Finite Group Databasebeta

← C2×#22597285 #32861830

Subgroups — C2×#22597285 #32861830

Order 18176.

1938 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986553C211yesmaximal, characteristic
2#22597285C2116yesmaximal, direct product factor
3C2×#17986130C211yesmaximal, characteristic, complemented
4C2×#17986128C211yesmaximal, characteristic, complemented
5C2×#17986128C211yesmaximal, characteristic, complemented
6C2×#17986127C211yesmaximal, characteristic, complemented
7C2×#17986127C211yesmaximal, characteristic, complemented
8C2×C8×Dic142C211yesmaximal, characteristic, complemented
9C2×#17986123C211yesmaximal, characteristic, complemented
10C2×#17986024C211yesmaximal, characteristic
11C2×#17986024C211yesmaximal, characteristic
12C2×C4⋊C8×D71C211yesmaximal, characteristic
13C2×#17985956C211yesmaximal, characteristic
14C2×#17985953C211yesmaximal, characteristic
15C2×#17985951C211yesmaximal, characteristic
16C2×#446×C71C211yesmaximal, characteristic, complemented
17C22×#11765848C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20C22×C8×D71C2211yescharacteristic
21#17986553C418yes—
22#17986553C2218yes—
23C2×#14556127C411yescharacteristic
24C2×#14556126C411yescharacteristic
25C2×#14556118C411yescharacteristic
26C2×#14556118C411yescharacteristic
27C2×#14556108C411yescharacteristic
28C2×#14556106C411yescharacteristic
29C2×#14556106C411yescharacteristic
30C2×#14556104C411yescharacteristic
31C2×C4×Dic142C2211yescharacteristic
32C2×C4×Dic142C2211yescharacteristic
33C2×C4×Dic142C2211yescharacteristic
34C2×#14556085C2211yescharacteristic
35C2×#14556085C2211yescharacteristic
36C2×C42×D71C2211yescharacteristic
37#17986130C2218yescomplemented
38#17986128C2218yescomplemented
39#17986128C2218yescomplemented
40#17986127C2218yescomplemented
41#17986127C2218yescomplemented
42C8×Dic142C2218yescomplemented
43#17986123C2218yescomplemented
44#17986024C2218yes—
45#17986024C2218yes—
46C2×C4⋊(C71⋊C8)C2211yescharacteristic
47C2×C4⋊(C71⋊C8)C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49C2×Dic71⋊C8C2211yescharacteristic
50C2×Dic71⋊C8C2211yescharacteristic
51C2×Dic71⋊C8C2211yescharacteristic
52C2×Dic71⋊C8C2211yescharacteristic
53C2×Dic71⋊C8C2211yescharacteristic
54C2×Dic71⋊C8C2211yescharacteristic
55C4⋊C8×D71C2218yes—
56#17985956C2218yes—
57#17985953C2218yes—
58#17985951C2218yes—
59C2×#14556039C2211yescharacteristic
60C2×#14556039C2211yescharacteristic
61C2×#14556038C2211yescharacteristic
62C2×#14556038C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64C2×C8×Dic71C2211yescharacteristic
65C2×C8×Dic71C2211yescharacteristic
66C2×C8×Dic71C2211yescharacteristic
67C2×C8×Dic71C2211yescharacteristic
68C2×C4×Q8×C71C2211yescharacteristic
69#446×C71C2218yescomplemented
70C2×C4⋊C8×C71C2211yescharacteristic
71C2×C4⋊C8×C71C2211yescharacteristic
72C2×C4⋊C8×C71C2211yescharacteristic
73C2×#97×C71C2211yescharacteristic
74C2×#97×C71C2211yescharacteristic
