Finite Group Databasebeta

← C2×#19137223 #25255230

Subgroups — C2×#19137223 #25255230

Order 11008.

3262 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2#19137223C2116yesmaximal, direct product factor
3C2×#14582791C211yesmaximal, characteristic, complemented
4C2×#14582789C211yesmaximal, characteristic, complemented
5C2×#14582786C211yesmaximal, characteristic, complemented
6C2×#14582780C211yesmaximal, characteristic, complemented
7C2×#14582778C211yesmaximal, characteristic
8C2×#14582776C211yesmaximal, characteristic
9C2×#14582774C211yesmaximal, characteristic, complemented
10C2×#14582766C211yesmaximal, characteristic, complemented
11C2×#14582764C211yesmaximal, characteristic, complemented
12C2×#14582761C211yesmaximal, characteristic, complemented
13C2×#14582756C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
15C22×C43⋊#95C211yesmaximal, characteristic, complemented
16C2×C43×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×(C22⋊D43)⋊C4C4116yescomplemented
22C2×(C22⋊D43)⋊C4C2218yes—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582791C2218yescomplemented
36#14582789C2218yescomplemented
37#14582786C2218yescomplemented
38#14582780C2218yescomplemented
39#14582778C2218yes—
40#14582776C2218yes—
41#14582774C2218yescomplemented
42#14582766C2218yescomplemented
43#14582764C2218yescomplemented
44#14582761C2218yescomplemented
45#14582756C2218yescomplemented
46C22⋊C4×Dic43C2218yescomplemented
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
59C2×C43⋊#95C2218yescomplemented
60C24×C4×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C43×#385C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C22×C22⋊D43—24no—
70C22×C22⋊D43—24no—
71C22×C22⋊D43C2×C418yes—
72C22×C22⋊D43C2314yes—
73C23×Dic43—24no—
74C23×Dic43—42no—
75C23×Dic43—42no—
76C23×Dic43—42no—
77C23×Dic43—42no—
78C23×Dic43C2×C418yes—
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2314yes—
87C23×Dic43C2314yes—
88C22×C4×D43—42no—
89C22×C4×D43—42no—
90C22×C4×D43C2×C418yescomplemented
91C22×C4×D43C2314yes—
92(C22⋊D43)⋊C4C2×C4164yescomplemented
93C2×C4⋊Dic43—42no—
94C2×C4⋊Dic43—42no—
95C2×C4⋊Dic43C2314yes—
96C2×C4⋊Dic43C2314yes—
97C2×Dic43⋊C4C2×C418yescomplemented
98C2×Dic43⋊C4C2314yes—
99C2×C22⋊Dic43—24no—
100C2×C22⋊Dic43C2314yes—
101C2×(C2×D43)⋊C4—42no—
102C2×(C2×D43)⋊C4—42no—
103C2×(C2×D43)⋊C4—42no—
104C2×(C2×D43)⋊C4—42no—
105C2×(C2×D43)⋊C4C2×C418yescomplemented
106C2×(C2×D43)⋊C4C2314yes—
107C2×(C2×D43)⋊C4C2314yes—
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×C4×Dic43—42no—
112C2×C4×Dic43—42no—
113C2×C4×Dic43C2×C418yescomplemented
114C2×C4×Dic43C2314yes—
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C25×C43C2311yescharacteristic
130C23×C4×C43—24no—
131C23×C4×C43—42no—
132C23×C4×C43—42no—
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2314yes—
140C2×C4⋊C4×C43—42no—
141C2×C4⋊C4×C43—42no—
142C2×C4⋊C4×C43C2314yes—
143C2×C4⋊C4×C43C2314yes—
144C2×C22⋊C4×C43—24no—
145C2×C22⋊C4×C43C2×C418yes—
146C2×C22⋊C4×C43C2314yes—
147C2×C22⋊C4×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43C22×C414yes—
