Finite Group Databasebeta

← C2×#19139973 #25266824

Subgroups — C2×#19139973 #25266824

Order 11008.

3094 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063303C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic
3#19139973C2116yesmaximal, direct product factor
4C2×#14582833C211yesmaximal, characteristic, complemented
5C2×#14582832C211yesmaximal, characteristic, complemented
6C2×#14582820C211yesmaximal, characteristic, complemented
7C2×#14582819C211yesmaximal, characteristic, complemented
8C2×#14582797C211yesmaximal, characteristic, complemented
9C2×#14582794C211yesmaximal, characteristic, complemented
10C2×#14582794C211yesmaximal, characteristic, complemented
11C2×#14582773C211yesmaximal, characteristic
12C2×#14582773C211yesmaximal, characteristic
13C2×#14582770C211yesmaximal, characteristic
14C2×#14582770C211yesmaximal, characteristic
15C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
16C2×C43×#389C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063303—28no—
22C2×#13063303C2218yes—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C2×C4⋊C4×D43—28no—
35C2×C4⋊C4×D43C2218yes—
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41#14582833C2218yescomplemented
42#14582832C2218yescomplemented
43#14582820C2218yescomplemented
44#14582819C2218yescomplemented
45#14582797C2218yescomplemented
46#14582794C2218yescomplemented
47#14582794C2218yescomplemented
48#14582773C2218yes—
49#14582773C2218yes—
50#14582770C2218yes—
51#14582770C2218yes—
52C4×(C2×D43)⋊C4C2218yes—
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C42×C43C2211yescharacteristic
66C43×#389C2218yescomplemented
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C22×Dic86—24no—
71C22×Dic86—42no—
72C22×Dic86—42no—
73C22×Dic86C2314yes—
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C22×C4×D43—24no—
82C22×C4×D43—24no—
83C22×C4×D43—24no—
84C22×C4×D43—24no—
85C22×C4×D43—42no—
86C22×C4×D43—42no—
87C22×C4×D43—42no—
88C22×C4×D43—42no—
89C22×C4×D43D418yes—
90C22×C4×D43C2314yes—
91C22×C4×D43C2314yes—
92C22×C4×D43C2314yes—
93#13063303—232no—
94C2×C4⋊Dic43—24no—
95C2×C4⋊Dic43—24no—
96C2×C4⋊Dic43—42no—
97C2×C4⋊Dic43C2314yes—
98C2×C4⋊Dic43C2314yes—
99C2×C4⋊Dic43C2314yes—
100C2×Dic43⋊C4—24no—
101C2×Dic43⋊C4—24no—
102C2×Dic43⋊C4—24no—
103C2×Dic43⋊C4—24no—
104C2×Dic43⋊C4—24no—
105C2×Dic43⋊C4—24no—
106C2×Dic43⋊C4—42no—
107C2×Dic43⋊C4—42no—
108C2×Dic43⋊C4C2314yes—
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2314yes—
111C2×Dic43⋊C4C2314yes—
112C2×Dic43⋊C4C2314yes—
113C2×Dic43⋊C4C2314yes—
114C2×Dic43⋊C4C2314yes—
115C2×Dic43⋊C4C2314yes—
116C4⋊C4×D43—232no—
117C2×(C2×D43)⋊C4—24no—
118C2×(C2×D43)⋊C4—24no—
119C2×(C2×D43)⋊C4Q818yescomplemented
120C2×(C2×D43)⋊C4Q818yescomplemented
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×C4×Dic43—42no—
126C2×C4×Dic43C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43—24no—
