Finite Group Databasebeta

← C2×#19137454 #25255822

Subgroups — C2×#19137454 #25255822

Order 11008.

3006 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063283C211yesmaximal, characteristic
2#19137454C2116yesmaximal, direct product factor
3C2×#14582785C211yesmaximal, characteristic, complemented
4C2×#14582784C211yesmaximal, characteristic, complemented
5C2×#14582782C211yesmaximal, characteristic, complemented
6C2×#14582773C211yesmaximal, characteristic
7C2×#14582770C211yesmaximal, characteristic
8C2×#14582766C211yesmaximal, characteristic, complemented
9C2×#14582764C211yesmaximal, characteristic, complemented
10C2×#14582761C211yesmaximal, characteristic
11C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
13C2×#14582746C211yesmaximal, characteristic
14C2×#14582744C211yesmaximal, characteristic, complemented
15C2×#95×D43C211yesmaximal, characteristic
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063283C4116yescomplemented
21C2×#13063283C2218yes—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582785C2218yescomplemented
36#14582784C2218yescomplemented
37#14582782C2218yescomplemented
38#14582773C2218yes—
39#14582770C2218yes—
40#14582766C2218yescomplemented
41#14582764C2218yescomplemented
42#14582761C2218yes—
43C4×Dic43⋊C4C2218yescomplemented
44C4×(C2×D43)⋊C4C2218yes—
45#14582746C2218yes—
46#14582744C2218yescomplemented
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59#95×D43C2218yes—
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C42×C43C2211yescharacteristic
63C43×#387C2218yescomplemented
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C22×C4×D43—24no—
77C22×C4×D43—24no—
78C22×C4×D43—24no—
79C22×C4×D43—24no—
80C22×C4×D43—24no—
81C22×C4×D43—24no—
82C22×C4×D43—42no—
83C22×C4×D43—42no—
84C22×C4×D43C2×C418yes—
85C22×C4×D43C2314yes—
86C22×C4×D43C2314yes—
87C22×C4×D43C2314yes—
88#13063283C2×C4164yescomplemented
89C2×C4⋊Dic43—42no—
90C2×C4⋊Dic43C2×C418yescomplemented
91C2×C4⋊Dic43C2314yes—
92C2×C4⋊Dic43C2314yes—
93C2×Dic43⋊C4—24no—
94C2×Dic43⋊C4—24no—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×(C2×D43)⋊C4—24no—
98C2×(C2×D43)⋊C4—24no—
99C2×(C2×D43)⋊C4C2×C418yes—
100C2×(C2×D43)⋊C4C2×C418yes—
101C2×(C2×D43)⋊C4C2314yes—
102C2×(C2×D43)⋊C4C2314yes—
103C2×(C2×D43)⋊C4C2314yes—
104C2×(C2×D43)⋊C4C2314yes—
105C2×C4×Dic43—24no—
106C2×C4×Dic43—24no—
107C2×C4×Dic43—42no—
108C2×C4×Dic43C2×C418yescomplemented
109C2×C4×Dic43C2×C418yescomplemented
110C2×C4×Dic43C2314yes—
111C2×C4×Dic43C2314yes—
112C2×C4×Dic43C2314yes—
113C2×C4×Dic43C2314yes—
114C2×C4×Dic43C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43—42no—
135C2×C4⋊C4×C43C2×C418yescomplemented
136C2×C4⋊C4×C43C2314yes—
137C2×C4⋊C4×C43C2314yes—
138C2×C42×C43—42no—
139C2×C42×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144C24×C43C2411yescharacteristic
145C23×D43—22no—
146C23×D43—22no—
147C23×D43—22no—
148C23×D43—22no—
149C23×D43C22×C414yes—
150C23×D43#4114yes—
151C23×D43#4114yes—
152C23×D43C2412yes—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
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×C43C22×C414yes—
171C22×C4×C43C22×C414yes—
172C22×C4×C43C22×C414yes—
173C22×C4×C43#4114yes—
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43C22×C414yes—
199C22×Dic43C22×C414yes—
200C22×Dic43C22×C414yes—
201C22×Dic43#4114yes—
202C22×Dic43C2412yes—
203C22×Dic43C2412yes—
204C22×Dic43C2412yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C2×C4×D43—28no—
