Finite Group Databasebeta

← C2×#19143698 #25961563

Subgroups — C2×#19143698 #25961563

Order 11008.

1706 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2#19143698C2116yesmaximal, direct product factor
3C2×#14583030C211yesmaximal, characteristic, complemented
4C2×#14583029C211yesmaximal, characteristic, complemented
5C2×#14583028C211yesmaximal, characteristic, complemented
6C2×#14583028C211yesmaximal, characteristic, complemented
7C2×#14583027C211yesmaximal, characteristic, complemented
8C2×#14583027C211yesmaximal, characteristic, complemented
9C2×#14583026C211yesmaximal, characteristic, complemented
10C2×#14582961C211yesmaximal, characteristic
11C2×#14582959C211yesmaximal, characteristic
12C2×#14582959C211yesmaximal, characteristic
13C2×#14582958C211yesmaximal, characteristic
14C2×#14582955C211yesmaximal, characteristic
15C2×#14582954C211yesmaximal, characteristic
16C2×C43×#446C211yesmaximal, characteristic, complemented
17#14583453C418yes—
18#14583453C2218yes—
19C2×#13063324C411yescharacteristic
20C2×#13063323C411yescharacteristic
21C2×#13063315C411yescharacteristic
22C2×#13063315C411yescharacteristic
23C2×#13063305C411yescharacteristic
24C2×#13063303C411yescharacteristic
25C2×#13063303C411yescharacteristic
26C2×#13063301C411yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×Dic86C2211yescharacteristic
30C2×#13063282C2211yescharacteristic
31C2×#13063282C2211yescharacteristic
32C2×C42×D43C2211yescharacteristic
33#14583030C2218yescomplemented
34#14583029C2218yescomplemented
35#14583028C2218yescomplemented
36#14583028C2218yescomplemented
37#14583027C2218yescomplemented
38#14583027C2218yescomplemented
39#14583026C2218yescomplemented
40#14582961C2218yes—
41#14582959C2218yes—
42#14582959C2218yes—
43#14582958C2218yes—
44#14582955C2218yes—
45#14582954C2218yes—
46C2×C4⋊(C43⋊C8)C2211yescharacteristic
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48C2×C4⋊(C43⋊C8)C2211yescharacteristic
49C2×Dic43⋊C8C2211yescharacteristic
50C2×Dic43⋊C8C2211yescharacteristic
51C2×Dic43⋊C8C2211yescharacteristic
52C2×Dic43⋊C8C2211yescharacteristic
53C2×Dic43⋊C8C2211yescharacteristic
54C2×Dic43⋊C8C2211yescharacteristic
55C2×(C2×D43)⋊C8C2211yescharacteristic
56C2×(C2×D43)⋊C8C2211yescharacteristic
57C2×(C2×D43)⋊C8C2211yescharacteristic
58C2×(C2×D43)⋊C8C2211yescharacteristic
59C2×#13063236C2211yescharacteristic
60C2×#13063236C2211yescharacteristic
61C2×#13063235C2211yescharacteristic
62C2×#13063235C2211yescharacteristic
63C2×#13063235C2211yescharacteristic
64C2×#13063235C2211yescharacteristic
65C2×C4×C43⋊C8C2211yescharacteristic
66C2×C8×Dic43C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C2×C4×Q8×C43C2211yescharacteristic