155C24×C43#4114yes—
156C24×C43#4114yes—
157C24×C43C2412yes—
158C24×C43C2411yescharacteristic
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43C22×C414yes—
166C23×D43C2412yes—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—28no—
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×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—44no—
185C22×C4×C43—44no—
186C22×C4×C43—416no—
187C22×C4×C43C22×C414yes—
188C22×C4×C43C22×C414yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C2×C22⋊D43—232no—
196C2×C22⋊D43—28no—
197C2×C22⋊D43—28no—
198C2×C22⋊D43C22×C4116yes—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—28no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—416no—
219C22×Dic43—44no—
220C22×Dic43—44no—
221C22×Dic43—44no—
222C22×Dic43—44no—
223C22×Dic43—416no—
224C22×Dic43C22×C414yes—
225C22×Dic43C22×C414yes—
226C22×Dic43C22×C414yes—
227C22×Dic43C22×C4116yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C2×C4×D43—416no—
236C2×C4×D43—44no—
237C2×C4×D43—44no—
238C2×C4×D43C22×C4116yescomplemented
239C4⋊C4×C43—44no—
240C4⋊C4×C43—44no—
241C22⋊C4×C43—28no—
242C22⋊C4×C43C22×C4116yes—
243C22⋊Dic43—28no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4—44no—
246(C2×D43)⋊C4—44no—
247(C2×D43)⋊C4—44no—
248(C2×D43)⋊C4C22×C4116yescomplemented
249C4⋊Dic43—44no—
250C4⋊Dic43—44no—
251Dic43⋊C4C22×C4116yescomplemented
252C4×Dic43—44no—
253C4×Dic43—44no—
254C4×Dic43C22×C4116yescomplemented
255C23×C43—28no—
256C23×C43—28no—
257C23×C43—28no—
258C23×C43—28no—
259C23×C43—28no—
260C23×C43—28no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43#117116yes—
266C23×C43C23×C414yes—
267C23×C43C23×C412yes—
268C23×C43C2×#4114yes—
269C23×C43C2×#4112yes—
270C23×C43C2×#4114yes—
271C23×C43C2×#4112yes—
272C23×C43H(5,𝔽2)12yes—
273C23×C43H(5,𝔽2)12yes—
274C23×C43H(5,𝔽2)12yes—
275C23×C432−1+412yes—
276C23×C43C2511yescharacteristic
277C22×D43—28no—
278C22×D43—28no—
279C22×D43—28no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43C23×C414yes—
291C2×C4×C43—28no—
292C2×C4×C43—28no—
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—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—416no—
310C2×C4×C43—44no—
311C2×C4×C43—44no—
312C2×C4×C43—44no—
313C2×C4×C43—44no—
314C2×C4×C43C23×C414yes—
315C2×C4×C43C23×C414yes—
316C22⋊D43—232no—
317C2×Dic43—28no—
318C2×Dic43—28no—
319C2×Dic43—28no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—416no—
339C2×Dic43—416no—
340C2×Dic43—44no—
341C2×Dic43—44no—
342C2×Dic43—44no—
343C2×Dic43—44no—
344C2×Dic43C23×C414yes—
345C2×Dic43C23×C414yes—
346C2×Dic43C23×C414yes—
347C4×D43—416no—
348C2×#2318—431nomaximal, Sylow
349C22×C43—232no—
350C22×C43—24no—
351C22×C43—24no—
352C22×C43—24no—
353C22×C43—24no—
354C22×C43—24no—
355C22×C43—24no—
356C22×C43C2×#11718yes—
357C22×C43C2×#11714yes—
358C22×C43#51814yes—
359C22×C43#52014yes—
360C22×C43#53814yes—
361C22×C43#53814yes—
362C22×C43#53914yes—
363C22×C43#53914yes—
364C22×C43C24×C411yescharacteristic
365C22×C43C22×#4111yescharacteristic