75C2×C4×C8×C71C2211yescharacteristic
76C22×Dic142C2×C411yescharacteristic
77C22×Dic142C2×C411yescharacteristic
78C22×Dic142C2×C411yescharacteristic
79C22×C4×D71C2×C411yescharacteristic
80C22×C4×D71C2×C411yescharacteristic
81C22×C4×D71C2311yescharacteristic
82C2×#11765848—24no—
83C2×#11765848Q818yescomplemented
84C2×#11765848C2314yes—
85C2×#11765848C2314yes—
86C22×C71⋊C8C2311yescharacteristic
87C22×C71⋊C8C2311yescharacteristic
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C2×C8×D71—24no—
91C2×C8×D71—24no—
92C2×C8×D71C2314yes—
93C2×C8×D71C2314yes—
94#14556127C2×C418yes—
95#14556126C2×C418yes—
96#14556118C2×C418yes—
97#14556118C2×C418yes—
98#14556108C2×C418yes—
99#14556106C2×C418yes—
100#14556106C2×C418yes—
101#14556104C2×C418yes—
102C4×Dic142C2×C414yes—
103C4×Dic142C2×C414yes—
104C4×Dic142C2×C414yes—
105C4×Dic142C2314yes—
106C4×Dic142C2314yes—
107C4×Dic142C2314yes—
108#14556085C2×C414yes—
109#14556085C2×C414yes—
110#14556085C2314yes—
111#14556085C2314yes—
112C2×C4⋊Dic71C2×C411yescharacteristic
113C2×C4⋊Dic71C2×C411yescharacteristic
114C2×C4⋊Dic71C2×C411yescharacteristic
115C2×Dic71⋊C4C2×C411yescharacteristic
116C2×Dic71⋊C4C2×C411yescharacteristic
117C2×Dic71⋊C4C2×C411yescharacteristic
118C2×Dic71⋊C4C2×C411yescharacteristic
119C2×Dic71⋊C4C2×C411yescharacteristic
120C2×Dic71⋊C4C2×C411yescharacteristic
121C2×Dic71⋊C4C2×C411yescharacteristic
122C2×Dic71⋊C4C2×C411yescharacteristic
123C2×Dic71⋊C4C2×C411yescharacteristic
124C2×Dic71⋊C4C2×C411yescharacteristic
125C2×(C2×D71)⋊C4C2×C411yescharacteristic
126C2×(C2×D71)⋊C4C2×C411yescharacteristic
127C2×(C2×D71)⋊C4C2×C411yescharacteristic
128C2×(C2×D71)⋊C4C2×C411yescharacteristic
129C2×C4×Dic71C2×C411yescharacteristic
130C2×C4×Dic71C2×C411yescharacteristic
131C2×C4×Dic71C2311yescharacteristic
132C2×C4×Dic71C2311yescharacteristic
133C2×C4×Dic71C2311yescharacteristic
134C42×D71C2×C414yes—
135C42×D71C2314yes—
136C4⋊(C71⋊C8)C2314yes—
137C4⋊(C71⋊C8)C2314yes—
138C4⋊(C71⋊C8)C2314yes—
139Dic71⋊C8C2314yes—
140Dic71⋊C8C2314yes—
141Dic71⋊C8C2314yes—
142Dic71⋊C8C2314yes—
143Dic71⋊C8C2314yes—
144Dic71⋊C8C2314yes—
145#14556039C2314yes—
146#14556039C2314yes—
147#14556038C2314yes—
148#14556038C2314yes—
149C4×C71⋊C8C2314yes—
150C8×Dic71C2314yes—
151C8×Dic71C2314yes—
152C8×Dic71C2314yes—
153C8×Dic71C2314yes—
154C22×Q8×C71C2×C411yescharacteristic
155C22×C8×C71C2311yescharacteristic
156C22×C8×C71C2311yescharacteristic
157C22×C8×C71C2311yescharacteristic
158C22×C8×C71C2311yescharacteristic
159C4×Q8×C71C2×C414yes—
160C4×Q8×C71C2314yes—
161C2×C4⋊C4×C71C2×C411yescharacteristic
162C2×C4⋊C4×C71C2×C411yescharacteristic
163C2×C4⋊C4×C71C2×C411yescharacteristic
164C2×C42×C71C2311yescharacteristic
165C2×C42×C71C2311yescharacteristic
166C2×C42×C71C2311yescharacteristic
167C4⋊C8×C71C2314yes—
168C4⋊C8×C71C2314yes—
169C4⋊C8×C71C2314yes—
170#97×C71C2314yes—
171#97×C71C2314yes—
172C4×C8×C71C2314yes—
173C23×D71C22×C411yescharacteristic