210C2×C4×D43—28no—
211C2×C4×D43—232no—
212C2×C4×D43—28no—
213C2×C4×D43—28no—
214C2×C4×D43—28no—
215C2×C4×D43—28no—
216C2×C4×D43—44no—
217C2×C4×D43—44no—
218C2×C4×D43—416no—
219C2×C4×D43—416no—
220C2×C4×D43C22×C4116yes—
221C4⋊C4×C43—44no—
222C4⋊C4×C43C22×C4116yescomplemented
223C42×C43—44no—
224(C2×D43)⋊C4—28no—
225(C2×D43)⋊C4—28no—
226(C2×D43)⋊C4C22×C4116yes—
227(C2×D43)⋊C4C22×C4116yes—
228C4⋊Dic43—44no—
229C4⋊Dic43C22×C4116yescomplemented
230Dic43⋊C4—28no—
231Dic43⋊C4—28no—
232C4×Dic43—28no—
233C4×Dic43—28no—
234C4×Dic43—44no—
235C4×Dic43C22×C4116yescomplemented
236C4×Dic43C22×C4116yescomplemented
237C23×C43C23×C412yes—
238C23×C43C2×#4112yes—
239C23×C43C2×#4112yes—
240C23×C43C2×#4112yes—
241C23×C43C2×#4112yes—
242C23×C43H(5,𝔽2)12yes—
243C23×C432−1+412yes—
244C23×C43C2511yescharacteristic
245C22×D43—28no—
246C22×D43—28no—
247C22×D43—28no—
248C22×D43—28no—
249C22×D43—28no—
250C22×D43—28no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—22no—
255C22×D43#117116yes—
256C22×D43C23×C414yes—
257C22×D43C2×#4114yes—
258C22×D43C2×#4114yes—
259C2×C4×C43—28no—
260C2×C4×C43—28no—
261C2×C4×C43—28no—
262C2×C4×C43—28no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—44no—
281C2×C4×C43—44no—
282C2×C4×C43—44no—
283C2×C4×C43C23×C414yes—
284C2×C4×C43C23×C414yes—
285C2×C4×C43C23×C414yes—
286C2×C4×C43C2×#4114yes—
287C2×Dic43—28no—
288C2×Dic43—28no—
289C2×Dic43—28no—
290C2×Dic43—28no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—44no—
309C2×Dic43—44no—
310C2×Dic43—44no—
311C2×Dic43C23×C414yes—
312C2×Dic43C23×C414yes—
313C2×Dic43C23×C414yes—
314C2×Dic43C2×#4114yes—
315C4×D43—232no—
316C4×D43—416no—
317C4×D43—416no—
318C2×#2343—431nomaximal, Sylow
319C22×C43C2×#11714yes—
320C22×C43C4×#4114yes—
321C22×C43#52014yes—
322C22×C43#55114yes—
323C22×C43#55114yes—
324C22×C43#55214yes—
325C22×C43#55214yes—
326C22×C43C24×C411yescharacteristic
327C22×C43C22×#4111yescharacteristic
328C22×C43C22×#4111yescharacteristic
329C22×C43C22×#4111yescharacteristic
330C22×C43C22×#4111yescharacteristic
331C22×C43C2×H(5,𝔽2)11yescharacteristic
332C22×C43C2×2−1+411yescharacteristic
333C2×D43—232no—
334C2×D43—24no—
335C2×D43—24no—
336C2×D43—24no—
337C2×D43—24no—
338C2×D43—24no—
339C2×D43—24no—
340C2×D43C2×#11718yes—
341C4×C43—24no—
342C4×C43—24no—
343C4×C43—24no—
344C4×C43—24no—
345C4×C43—42no—
346C4×C43—42no—
347C4×C43—42no—
348Dic43—24no—
349Dic43—24no—
350Dic43—24no—
351Dic43—24no—
352Dic43—42no—
353Dic43—42no—
354Dic43—42no—
355C22×#117—431no—
356#2343—4316no—
357C2×#387—431no—
358C2×#387—431no—
359C2×#387—431no—
360C2×#387D4311yescharacteristic, complemented
361C2×#385—431no—
362C2×#385—431no—
363C2×#383—431no—
364C2×#382—431no—
365C2×#381—431no—
366C2×C4×C4⋊C4—431no—
367C2×C4×C22⋊C4—431no—
368C2×C4×C22⋊C4—431no—
369C2×#376—431no—
370C22×#95—431no—
371C2×C43#234318yescomplemented
372C2×C43C22×#11711yescharacteristic
373C2×C43C2×C4×#4111yescharacteristic
374C2×C43C2×#52011yescharacteristic
375C2×C43C2×#55111yescharacteristic
376C2×C43C2×#55111yescharacteristic
377C2×C43C2×#55211yescharacteristic
378C2×C43C2×#55211yescharacteristic
379D43—28no—
380C24×C4—431no—
381C24×C4—431no—
382C24×C4—431no—
383C2×#117—438no—
384C2×#117—4316no—
385C22×C4⋊C4—431no—
386C22×C4⋊C4—431no—
387C22×C4⋊C4—431no—
388C22×C4⋊C4—431no—
389C22×C4⋊C4C2×D4311yescharacteristic
390C22×C4⋊C4C2×D4311yescharacteristic
391C22×C22⋊C4—431no—