366C22×C43C22×#4111yescharacteristic
367C22×C43C2×H(5,𝔽2)11yescharacteristic
368C22×C43C2×H(5,𝔽2)11yescharacteristic
369C22×C43C2×H(5,𝔽2)11yescharacteristic
370C22×C43C2×2−1+411yescharacteristic
371C2×D43—24no—
372C2×D43—24no—
373C2×D43—24no—
374C2×D43—416no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C4×C43—24no—
380C4×C43—24no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—42no—
385Dic43—24no—
386Dic43—24no—
387Dic43—24no—
388Dic43—42no—
389Dic43—42no—
390Dic43—42no—
391Dic43—42no—
392C22×C4×D4—431no—
393#2318—4316no—
394C2×#388—431no—
395C2×#388—431no—
396C2×#387—431no—
397C2×#387—431no—
398C2×#386—431no—
399C2×#386—431no—
400C2×#385—431no—
401C2×#385D4311yescharacteristic, complemented
402C2×#383—431no—
403C2×#382—431no—
404C2×#381—431no—
405C2×#380—431no—
406C2×C4×C22⋊C4—431no—
407C22×#95—431no—
408C2×C43—28no—
409C2×C43#231818yescomplemented
410C2×C43C22×#11711yescharacteristic
411C2×C43C2×#51811yescharacteristic
412C2×C43C2×#52011yescharacteristic
413C2×C43C2×#53811yescharacteristic
414C2×C43C2×#53811yescharacteristic
415C2×C43C2×#53911yescharacteristic
416C2×C43C2×#53911yescharacteristic
417D43—44no—
418C23×D4—431no—
419C24×C4—431no—
420C24×C4—431no—
421C24×C4—431no—
422C24×C4C2×D4311yescharacteristic
423C2×C4×D4—438no—
424C2×C4×D4—4316no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4C2×D4311yescharacteristic
429C22×C4⋊C4C2×D4311yescharacteristic
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4—431no—
433C22×C22⋊C4—431no—
434C22×C22⋊C4—431no—
435C22×C22⋊C4—431no—
436C22×C22⋊C4C2×D4311yescharacteristic
437C22×C22⋊C4C2×D4311yescharacteristic
438C22×C42—431no—
439C22×C42—431no—
440C22×C42—431no—
441#388—438no—
442#388—438no—
443#387—438no—
444#387—438no—
445#386—438no—
446#386—438no—
447#385—438no—
448#385C2×D4318yescomplemented
449#383—438no—
450#382—438no—
451#381—438no—
452#380—438no—
453C4×C22⋊C4—438no—
454C2×#95—438no—
455C2×#95—431no—
456C2×#95—431no—
457C2×#95—431no—
458C2×#95—431no—
459C2×#95—431no—
460C2×#95—431no—
461C2×#95—431no—
462C2×#95—431no—
463C2×#95—431no—
464C2×#95—431no—
465C2×#95—431no—
466C2×#95—431no—
467C2×#95C2×D4311yescharacteristic
468C2×#95C2×D4311yescharacteristic
469C43C2×#231811yescharacteristic, complemented, Sylow
470C25—431no—
471C25C22×D4311yescharacteristic
472C22×D4—438no—
473C22×D4—434no—
474C22×D4—864no—
475C22×D4—864no—
476C23×C4—24no—
477C23×C4—42no—
478C23×C4—42no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—438no—
483C23×C4—434no—
484C23×C4—438no—
485C23×C4—434no—
486C23×C4—431no—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—434no—
491C23×C4—864no—
492C23×C4—1722no—
493C23×C4—1722no—
494C23×C4—1722no—
495C23×C4—1722no—
496C23×C4—1722no—
497C23×C4—1722no—
498C23×C4C22×D4311yescharacteristic
499C23×C4C22×D4311yescharacteristic
500C23×C4C22×D4311yescharacteristic
501C23×C4C22×D4311yescharacteristic
502C23×C4C22×D4311yescharacteristic
503C23×C4C22×D4311yescharacteristic
504C23×C4C22×D4314yes—
505C4×D4—4364no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—438no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—434no—