174C2×Dic142—24no—
175C2×Dic142—24no—
176C2×Dic142—42no—
177C2×Dic142C22×C414yes—
178C2×Dic142C22×C414yes—
179C2×Dic142C22×C414yes—
180C22×Dic71C22×C411yescharacteristic
181C22×Dic71C22×C411yescharacteristic
182C22×Dic71C22×C411yescharacteristic
183C22×Dic71C22×C411yescharacteristic
184C22×Dic71C22×C411yescharacteristic
185C22×Dic71C22×C411yescharacteristic
186C22×Dic71C22×C411yescharacteristic
187C2×C4×D71—24no—
188C2×C4×D71—42no—
189C2×C4×D71C22×C414yes—
190C2×C4×D71C22×C414yes—
191C2×C4×D71C22×C412yes—
192C2×C4×D71C2×Q814yes—
193C2×C4×D71#4114yes—
194C2×C4×D71C2412yes—
195#11765848—28no—
196#11765848C2×Q8116yescomplemented
197C2×C71⋊C8—22no—
198C2×C71⋊C8—22no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8C2×Q814yes—
201C2×C71⋊C8C2412yes—
202C2×C71⋊C8C2412yes—
203C2×C71⋊C8C2412yes—
204C2×C71⋊C8C2412yes—
205C8×D71—28no—
206C8×D71—28no—
207C4⋊Dic71C22×C414yes—
208C4⋊Dic71C22×C414yes—
209C4⋊Dic71C22×C414yes—
210Dic71⋊C4C22×C414yes—
211Dic71⋊C4C22×C414yes—
212Dic71⋊C4C22×C414yes—
213Dic71⋊C4C22×C414yes—
214Dic71⋊C4C22×C414yes—
215Dic71⋊C4C22×C414yes—
216Dic71⋊C4C22×C414yes—
217Dic71⋊C4C22×C414yes—
218Dic71⋊C4C22×C414yes—
219Dic71⋊C4C22×C414yes—
220(C2×D71)⋊C4C22×C414yes—
221(C2×D71)⋊C4C22×C414yes—
222(C2×D71)⋊C4C22×C414yes—
223(C2×D71)⋊C4C22×C414yes—
224C4×Dic71C22×C412yes—
225C4×Dic71C22×C414yes—
226C4×Dic71C22×C414yes—
227C4×Dic71C22×C412yes—
228C4×Dic71C22×C412yes—
229C4×Dic71C2412yes—
230C4×Dic71C2412yes—
231C4×Dic71C2412yes—
232C2×Q8×C71—42no—
233C2×Q8×C71C22×C414yes—
234C22×C4×C71C22×C411yescharacteristic
235C22×C4×C71C22×C411yescharacteristic
236C22×C4×C71C22×C411yescharacteristic
237C22×C4×C71C22×C411yescharacteristic
238C22×C4×C71C22×C411yescharacteristic
239C22×C4×C71C22×C411yescharacteristic
240C22×C4×C71C2411yescharacteristic
241C2×C8×C71—22no—
242C2×C8×C71—22no—
243C2×C8×C71—22no—
244C2×C8×C71C2×Q814yes—
245C2×C8×C71C2412yes—
246C2×C8×C71C2412yes—
247C2×C8×C71C2412yes—
248C2×C8×C71C2412yes—
249C4⋊C4×C71C22×C414yes—
250C4⋊C4×C71C22×C414yes—
251C4⋊C4×C71C22×C414yes—
252C42×C71C22×C412yes—
253C42×C71C22×C412yes—
254C42×C71C22×C412yes—
255C42×C71C2412yes—
256C42×C71C2412yes—
257C42×C71C2412yes—
258C23×C71C23×C411yescharacteristic
259C22×D71—22no—
260C22×D71—22no—
261C22×D71C4×Q814yes—
262C22×D71C23×C412yes—
263Q8×C71—44no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71C23×C412yes—
271C2×C4×C71C23×C412yes—
272C2×C4×C71C23×C412yes—
273C2×C4×C71C23×C412yes—
274C2×C4×C71C23×C412yes—
275C2×C4×C71C23×C412yes—
276C2×C4×C71C23×C411yescharacteristic
277C2×C4×C71C22×Q812yes—
278C2×C4×C71C2×#4112yes—
279C2×C4×C71C2511yescharacteristic
280C2×Dic71—22no—
281C2×Dic71—22no—
282C2×Dic71—22no—
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71C4×Q814yes—
286C2×Dic71#13114yes—
287C2×Dic71C23×C412yes—
288C2×Dic71C23×C412yes—
289C2×Dic71C23×C412yes—
290C2×Dic71C23×C412yes—
291C2×Dic71C23×C412yes—