392C22×C22⋊C4—431no—
393C22×C22⋊C4—431no—
394C22×C22⋊C4—431no—
395C22×C42—431no—
396C22×C42—431no—
397C22×C42—431no—
398C22×C42—431no—
399C22×C42—431no—
400C22×C42C2×D4311yescharacteristic
401#387—438no—
402#387—438no—
403#387—438no—
404#387C2×D4318yescomplemented
405#385—438no—
406#385—438no—
407#383—438no—
408#382—438no—
409#381—438no—
410C4×C4⋊C4—438no—
411C4×C22⋊C4—438no—
412C4×C22⋊C4—438no—
413#376—438no—
414C2×#95—431no—
415C2×#95—431no—
416C2×#95—431no—
417C2×#95—431no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95—431no—
421C2×#95—431no—
422C2×#95—431no—
423C2×#95—431no—
424C2×#95—431no—
425C2×#95—431no—
426C2×#95—438no—
427C2×#95C2×D4311yescharacteristic
428C2×#95C2×D4311yescharacteristic
429C2×#95C2×D4311yescharacteristic
430C2×#95C2×D4311yescharacteristic
431C43C2×#234311yescharacteristic, complemented, Sylow
432C25—431no—
433C23×C4—431no—
434C23×C4—431no—
435C23×C4—431no—
436C23×C4—431no—
437C23×C4—438no—
438C23×C4—434no—
439C23×C4—431no—
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—434no—
443C23×C4—434no—
444C23×C4—864no—
445C23×C4—864no—
446C23×C4—864no—
447C23×C4—864no—
448C23×C4—864no—
449C23×C4—864no—
450C23×C4—1722no—
451C23×C4—1722no—
452C23×C4C22×D4311yescharacteristic
453C23×C4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C23×C4C22×D4311yescharacteristic
456C23×C4C22×D4311yescharacteristic
457C23×C4C22×D4311yescharacteristic
458C23×C4C22×D4311yescharacteristic
459#117—4364no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—438no—
462C2×C4⋊C4—434no—
463C2×C4⋊C4—434no—
464C2×C4⋊C4—434no—
465C2×C4⋊C4—434no—
466C2×C4⋊C4—864no—
467C2×C4⋊C4—864no—
468C2×C4⋊C4—1722no—
469C2×C4⋊C4C4×D4318yescomplemented
470C2×C4⋊C4C22×D4314yes—
471C2×C4⋊C4C22×D4314yes—
472C2×C22⋊C4—438no—
473C2×C22⋊C4—438no—
474C2×C22⋊C4—434no—
475C2×C22⋊C4—434no—
476C2×C22⋊C4—434no—
477C2×C22⋊C4—434no—
478C2×C22⋊C4—864no—
479C2×C22⋊C4—864no—
480C2×C42—42no—
481C2×C42—438no—
482C2×C42—438no—
483C2×C42—434no—
484C2×C42—434no—
485C2×C42—434no—
486C2×C42—434no—
487C2×C42—434no—
488C2×C42—864no—
489C2×C42—864no—
490C2×C42—1722no—
491C2×C42C22×D4314yes—
492#95—434no—
493#95—434no—
494#95—434no—
495#95—434no—
496#95—434no—
497#95—434no—
498#95—434no—
499#95—434no—
500#95—434no—
501#95—434no—
502#95—434no—
503#95—434no—
504#95C22×D4314yes—
505#95C22×D4314yes—
506#95C22×D4314yes—
507#95C22×D4314yes—
508C24—434no—
509C24—434no—
510C24—434no—
511C24—432no—
512C24—862no—
513C24—862no—
514C24—862no—
515C24—862no—
516C24C23×D4311yescharacteristic
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—434no—
535C22×C4—434no—
536C22×C4—434no—
537C22×C4—434no—
538C22×C4—432no—
539C22×C4—432no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—4316no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—868no—
547C22×C4—8632no—
548C22×C4—868no—
549C22×C4—868no—
550C22×C4—868no—
551C22×C4—868no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—868no—
570C22×C4—1724no—
571C22×C4—1724no—
572C22×C4—17216no—
573C22×C4—17216no—
574C22×C4C2×C4×D4314yes—
575C22×C4C2×C4×D4314yes—
576C22×C4C2×C4×D4314yes—
577C22×C4#1062190214yes—
578C22×C4C23×D4312yes—
579C22×C4C23×D4312yes—
580C22×C4C23×D4312yes—
581C22×C4C23×D4312yes—
582C22×C4C23×D4312yes—
583C22×C4C23×D4312yes—
584C22×C4C23×D4312yes—
585C4⋊C4—44no—
586C4⋊C4—4316no—
587C4⋊C4—868no—
588C4⋊C4—868no—
589C4⋊C4—1724no—
590C4⋊C4C2×C4×D43116yescomplemented
591C22⋊C4—4316no—
