23×C71C25
hypercenterC2×#388D71
hypocenterC71C2×#2323
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic142C2semidirect
4. #22591019C2direct (N × H)
5. C2×#17985903C2semidirect
6. C2×#17985896C2semidirect
7. C2×#17985895C2semidirect
8. C2×#17985894C2semidirect
12. C2×#17985884C2semidirect
13. C2×#17985883C2semidirect
15. C2×#17985850C2semidirect
19. C2×#14556105C4semidirect
22. C2×C4×Dic142C22semidirect
43. #17985903C22semidirect
44. #17985896C22semidirect
45. #17985895C22semidirect
46. #17985894C22semidirect
50. #17985884C22semidirect
51. #17985883C22semidirect
53. #17985850C22semidirect
86. #14556105C2×C4semidirect
366. C2×C71#2323semidirect
390. C71C2×#2323semidirect
739. C2#22591019direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561052
C22×C4×Dic1422
C22×#145560842
#225910192
C2×#179859032
C2×#179858962
C2×#179858952
C2×#179858942
C2×#179858922
C2×#179858872
C2×#179858842
C2×#179858832
C2×#179858572
C2×#179858502
C2×#388×C712
C2×#232371