292C2×Dic71C23×C412yes—
293C2×Dic71C23×C412yes—
294C4×D71—28no—
295C4×D71—44no—
296C4×D71C4×Q818yes—
297C4×D71C22×Q814yes—
298C4×D71C2×#4114yes—
299Dic142—28no—
300Dic142—28no—
301Dic142—44no—
302C8×C71—22no—
303C8×C71—22no—
304C8×C71—22no—
305C8×C71C22×Q814yes—
306C71⋊C8—22no—
307C71⋊C8—22no—
308C71⋊C8—22no—
309C71⋊C8C22×Q814yes—
310C22×C71C2×C4×Q812yes—
311C22×C71C2×#13112yes—
312C22×C71#56812yes—
313C22×C71C24×C411yescharacteristic
314C2×D71—28no—
315C2×D71—22no—
316C2×D71—22no—
317C2×D71C2×C4×Q814yes—
318C4×C71—22no—
319C4×C71—22no—
320C4×C71—22no—
321C4×C71—22no—
322C4×C71—22no—
323C4×C71—22no—
324C4×C71C2×C4×Q812yes—
325C4×C71C23×Q811yescharacteristic
326C4×C71C22×#4111yescharacteristic
327Dic71—22no—
328Dic71—22no—
329Dic71—22no—
330Dic71—22no—
331Dic71—22no—
332Dic71C2×C4×Q814yes—
333Dic71C2×#13114yes—
334C2×#2962—711nomaximal, Sylow
335C2×C71#296214yescomplemented
336C2×C71C22×C4×Q811yescharacteristic
337C2×C71C22×#13111yescharacteristic
338C2×C71C2×#56811yescharacteristic
339D71—24no—
340C2×#533—711no—
341#2962—7116no—
342C2×#446—711no—
343C2×#446—711no—
344C2×#446—711no—
345C2×#446—711no—
346C2×#446—711no—
347C2×#446D7111yescharacteristic, complemented
348C2×C8×Q8—711no—
349C2×C8×Q8—711no—
350C2×#424—711no—
351C2×#424—711no—
352C22×C4⋊C8—711no—
353C2×#405—711no—
354C2×#405—711no—
355C2×C4×M16—711no—
356C71C2×#296211yescharacteristic, complemented, Sylow
357C22×M16—711no—
358C22×M16—711no—
359C23×C8—711no—
360C23×C8—711no—
361#533—718no—
362#533—718no—
363C2×C4⋊Q8—711no—
364C2×C4⋊Q8—711no—
365C2×#125—711no—
366C2×#125—711no—
367C2×C22⋊Q8—711no—
368C2×C22⋊Q8—711no—
369C2×C22⋊Q8—711no—
370C2×C22⋊Q8—711no—
371C2×C4×Q8—711no—
372C2×C4×Q8—711no—
373C2×C4×Q8—711no—
374C2×C4×Q8C2×D7111yescharacteristic
375C2×#117—711no—
376C2×#117—711no—
377C22×C42—711no—
378#446—718no—
379#446—718no—
380#446—718no—
381#446—718no—
382#446—718no—
383#446C2×D7118yescomplemented
384C8×Q8—718no—
385C8×Q8—718no—
386#424—718no—
387#424—718no—
388C2×C4⋊C8—711no—
389C2×C4⋊C8—711no—
390C2×C4⋊C8—711no—
391C2×C4⋊C8—711no—
392C2×C4⋊C8—711no—
393C2×C4⋊C8—711no—
394C2×C4⋊C8—711no—
395C2×C4⋊C8—711no—
396C2×C4⋊C8—711no—
397C2×C4⋊C8—718no—
398C2×C4⋊C8C2×D7111yescharacteristic
399C2×C4⋊C8C2×D7111yescharacteristic
400C2×C4⋊C8C2×D7111yescharacteristic
401#405—718no—
402#405—718no—
403C4×M16—718no—
404C2×#97—711no—
405C2×#97—711no—
406C2×#97—711no—
407C2×#97—711no—
408C2×#97C2×D7111yescharacteristic
409C2×#97C2×D7111yescharacteristic
410C2×C4×C8—711no—
411C2×C4×C8—711no—
412C2×C4×C8—711no—
413C2×C4×C8—711no—
414C2×C4×C8—711no—
415C2×C4×C8C2×D7111yescharacteristic
416C22×Q8—711no—
417C22×Q8—711no—
418C22×Q8—711no—
419C22×Q8C4×D7111yescharacteristic
420C23×C4—711no—
421C23×C4—711no—
422C23×C4—711no—
423C2×M16—718no—
424C2×M16—714no—
425C2×M16—714no—
426C2×M16—1424no—
427C22×C8—711no—
428C22×C8—711no—
429C22×C8—711no—
430C22×C8—711no—
431C22×C8—714no—
432C22×C8—714no—