592C22⋊C4—4316no—
593C22⋊C4—868no—
594C22⋊C4—868no—
595C42—44no—
596C42—4316no—
597C42—4316no—
598C42—868no—
599C42—868no—
600C42—1724no—
601C23—4316no—
602C23—434no—
603C23—434no—
604C23—434no—
605C23—868no—
606C23—868no—
607C23—868no—
608C23—868no—
609C23—868no—
610C23—868no—
611C23—862no—
612C23—862no—
613C23—862no—
614C23—862no—
615C23C22×C4×D4312yes—
616C23#41×D4312yes—
617C23#41×D4312yes—
618C23#41×D4312yes—
619C23C2×#1062190212yes—
620C23#1306337012yes—
621C23#1306337212yes—
622C23C24×D4311yescharacteristic
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—434no—
648C2×C4—434no—
649C2×C4—434no—
650C2×C4—434no—
651C2×C4—8632no—
652C2×C4—868no—
653C2×C4—868no—
654C2×C4—868no—
655C2×C4—868no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—17216no—
674C2×C4—17216no—
675C2×C4—1724no—
676C2×C4—1724no—
677C2×C4—1724no—
678C2×C4C22×C4×D4314yes—
679C2×C4C22×C4×D4314yes—
680C2×C4C22×C4×D4314yes—
681C2×C4C2×#1062190214yes—
682C22—438no—
683C22—864no—
684C22—864no—
685C22—864no—
686C22—864no—
687C22—864no—
688C22—864no—
689C22—8632no—
690C22#117×D4314yes—
691C22C4×#1062190214yes—
692C22#1458337814yes—
693C22#1458357614yes—
694C22#1458357714yes—
695C22#1458358514yes—
696C22#1458358714yes—
697C22C23×C4×D4311yescharacteristic
698C22C2×#41×D4311yescharacteristic
699C22C2×#41×D4311yescharacteristic
700C22C2×#41×D4311yescharacteristic
701C22C22×#1062190211yescharacteristic
702C22C2×#1306337011yescharacteristic
703C22C2×#1306337211yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—24no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—864no—
712C4—864no—
713C4—864no—
714C4—864no—
715C4—1722no—
716C4—1722no—
717C4—1722no—
718C2—868no—
719C2#1913745418yesdirect product factor
720C2C2×#117×D4311yescharacteristic
721C2C2×C4×#1062190211yescharacteristic
722C2C2×#1458337811yescharacteristic
723C2C2×#1458357611yescharacteristic
724C2C2×#1458357711yescharacteristic
725C2C2×#1458358511yescharacteristic
726C2C2×#1458358711yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC23×C43C25
hypercenterC2×#387D43
hypocenterC43C2×#2343
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #19137454C2direct (N × H)
3. C2×#14582785C2semidirect
4. C2×#14582784C2semidirect
5. C2×#14582782C2semidirect
8. C2×#14582766C2semidirect
9. C2×#14582764C2semidirect
11. C2×C4×Dic43⋊C4C2semidirect
14. C2×#14582744C2semidirect
16. C2×C43×#387C2semidirect
20. C2×#13063283C4semidirect
35. #14582785C22semidirect
36. #14582784C22semidirect
37. #14582782C22semidirect
40. #14582766C22semidirect
41. #14582764C22semidirect
43. C4×Dic43⋊C4C22semidirect
46. #14582744C22semidirect
63. C43×#387C22semidirect
88. #13063283C2×C4semidirect
90. C2×C4⋊Dic43C2×C4semidirect
108. C2×C4×Dic43C2×C4semidirect
109. C2×C4×Dic43C2×C4semidirect
135. C2×C4⋊C4×C43C2×C4semidirect
222. C4⋊C4×C43C22×C4semidirect
229. C4⋊Dic43C22×C4semidirect
235. C4×Dic43C22×C4semidirect
236. C4×Dic43C22×C4semidirect
360. C2×#387D43semidirect
371. C2×C43#2343semidirect
404. #387C2×D43semidirect
431. C43C2×#2343semidirect
469. C2×C4⋊C4C4×D43semidirect
590. C4⋊C4C2×C4×D43semidirect
719. C2#19137454direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632832
#191374542
C2×#145827852
C2×#145827842
C2×#145827822
C2×#145827732
C2×#145827702
C2×#145827662
C2×#145827642
C2×#145827612
C2×C4×Dic43⋊C42
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×#145827442
C2×#95×D432
C2×C43×#3872
C2×#234343