143C2×C4⋊C4×C43—24no—
144C2×C4⋊C4×C43—24no—
145C2×C4⋊C4×C43—42no—
146C2×C4⋊C4×C43C2314yes—
147C2×C4⋊C4×C43C2314yes—
148C2×C4⋊C4×C43C2314yes—
149C2×C4⋊C4×C43C2314yes—
150C2×C42×C43—42no—
151C2×C42×C43C2314yes—
152#95×C43C2314yes—
153#95×C43C2314yes—
154C24×C43C2411yescharacteristic
155C23×D43—22no—
156C23×D43—22no—
157C23×D43—22no—
158C23×D43—22no—
159C23×D43C2×D414yes—
160C23×D43C2×Q814yes—
161C23×D43C2×Q814yes—
162C23×D43C2412yes—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43C2×D414yes—
181C22×C4×C43C2×Q814yes—
182C22×C4×C43C2×Q814yes—
183C22×C4×C43#4114yes—
184C22×C4×C43C2412yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43C2×D414yes—
209C22×Dic43C2×Q814yes—
210C22×Dic43C2×Q814yes—
211C22×Dic43#4114yes—
212C22×Dic43C2412yes—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C22×Dic43C2412yes—
216C22×Dic43C2412yes—
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C2×C4×D43—232no—
220C2×C4×D43—28no—
221C2×C4×D43—28no—
222C2×C4×D43—28no—
223C2×C4×D43—28no—
224C2×C4×D43—416no—
225C2×C4×D43—44no—
226C2×C4×D43—44no—
227C2×C4×D43—44no—
228C2×C4×D43—44no—
229C2×C4×D43—416no—
230C2×C4×D43C2×D4116yes—
231C2×Dic86—28no—
232C2×Dic86—44no—
233C2×Dic86—44no—
234C2×Dic86—416no—
235C4⋊C4×C43—28no—
236C4⋊C4×C43—28no—
237C4⋊C4×C43—28no—
238C4⋊C4×C43—44no—
239C42×C43—44no—
240(C2×D43)⋊C4—28no—
241(C2×D43)⋊C4—28no—
242(C2×D43)⋊C4C2×Q8116yescomplemented
243(C2×D43)⋊C4C2×Q8116yescomplemented
244C4⋊Dic43—28no—
245C4⋊Dic43—28no—
246C4⋊Dic43—44no—
247Dic43⋊C4—28no—
248Dic43⋊C4—28no—
249Dic43⋊C4—28no—
250Dic43⋊C4—28no—
251Dic43⋊C4—28no—
252Dic43⋊C4—28no—
253Dic43⋊C4—44no—
254Dic43⋊C4—44no—
255C4×Dic43—44no—
256C23×C43C22×D412yes—
257C23×C43C22×Q812yes—
258C23×C43C22×Q812yes—
259C23×C43C2×#4112yes—
260C23×C43C2×#4112yes—
261C23×C43H(5,𝔽2)12yes—
262C23×C43H(5,𝔽2)12yes—
263C23×C43C2511yescharacteristic
264C22×D43—28no—
265C22×D43—28no—
266C22×D43—28no—
267C22×D43—28no—
268C22×D43—28no—
269C22×D43—28no—
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43C4⋊Q8116yes—
275C22×D43C22×D414yes—
276C22×D43C22×Q814yes—
277C22×D43C22×Q814yes—
278C2×C4×C43—28no—
279C2×C4×C43—28no—
280C2×C4×C43—28no—
281C2×C4×C43—28no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—44no—
300C2×C4×C43—44no—
301C2×C4×C43—44no—
302C2×C4×C43C22×D414yes—
303C2×C4×C43C22×Q814yes—
304C2×C4×C43C22×Q814yes—
305C2×C4×C43C2×#4114yes—
306C2×Dic43—28no—
307C2×Dic43—28no—
308C2×Dic43—28no—
309C2×Dic43—28no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—44no—
328C2×Dic43—44no—
329C2×Dic43—44no—
330C2×Dic43C22×D414yes—
331C2×Dic43C22×Q814yes—
332C2×Dic43C22×Q814yes—
333C2×Dic43C2×#4114yes—
334C4×D43—232no—
335C4×D43—416no—
336C4×D43—416no—
337Dic86—416no—
338C2×#2583—431nomaximal, Sylow
339C22×C43#52514yes—
340C22×C43C2×C4⋊Q814yes—
341C22×C43#53414yes—