433C22×C8—1424no—
434C22×C8—1424no—
435C22×C8C22×D7111yescharacteristic
436C22×C8C22×D7111yescharacteristic
437C22×C8C22×D7111yescharacteristic
438C22×C8C22×D7111yescharacteristic
439C4⋊Q8—718no—
440C4⋊Q8—718no—
441#125—718no—
442#125—718no—
443C22⋊Q8—718no—
444C22⋊Q8—718no—
445C22⋊Q8—718no—
446C22⋊Q8—718no—
447C4×Q8—714no—
448C4×Q8—714no—
449C4×Q8—714no—
450C4×Q8—714no—
451C4×Q8—714no—
452C4×Q8—714no—
453C4×Q8C4×D7114yes—
454C4×Q8C22×D7114yes—
455#117—714no—
456#117—714no—
457#117—714no—
458#117—714no—
459C2×C4⋊C4—711no—
460C2×C4⋊C4—711no—
461C2×C4⋊C4—711no—
462C2×C4⋊C4—711no—
463C2×C4⋊C4—711no—
464C2×C4⋊C4—711no—
465C2×C4⋊C4—711no—
466C2×C4⋊C4—711no—
467C2×C4⋊C4—711no—
468C2×C4⋊C4—711no—
469C2×C4⋊C4—711no—
470C2×C4⋊C4—711no—
471C2×C4⋊C4—711no—
472C2×C4⋊C4C4×D7111yescharacteristic
473C2×C4⋊C4C4×D7111yescharacteristic
474C2×C4⋊C4C4×D7111yescharacteristic
475C2×C22⋊C4—711no—
476C2×C22⋊C4—711no—
477C2×C22⋊C4—711no—
478C2×C22⋊C4—711no—
479C2×C42—711no—
480C2×C42—711no—
481C2×C42—711no—
482C2×C42—711no—
483C2×C42—711no—
484C2×C42—714no—
485C2×C42—714no—
486C2×C42C22×D7111yescharacteristic
487C2×C42C22×D7111yescharacteristic
488C2×C42C22×D7111yescharacteristic
489C4⋊C8—714no—
490C4⋊C8—714no—
491C4⋊C8—714no—
492C4⋊C8—714no—
493C4⋊C8—714no—
494C4⋊C8—714no—
495C4⋊C8—714no—
496C4⋊C8—714no—
497C4⋊C8—714no—
498C4⋊C8C22×D7114yes—
499C4⋊C8C22×D7114yes—
500C4⋊C8C22×D7114yes—
501#97—714no—
502#97—714no—
503#97—714no—
504#97—714no—
505#97C22×D7114yes—
506#97C22×D7114yes—
507C4×C8—714no—
508C4×C8—714no—
509C4×C8—714no—
510C4×C8—714no—
511C4×C8—714no—
512C4×C8C22×D7114yes—
513C24—711no—
514C2×Q8—42no—
515C2×Q8—2842no—
516C2×Q8—714no—
517C2×Q8—714no—
518C2×Q8—714no—
519C2×Q8—1424no—
520C2×Q8—1424no—
521C2×Q8C2×C4×D7114yes—
522C22×C4—2842no—
523C22×C4—714no—
524C22×C4—711no—
525C22×C4—711no—
526C22×C4—712no—
527C22×C4—714no—
528C22×C4—714no—
529C22×C4—712no—
530C22×C4—711no—
531C22×C4—711no—
532C22×C4—711no—
533C22×C4—711no—
534C22×C4—711no—
535C22×C4—714no—
536C22×C4—1424no—
537C22×C4C2×C4×D7111yescharacteristic
538C22×C4C2×C4×D7111yescharacteristic
539C22×C4C2×C4×D7111yescharacteristic
540C22×C4C2×C4×D7111yescharacteristic
541C22×C4C2×C4×D7111yescharacteristic
542C22×C4C2×C4×D7111yescharacteristic
543C22×C4C23×D7111yescharacteristic
544M16—7116no—
545M16—1428no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—714no—
550C2×C8—712no—
551C2×C8—712no—
552C2×C8—712no—
553C2×C8—712no—
554C2×C8—1428no—
555C2×C8—1428no—
556C2×C8—1422no—
557C2×C8—1422no—
558C2×C8—1422no—
559C2×C8Q8×D7114yes—
560C2×C8C23×D7112yes—
561C2×C8C23×D7112yes—
562C2×C8C23×D7112yes—
563C2×C8C23×D7112yes—
564C4⋊C4—714no—
565C4⋊C4—714no—
566C4⋊C4—714no—
567C4⋊C4—714no—
568C4⋊C4—714no—
569C4⋊C4—714no—
570C4⋊C4—714no—
571C4⋊C4—714no—
572C4⋊C4—714no—
573C4⋊C4—714no—
574C4⋊C4—714no—
575C4⋊C4—714no—
576C4⋊C4—714no—
577C4⋊C4C2×C4×D7114yes—
578C4⋊C4C2×C4×D7114yes—
579C4⋊C4C2×C4×D7114yes—