69C43×#446C2218yescomplemented
70C2×C4⋊C8×C43C2211yescharacteristic
71C2×C4⋊C8×C43C2211yescharacteristic
72C2×C4⋊C8×C43C2211yescharacteristic
73C2×#97×C43C2211yescharacteristic
74C2×#97×C43C2211yescharacteristic
75C2×C4×C8×C43C2211yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×Dic86C2×C411yescharacteristic
78C22×Dic86C2×C411yescharacteristic
79C22×C4×D43C2×C411yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86#13063324C2×C418yes—
87#13063323C2×C418yes—
88#13063315C2×C418yes—
89#13063315C2×C418yes—
90#13063305C2×C418yes—
91#13063303C2×C418yes—
92#13063303C2×C418yes—
93#13063301C2×C418yes—
94C4×Dic86C2×C414yes—
95C4×Dic86C2×C414yes—
96C4×Dic86C2×C414yes—
97C4×Dic86C2314yes—
98C4×Dic86C2314yes—
99C4×Dic86C2314yes—
100#13063282C2×C414yes—
101#13063282C2×C414yes—
102#13063282C2314yes—
103#13063282C2314yes—
104C2×C4⋊Dic43C2×C411yescharacteristic
105C2×C4⋊Dic43C2×C411yescharacteristic
106C2×C4⋊Dic43C2×C411yescharacteristic
107C2×Dic43⋊C4C2×C411yescharacteristic
108C2×Dic43⋊C4C2×C411yescharacteristic
109C2×Dic43⋊C4C2×C411yescharacteristic
110C2×Dic43⋊C4C2×C411yescharacteristic
111C2×Dic43⋊C4C2×C411yescharacteristic
112C2×Dic43⋊C4C2×C411yescharacteristic
113C2×Dic43⋊C4C2×C411yescharacteristic
114C2×Dic43⋊C4C2×C411yescharacteristic
115C2×Dic43⋊C4C2×C411yescharacteristic
116C2×Dic43⋊C4C2×C411yescharacteristic
117C2×(C2×D43)⋊C4C2×C411yescharacteristic
118C2×(C2×D43)⋊C4C2×C411yescharacteristic
119C2×(C2×D43)⋊C4C2×C411yescharacteristic
120C2×(C2×D43)⋊C4C2×C411yescharacteristic
121C2×C4×Dic43C2×C411yescharacteristic
122C2×C4×Dic43C2×C411yescharacteristic
123C2×C4×Dic43C2311yescharacteristic
124C2×C4×Dic43C2311yescharacteristic
125C2×C4×Dic43C2311yescharacteristic
126C42×D43C2×C414yes—
127C42×D43C2314yes—
128C4⋊(C43⋊C8)C2314yes—
129C4⋊(C43⋊C8)C2314yes—
130C4⋊(C43⋊C8)C2314yes—
131Dic43⋊C8C2314yes—
132Dic43⋊C8C2314yes—
133Dic43⋊C8C2314yes—
134Dic43⋊C8C2314yes—
135Dic43⋊C8C2314yes—
136Dic43⋊C8C2314yes—
137(C2×D43)⋊C8C2314yes—
138(C2×D43)⋊C8C2314yes—
139(C2×D43)⋊C8C2314yes—
140(C2×D43)⋊C8C2314yes—
141#13063236C2314yes—
142#13063236C2314yes—
143#13063235C2314yes—
144#13063235C2314yes—
145#13063235C2314yes—
146#13063235C2314yes—
147C4×C43⋊C8C2314yes—
148C8×Dic43C2314yes—
149C8×Dic43C2314yes—
150C22×Q8×C43C2×C411yescharacteristic
151C22×C8×C43C2311yescharacteristic
152C22×C8×C43C2311yescharacteristic
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C4×Q8×C43C2×C414yes—
156C4×Q8×C43C2314yes—
157C2×C4⋊C4×C43C2×C411yescharacteristic
158C2×C4⋊C4×C43C2×C411yescharacteristic
159C2×C4⋊C4×C43C2×C411yescharacteristic
160C2×C42×C43C2311yescharacteristic