342C22×C43#55414yes—
343C22×C43#55414yes—
344C22×C43#55414yes—
345C22×C43#55414yes—
346C22×C43C23×D411yescharacteristic
347C22×C43C23×Q811yescharacteristic
348C22×C43C23×Q811yescharacteristic
349C22×C43C22×#4111yescharacteristic
350C22×C43C22×#4111yescharacteristic
351C22×C43C2×H(5,𝔽2)11yescharacteristic
352C22×C43C2×H(5,𝔽2)11yescharacteristic
353C2×D43—232no—
354C2×D43—24no—
355C2×D43—24no—
356C2×D43—24no—
357C2×D43—24no—
358C2×D43—24no—
359C2×D43—24no—
360C2×D43C2×C4⋊Q818yes—
361C4×C43—24no—
362C4×C43—24no—
363C4×C43—24no—
364C4×C43—24no—
365C4×C43—42no—
366C4×C43—42no—
367C4×C43—42no—
368Dic43—24no—
369Dic43—24no—
370Dic43—24no—
371Dic43—24no—
372Dic43—42no—
373Dic43—42no—
374Dic43—42no—
375C22×C22⋊Q8—431no—
376C23×C4⋊C4—431no—
377#2583—4316no—
378C2×#398—431no—
379C2×#398—431no—
380C2×#395—431no—
381C2×#395—431no—
382C2×#389—431no—
383C2×#389—431no—
384C2×#389—431no—
385C2×#389D4311yescharacteristic, complemented
386C2×#385—431no—
387C2×#385—431no—
388C2×#385—431no—
389C2×#385—431no—
390C2×C4×C22⋊C4—431no—
391C2×C43#258318yescomplemented
392C2×C43C2×#52511yescharacteristic
393C2×C43C22×C4⋊Q811yescharacteristic
394C2×C43C2×#53411yescharacteristic
395C2×C43C2×#55411yescharacteristic
396C2×C43C2×#55411yescharacteristic
397C2×C43C2×#55411yescharacteristic
398C2×C43C2×#55411yescharacteristic
399D43—28no—
400C23×Q8—431no—
401C24×C4—431no—
402C24×C4—431no—
403C24×C4—431no—
404C2×C22⋊Q8—438no—
405C2×C22⋊Q8—868no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4—431no—
408C22×C4⋊C4—431no—
409C22×C4⋊C4—431no—
410C22×C4⋊C4—431no—
411C22×C4⋊C4—431no—
412C22×C4⋊C4—431no—
413C22×C4⋊C4—431no—
414C22×C4⋊C4—431no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—438no—
418C22×C4⋊C4—868no—
419C22×C4⋊C4C2×D4311yescharacteristic
420C22×C4⋊C4C2×D4311yescharacteristic
421C22×C4⋊C4C2×D4311yescharacteristic
422C22×C4⋊C4C2×D4311yescharacteristic
423C22×C22⋊C4—431no—
424C22×C22⋊C4—431no—
425C22×C22⋊C4—431no—
426C22×C22⋊C4—431no—
427C22×C42—431no—
428C22×C42C2×D4311yescharacteristic
429#398—438no—
430#398—438no—
431#395—438no—
432#395—438no—
433#389—438no—
434#389—438no—
435#389—438no—
436#389C2×D4318yescomplemented
437#385—438no—
438#385—438no—
439#385—438no—
440#385—438no—
441C4×C22⋊C4—438no—
442C2×#95—431no—
443C2×#95—431no—
444C2×#95—431no—
445C2×#95—431no—
446C2×#95—431no—
447C2×#95—431no—
448C2×#95—431no—
449C2×#95—431no—
450C2×#95C2×D4311yescharacteristic
451C2×#95C2×D4311yescharacteristic
452C43C2×#258311yescharacteristic, complemented, Sylow
453C25—431no—
454C22×Q8—434no—
455C22×Q8—864no—
456C22×Q8—1722no—
457C22×Q8—1722no—
458C23×C4—431no—
459C23×C4—431no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—438no—
463C23×C4—434no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—434no—
468C23×C4—434no—
469C23×C4—864no—
470C23×C4—864no—
471C23×C4—864no—
472C23×C4—864no—