580C22⋊C4—714no—
581C22⋊C4—714no—
582C22⋊C4—714no—
583C22⋊C4—714no—
584C42—712no—
585C42—714no—
586C42—714no—
587C42—712no—
588C42—712no—
589C42—712no—
590C42—712no—
591C42—712no—
592C42C2×C4×D7112yes—
593C42C2×C4×D7112yes—
594C42C2×C4×D7112yes—
595C42C23×D7112yes—
596C42C23×D7112yes—
597C42C23×D7112yes—
598C23—712no—
599C23—714no—
600C23—1422no—
601C23—1422no—
602C23C22×C4×D7111yescharacteristic
603Q8—44no—
604Q8—2844no—
605Q8—1428no—
606Q8—1428no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—2844no—
614C2×C4—712no—
615C2×C4—712no—
616C2×C4—714no—
617C2×C4—714no—
618C2×C4—714no—
619C2×C4—714no—
620C2×C4—718no—
621C2×C4—712no—
622C2×C4—712no—
623C2×C4—712no—
624C2×C4—712no—
625C2×C4—712no—
626C2×C4—1428no—
627C2×C4—1422no—
628C2×C4—1422no—
629C2×C4—1422no—
630C2×C4—1422no—
631C2×C4—1422no—
632C2×C4C22×C4×D7112yes—
633C2×C4C22×C4×D7112yes—
634C2×C4C22×C4×D7112yes—
635C2×C4C22×C4×D7112yes—
636C2×C4C22×C4×D7112yes—
637C2×C4C22×C4×D7112yes—
638C2×C4C22×C4×D7111yescharacteristic
639C2×C4C2×Q8×D7112yes—
640C2×C4#41×D7112yes—
641C2×C4C24×D7111yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—714no—
646C8—1422no—
647C8—1422no—
648C8—1422no—
649C8C2×Q8×D7114yes—
650C22—714no—
651C22—1422no—
652C22—1422no—
653C22—1428no—
654C22C4×Q8×D7112yes—
655C22#131×D7112yes—
656C22#1798676512yes—
657C22C23×C4×D7111yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—714no—
665C4—714no—
666C4—1422no—
667C4—1422no—
668C4—1422no—
669C4—1422no—
670C4—1422no—
671C4C4×Q8×D7112yes—
672C4C22×Q8×D7111yescharacteristic
673C4C2×#41×D7111yescharacteristic
674C2—1424no—
675C2#2259728514yesdirect product factor
676C2C2×C4×Q8×D7111yescharacteristic
677C2C2×#131×D7111yescharacteristic
678C2C2×#1798676511yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutatorC22×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×#446×C71C2
socleC23×C71C23×C4
prime radicalC23×D71C22×C4
cosocleC2×C4×C71C25
hypercenterC2×#446D71
hypocenterC71C2×#2962
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #22597285C2direct (N × H)
3. C2×#17986130C2semidirect
4. C2×#17986128C2semidirect
5. C2×#17986128C2semidirect
6. C2×#17986127C2semidirect
7. C2×#17986127C2semidirect
8. C2×C8×Dic142C2semidirect
9. C2×#17986123C2semidirect
16. C2×#446×C71C2semidirect
37. #17986130C22semidirect
38. #17986128C22semidirect
39. #17986128C22semidirect
40. #17986127C22semidirect
41. #17986127C22semidirect
42. C8×Dic142C22semidirect
43. #17986123C22semidirect
69. #446×C71C22semidirect
83. C2×#11765848Q8semidirect
196. #11765848C2×Q8semidirect
335. C2×C71#2962semidirect
347. C2×#446D71semidirect
356. C71C2×#2962semidirect
383. #446C2×D71semidirect
675. C2#22597285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865532
#225972852
C2×#179861302
C2×#179861282
C2×#179861272
C2×C8×Dic1422
C2×#179861232
C2×#179860242
C2×C4⋊C8×D712
C2×#179859562
C2×#179859532
C2×#179859512
C2×#446×C712
C2×#296271