161C2×C42×C43C2311yescharacteristic
162C2×C42×C43C2311yescharacteristic
163C4⋊C8×C43C2314yes—
164C4⋊C8×C43C2314yes—
165C4⋊C8×C43C2314yes—
166#97×C43C2314yes—
167#97×C43C2314yes—
168C4×C8×C43C2314yes—
169C23×D43C22×C411yescharacteristic
170C2×Q8×C43—42no—
171C2×Q8×C43C22×C414yes—
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C22×C411yescharacteristic
175C22×C4×C43C22×C411yescharacteristic
176C22×C4×C43C22×C411yescharacteristic
177C22×C4×C43C22×C411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C22×Dic43C22×C411yescharacteristic
180C22×Dic43C22×C411yescharacteristic
181C22×Dic43C22×C411yescharacteristic
182C22×Dic43C22×C411yescharacteristic
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43C22×C412yes—
191C2×C4×D43C22×C414yes—
192C2×C4×D43C22×C414yes—
193C2×C4×D43C2412yes—
194C2×Dic86—42no—
195C2×Dic86—42no—
196C2×Dic86—42no—
197C2×Dic86C22×C414yes—
198C2×Dic86C22×C414yes—
199C2×Dic86C22×C414yes—
200C2×C8×C43—22no—
201C2×C8×C43—22no—
202C2×C8×C43—22no—
203C2×C8×C43—22no—
204C2×C8×C43C2412yes—
205C2×C8×C43C2412yes—
206C2×C8×C43C2412yes—
207C2×C8×C43C2412yes—
208C4⋊C4×C43C22×C414yes—
209C4⋊C4×C43C22×C414yes—
210C4⋊C4×C43C22×C414yes—
211C42×C43C22×C412yes—
212C42×C43C22×C412yes—
213C42×C43C22×C412yes—
214C42×C43C2412yes—
215C42×C43C2412yes—
216C42×C43C2412yes—
217(C2×D43)⋊C4C22×C414yes—
218(C2×D43)⋊C4C22×C414yes—
219(C2×D43)⋊C4C22×C414yes—
220(C2×D43)⋊C4C22×C414yes—
221C4⋊Dic43C22×C414yes—
222C4⋊Dic43C22×C414yes—
223C4⋊Dic43C22×C414yes—
224Dic43⋊C4C22×C414yes—
225Dic43⋊C4C22×C414yes—
226Dic43⋊C4C22×C414yes—
227Dic43⋊C4C22×C414yes—
228Dic43⋊C4C22×C414yes—
229Dic43⋊C4C22×C414yes—
230Dic43⋊C4C22×C414yes—
231Dic43⋊C4C22×C414yes—
232Dic43⋊C4C22×C414yes—
233Dic43⋊C4C22×C414yes—
234C4×Dic43C22×C412yes—
235C4×Dic43C22×C414yes—
236C4×Dic43C22×C414yes—
237C4×Dic43C22×C412yes—
238C4×Dic43C22×C412yes—
239C4×Dic43C2412yes—
240C4×Dic43C2412yes—
241C4×Dic43C2412yes—
242C2×C43⋊C8—22no—
243C2×C43⋊C8—22no—
244C2×C43⋊C8—22no—
245C2×C43⋊C8—22no—
246C2×C43⋊C8C2412yes—
247C2×C43⋊C8C2412yes—
248C2×C43⋊C8C2412yes—
249C2×C43⋊C8C2412yes—
250C23×C43C23×C411yescharacteristic
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43C23×C412yes—
255Q8×C43—44no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43C23×C412yes—
263C2×C4×C43C23×C412yes—
264C2×C4×C43C23×C412yes—
265C2×C4×C43C23×C412yes—
266C2×C4×C43C23×C412yes—
267C2×C4×C43C23×C412yes—
268C2×C4×C43C23×C411yescharacteristic
269C2×C4×C432−1+412yes—
270C2×C4×C432−1+412yes—
271C2×C4×C43C2511yescharacteristic
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43C23×C412yes—
280C2×Dic43C23×C412yes—
281C2×Dic43C23×C412yes—
282C2×Dic43C23×C412yes—