473C23×C4—1722no—
474C23×C4—1722no—
475C23×C4—1722no—
476C23×C4—1722no—
477C23×C4C22×D4311yescharacteristic
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4311yescharacteristic
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483C23×C4C22×D4311yescharacteristic
484C22⋊Q8—8632no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—434no—
490C2×C4⋊C4—434no—
491C2×C4⋊C4—434no—
492C2×C4⋊C4—434no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—434no—
495C2×C4⋊C4—434no—
496C2×C4⋊C4—434no—
497C2×C4⋊C4—434no—
498C2×C4⋊C4—434no—
499C2×C4⋊C4—434no—
500C2×C4⋊C4—8632no—
501C2×C4⋊C4—864no—
502C2×C4⋊C4—864no—
503C2×C4⋊C4—864no—
504C2×C4⋊C4—864no—
505C2×C4⋊C4—864no—
506C2×C4⋊C4—864no—
507C2×C4⋊C4—864no—
508C2×C4⋊C4—864no—
509C2×C4⋊C4—1722no—
510C2×C4⋊C4—1722no—
511C2×C4⋊C4—1722no—
512C2×C4⋊C4C22×D4314yes—
513C2×C4⋊C4C22×D4314yes—
514C2×C4⋊C4C22×D4314yes—
515C2×C4⋊C4C22×D4314yes—
516C2×C22⋊C4—438no—
517C2×C22⋊C4—438no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—434no—
521C2×C22⋊C4—434no—
522C2×C22⋊C4—864no—
523C2×C22⋊C4—864no—
524C2×C42—42no—
525C2×C42—434no—
526C2×C42—1722no—
527C2×C42C22×D4314yes—
528#95—434no—
529#95—434no—
530#95—434no—
531#95—434no—
532#95—434no—
533#95—434no—
534#95—434no—
535#95—434no—
536#95C22×D4314yes—
537#95C22×D4314yes—
538C24—434no—
539C24—434no—
540C24—434no—
541C24—432no—
542C24—862no—
543C24—862no—
544C24—862no—
545C24—862no—
546C24C23×D4311yescharacteristic
547C2×Q8—868no—
548C2×Q8—1724no—
549C2×Q8—1724no—
550C2×Q8—17216no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—434no—
569C22×C4—434no—
570C22×C4—434no—
571C22×C4—434no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—432no—
576C22×C4—4316no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—432no—
580C22×C4—868no—
581C22×C4—868no—
582C22×C4—8632no—
583C22×C4—868no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—868no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—17216no—
603C22×C4—1724no—
604C22×C4—1724no—
605C22×C4—1724no—
606C22×C4—1724no—
607C22×C4—17216no—
608C22×C4#1062189814yes—
609C22×C4D4×D4314yes—
610C22×C4Q8×D4314yes—
611C22×C4Q8×D4314yes—
612C22×C4C23×D4312yes—
613C22×C4C23×D4312yes—
614C22×C4C23×D4312yes—
615C22×C4C23×D4312yes—
616C22×C4C23×D4312yes—
617C22×C4C23×D4312yes—
618C22×C4C23×D4312yes—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—868no—
624C4⋊C4—868no—
625C4⋊C4—868no—
626C4⋊C4—868no—
627C4⋊C4—868no—
628C4⋊C4—868no—
629C4⋊C4—868no—
630C4⋊C4—868no—
631C4⋊C4—1724no—
632C4⋊C4—1724no—
633C4⋊C4—1724no—
634C22⋊C4—4316no—
635C22⋊C4—4316no—
636C22⋊C4—868no—
637C22⋊C4—868no—
638C42—44no—
639C42—1724no—
640C23—4316no—
641C23—434no—
642C23—434no—
643C23—434no—
644C23—868no—
645C23—868no—
646C23—868no—
647C23—868no—
648C23—868no—
649C23—868no—
650C23—862no—
651C23—862no—
652C23—862no—
653C23—862no—
654C23C2×D4×D4312yes—