283C2×Dic43C23×C412yes—
284C2×Dic43C23×C412yes—
285C2×Dic43C23×C412yes—
286C4×D43—24no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—44no—
290C4×D43—44no—
291Dic86—44no—
292Dic86—44no—
293Dic86—44no—
294C8×C43—22no—
295C8×C43—22no—
296C8×C43—22no—
297C8×C43—22no—
298C43⋊C8—22no—
299C43⋊C8—22no—
300C43⋊C8—22no—
301C43⋊C8—22no—
302C2×#2987—431nomaximal, Sylow
303C22×C43#51912yes—
304C22×C43#56812yes—
305C22×C43#56812yes—
306C22×C43C24×C411yescharacteristic
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—44no—
311C4×C43—22no—
312C4×C43—22no—
313C4×C43—22no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43#51912yes—
318C4×C43C2×2−1+411yescharacteristic
319C4×C43C2×2−1+411yescharacteristic
320Dic43—22no—
321Dic43—22no—
322Dic43—22no—
323Dic43—22no—
324Dic43—22no—
325Dic43—22no—
326Dic43—22no—
327C2×#533—431no—
328#2987—4316no—
329C2×#446—431no—
330C2×#446—431no—
331C2×#446—431no—
332C2×#446—431no—
333C2×#446—431no—
334C2×#446—431no—
335C2×#446—431no—
336C2×#446D4311yescharacteristic, complemented
337C2×#433—431no—
338C2×#433—431no—
339C2×#433—431no—
340C2×#433—431no—
341C2×#432—431no—
342C2×#432—431no—
343C2×C43#298714yescomplemented
344C2×C43C2×#51911yescharacteristic
345C2×C43C2×#56811yescharacteristic
346C2×C43C2×#56811yescharacteristic
347D43—42no—
348#533—438no—
349#533—438no—
350C2×C4⋊Q8—431no—
351C2×C4⋊Q8—431no—
352C2×#125—431no—
353C2×#125—431no—
354C2×C22⋊Q8—431no—
355C2×C22⋊Q8—431no—
356C2×C22⋊Q8—431no—
357C2×C22⋊Q8—431no—
358C2×C4×Q8—431no—
359C2×C4×Q8—431no—
360C2×C4×Q8—431no—
361C2×C4×Q8C2×D4311yescharacteristic
362C2×#117—431no—
363C2×#117—431no—
364C22×C42—431no—
365#446—438no—
366#446—438no—
367#446—438no—
368#446—438no—
369#446—438no—
370#446—438no—
371#446—438no—
372#446C2×D4318yescomplemented
373#433—438no—
374#433—438no—
375#433—438no—
376#433—438no—
377#432—438no—
378#432—438no—
379C2×C4⋊C8—431no—
380C2×C4⋊C8—431no—
381C2×C4⋊C8—431no—
382C2×C4⋊C8—431no—
383C2×C4⋊C8—431no—
384C2×C4⋊C8—431no—
385C2×C4⋊C8—431no—
386C2×C4⋊C8—431no—
387C2×C4⋊C8—431no—
388C2×C4⋊C8C2×D4311yescharacteristic
389C2×C4⋊C8C2×D4311yescharacteristic
390C2×C4⋊C8C2×D4311yescharacteristic
391C2×C22⋊C8—431no—
392C2×C22⋊C8—431no—
393C2×C22⋊C8—431no—
394C2×C22⋊C8—431no—
395C2×#97—431no—
396C2×#97—431no—
397C2×#97—431no—
398C2×#97—431no—
399C2×#97—431no—
400C2×#97—431no—
401C2×#97C2×D4311yescharacteristic
402C2×#97C2×D4311yescharacteristic
403C2×C4×C8—431no—
404C2×C4×C8—431no—
405C2×C4×C8—431no—
406C2×C4×C8C2×D4311yescharacteristic
407C43C2×#298711yescharacteristic, complemented, Sylow
408C22×Q8—431no—
409C22×Q8—431no—
410C22×Q8—431no—
411C22×Q8C4×D4311yescharacteristic
412C23×C4—431no—