655C23C2×Q8×D4312yes—
656C23C2×Q8×D4312yes—
657C23#41×D4312yes—
658C23C2×#1062189812yes—
659C23#1306337012yes—
660C23#1306337112yes—
661C23C24×D4311yescharacteristic
662Q8—17216no—
663C2×C4—28no—
664C2×C4—28no—
665C2×C4—28no—
666C2×C4—28no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—434no—
688C2×C4—434no—
689C2×C4—434no—
690C2×C4—434no—
691C2×C4—8632no—
692C2×C4—868no—
693C2×C4—868no—
694C2×C4—868no—
695C2×C4—868no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—17216no—
714C2×C4—17216no—
715C2×C4—1724no—
716C2×C4—1724no—
717C2×C4—1724no—
718C2×C4C2×D4×D4314yes—
719C2×C4C2×Q8×D4314yes—
720C2×C4C2×Q8×D4314yes—
721C2×C4C2×#1062189814yes—
722C22—438no—
723C22—864no—
724C22—864no—
725C22—864no—
726C22—864no—
727C22—864no—
728C22—864no—
729C22—8632no—
730C22#1458340814yes—
731C22C4⋊Q8×D4314yes—
732C22#1458345714yes—
733C22#1458360314yes—
734C22#1458360414yes—
735C22#1458360514yes—
736C22#1458360914yes—
737C22C22×D4×D4311yescharacteristic
738C22C22×Q8×D4311yescharacteristic
739C22C22×Q8×D4311yescharacteristic
740C22C2×#41×D4311yescharacteristic
741C22C22×#1062189811yescharacteristic
742C22C2×#1306337011yescharacteristic
743C22C2×#1306337111yescharacteristic
744C4—24no—
745C4—24no—
746C4—24no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—864no—
752C4—864no—
753C4—864no—
754C4—864no—
755C4—1722no—
756C4—1722no—
757C4—1722no—
758C2—868no—
759C2#1913997318yesdirect product factor
760C2C2×#1458340811yescharacteristic
761C2C2×C4⋊Q8×D4311yescharacteristic
762C2C2×#1458345711yescharacteristic
763C2C2×#1458360311yescharacteristic
764C2C2×#1458360411yescharacteristic
765C2C2×#1458360511yescharacteristic
766C2C2×#1458360911yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#389C2
socleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#389D43
hypocenterC43C2×#2583
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #19139973C2direct (N × H)
4. C2×#14582833C2semidirect
5. C2×#14582832C2semidirect
6. C2×#14582820C2semidirect
7. C2×#14582819C2semidirect
8. C2×#14582797C2semidirect
9. C2×#14582794C2semidirect
10. C2×#14582794C2semidirect
16. C2×C43×#389C2semidirect
41. #14582833C22semidirect
42. #14582832C22semidirect
43. #14582820C22semidirect
44. #14582819C22semidirect
45. #14582797C22semidirect
46. #14582794C22semidirect
47. #14582794C22semidirect
66. C43×#389C22semidirect
119. C2×(C2×D43)⋊C4Q8semidirect
120. C2×(C2×D43)⋊C4Q8semidirect
242. (C2×D43)⋊C4C2×Q8semidirect
243. (C2×D43)⋊C4C2×Q8semidirect
385. C2×#389D43semidirect
391. C2×C43#2583semidirect
436. #389C2×D43semidirect
452. C43C2×#2583semidirect
759. C2#19139973direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633032
C22×C4⋊C4×D432
#191399732
C2×#145828332
C2×#145828322
C2×#145828202
C2×#145828192
C2×#145827972
C2×#145827942
C2×#145827732
C2×#145827702
C2×C4×(C2×D43)⋊C42
C2×C43×#3892
C2×#258343