413C23×C4—431no—
414C23×C4—431no—
415C22×C8—431no—
416C22×C8—431no—
417C22×C8—431no—
418C22×C8—431no—
419C22×C8C22×D4311yescharacteristic
420C22×C8C22×D4311yescharacteristic
421C22×C8C22×D4311yescharacteristic
422C22×C8C22×D4311yescharacteristic
423C4⋊Q8—438no—
424C4⋊Q8—438no—
425#125—438no—
426#125—438no—
427C22⋊Q8—438no—
428C22⋊Q8—438no—
429C22⋊Q8—438no—
430C22⋊Q8—438no—
431C4×Q8—434no—
432C4×Q8—434no—
433C4×Q8—434no—
434C4×Q8—434no—
435C4×Q8—434no—
436C4×Q8—434no—
437C4×Q8C4×D4314yes—
438C4×Q8C22×D4314yes—
439#117—434no—
440#117—434no—
441#117—434no—
442#117—434no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4C4×D4311yescharacteristic
457C2×C4⋊C4C4×D4311yescharacteristic
458C2×C4⋊C4C4×D4311yescharacteristic
459C2×C22⋊C4—431no—
460C2×C22⋊C4—431no—
461C2×C22⋊C4—431no—
462C2×C22⋊C4—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—434no—
469C2×C42—434no—
470C2×C42C22×D4311yescharacteristic
471C2×C42C22×D4311yescharacteristic
472C2×C42C22×D4311yescharacteristic
473C4⋊C8—434no—
474C4⋊C8—434no—
475C4⋊C8—434no—
476C4⋊C8—434no—
477C4⋊C8—434no—
478C4⋊C8—434no—
479C4⋊C8—434no—
480C4⋊C8—434no—
481C4⋊C8—434no—
482C4⋊C8C22×D4314yes—
483C4⋊C8C22×D4314yes—
484C4⋊C8C22×D4314yes—
485C22⋊C8—434no—
486C22⋊C8—434no—
487C22⋊C8—434no—
488C22⋊C8—434no—
489#97—434no—
490#97—434no—
491#97—434no—
492#97—434no—
493#97—434no—
494#97—434no—
495#97C22×D4314yes—
496#97C22×D4314yes—
497C4×C8—434no—
498C4×C8—434no—
499C4×C8—434no—
500C4×C8C22×D4314yes—
501C24—431no—
502C2×Q8—42no—
503C2×Q8—434no—
504C2×Q8—434no—
505C2×Q8—434no—
506C2×Q8—1722no—
507C2×Q8—1722no—
508C2×Q8—1722no—
509C2×Q8C2×C4×D4314yes—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—432no—
518C22×C4—432no—
519C22×C4—434no—
520C22×C4—434no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4C2×C4×D4311yescharacteristic
526C22×C4C2×C4×D4311yescharacteristic
527C22×C4C2×C4×D4311yescharacteristic
528C22×C4C2×C4×D4311yescharacteristic
529C22×C4C2×C4×D4311yescharacteristic
530C22×C4C2×C4×D4311yescharacteristic
531C22×C4C23×D4311yescharacteristic
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—432no—
537C2×C8—432no—
538C2×C8—432no—
539C2×C8—432no—
540C2×C8—862no—
541C2×C8—862no—
542C2×C8—862no—
543C2×C8—862no—
544C2×C8C23×D4312yes—
545C2×C8C23×D4312yes—
546C2×C8C23×D4312yes—
547C2×C8C23×D4312yes—
548C4⋊C4—434no—
549C4⋊C4—434no—
550C4⋊C4—434no—
551C4⋊C4—434no—
552C4⋊C4—434no—
553C4⋊C4—434no—
554C4⋊C4—434no—
555C4⋊C4—434no—
556C4⋊C4—434no—
557C4⋊C4—434no—
558C4⋊C4—434no—
559C4⋊C4—434no—
560C4⋊C4—434no—
561C4⋊C4C2×C4×D4314yes—
562C4⋊C4C2×C4×D4314yes—
563C4⋊C4C2×C4×D4314yes—
564C22⋊C4—434no—
565C22⋊C4—434no—
566C22⋊C4—434no—
567C22⋊C4—434no—
568C42—432no—
569C42—434no—
570C42—434no—
571C42—432no—
572C42—432no—
573C42—432no—
574C42—432no—
575C42—432no—
576C42C2×C4×D4312yes—
577C42C2×C4×D4312yes—
578C42C2×C4×D4312yes—
579C42C23×D4312yes—
580C42C23×D4312yes—
581C42C23×D4312yes—
582C23—432no—
583C23—862no—
584C23—862no—
585C23—862no—
586C23C22×C4×D4311yescharacteristic
587Q8—44no—
588Q8—1724no—
589Q8—1724no—
590Q8—1724no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—432no—
598C2×C4—432no—
599C2×C4—432no—
600C2×C4—432no—
601C2×C4—432no—
602C2×C4—432no—
603C2×C4—432no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—864no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—1724no—
615C2×C4—1724no—
616C2×C4C22×C4×D4312yes—
617C2×C4C22×C4×D4312yes—
618C2×C4C22×C4×D4312yes—
619C2×C4C22×C4×D4312yes—
620C2×C4C22×C4×D4312yes—
621C2×C4C22×C4×D4312yes—
622C2×C4C22×C4×D4311yescharacteristic
623C2×C4#1306337212yes—
624C2×C4#1306337312yes—
625C2×C4C24×D4311yescharacteristic
626C8—22no—
627C8—22no—
628C8—22no—
629C8—22no—
630C8—862no—
631C8—862no—
632C8—862no—
633C8—862no—
634C22—862no—
635C22—862no—
636C22—862no—
637C22—1724no—
638C22#1458337512yes—
639C22#1458366412yes—
640C22#1458366512yes—
641C22C23×C4×D4311yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—862no—
649C4—862no—
650C4—862no—
651C4—862no—
652C4—862no—
653C4—862no—
654C4—862no—
655C4#1458337512yes—
656C4C2×#1306337211yescharacteristic
657C4C2×#1306337311yescharacteristic
658C2—1722no—
659C2#1914369814yesdirect product factor
660C2C2×#1458337511yescharacteristic
661C2C2×#1458366411yescharacteristic
662C2C2×#1458366511yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#446C2
socleC23×C43C23×C4
prime radicalC23×D43C22×C4
cosocleC2×C4×C43C25
hypercenterC2×#446D43
hypocenterC43C2×#2987
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #19143698C2direct (N × H)
3. C2×#14583030C2semidirect
4. C2×#14583029C2semidirect
5. C2×#14583028C2semidirect
6. C2×#14583028C2semidirect
7. C2×#14583027C2semidirect
8. C2×#14583027C2semidirect
9. C2×#14583026C2semidirect
16. C2×C43×#446C2semidirect
33. #14583030C22semidirect
34. #14583029C22semidirect
35. #14583028C22semidirect
36. #14583028C22semidirect
37. #14583027C22semidirect
38. #14583027C22semidirect
39. #14583026C22semidirect
69. C43×#446C22semidirect
336. C2×#446D43semidirect
343. C2×C43#2987semidirect
372. #446C2×D43semidirect
407. C43C2×#2987semidirect
659. C2#19143698direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834532
#191436982
C2×#145830302
C2×#145830292
C2×#145830282
C2×#145830272
C2×#145830262
C2×#145829612
C2×#145829592
C2×#145829582
C2×#145829552
C2×#145829542
C2×C43×#4462
C2×#298743