511C2×C4⋊C4—434no—
512C2×C4⋊C4—1722no—
513C2×C4⋊C4—1722no—
514C2×C4⋊C4C22×D4314yes—
515C2×C4⋊C4C22×D4314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—438no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—434no—
521C2×C22⋊C4—434no—
522C2×C22⋊C4—434no—
523C2×C22⋊C4—434no—
524C2×C22⋊C4—864no—
525C2×C22⋊C4—1722no—
526C2×C22⋊C4—1722no—
527C2×C22⋊C4—1722no—
528C2×C22⋊C4—1722no—
529C2×C22⋊C4C4×D4318yes—
530C2×C22⋊C4C22×D4314yes—
531C2×C22⋊C4C22×D4314yes—
532C2×C42—438no—
533C2×C42—434no—
534C2×C42—434no—
535C2×C42—434no—
536C2×C42—1722no—
537C2×C42—1722no—
538#95—434no—
539#95—434no—
540#95—434no—
541#95—434no—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95—434no—
547#95—434no—
548#95—434no—
549#95—434no—
550#95C22×D4314yes—
551#95C22×D4314yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—434no—
557C24—432no—
558C24—862no—
559C24—862no—
560C24—862no—
561C24—862no—
562C24—862no—
563C24—862no—
564C24C2×C4×D4314yes—
565C24#1062190014yes—
566C24#1062190214yes—
567C24C23×D4312yes—
568C24C23×D4311yescharacteristic
569C2×D4—4316no—
570C2×D4—8632no—
571C2×D4—868no—
572C2×D4—868no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—416no—
593C22×C4—434no—
594C22×C4—434no—
595C22×C4—434no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—4316no—
600C22×C4—4316no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—868no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—17216no—
625C22×C4—1724no—
626C22×C4—1724no—
627C22×C4—17216no—
628C22×C4—1724no—
629C22×C4—1724no—
630C22×C4—1724no—
631C22×C4—1724no—
632C22×C4—17216no—
633C22×C4C2×C4×D4314yes—
634C22×C4C2×C4×D4314yes—
635C22×C4C23×D4312yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4312yes—
638C22×C4C23×D4312yes—
639C22×C4C23×D4312yes—
640C22×C4C23×D4312yes—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—4316no—
644C4⋊C4—1724no—
645C4⋊C4—1724no—
646C22⋊C4—28no—
647C22⋊C4—4316no—
648C22⋊C4—868no—
649C22⋊C4—1724no—
650C22⋊C4—1724no—
651C22⋊C4—1724no—
652C22⋊C4—1724no—
653C22⋊C4C2×C4×D43116yes—
654C42—4316no—
655C42—1724no—
656C42—1724no—
657C23—28no—
658C23—28no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—434no—
668C23—868no—
669C23—868no—
670C23—868no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—1724no—
678C23—1724no—
679C23—1724no—
680C23—1724no—
681C23#13063283116yes—
682C23C22×C4×D4314yes—
683C23C22×C4×D4312yes—
684C23C2×#1062190014yes—
685C23C2×#1062190012yes—
686C23C2×#1062190214yes—
687C23C2×#1062190212yes—
688C23#1306337012yes—
689C23#1306337012yes—
690C23#1306337112yes—
691C23#1306337212yes—
692C23C24×D4311yescharacteristic
693D4—8632no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—416no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—434no—
718C2×C4—434no—
719C2×C4—434no—
720C2×C4—868no—
721C2×C4—868no—
722C2×C4—868no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—17216no—
742C2×C4—17216no—
743C2×C4—17216no—
744C2×C4—1724no—
745C2×C4—1724no—
746C2×C4—1724no—
747C2×C4—1724no—
748C2×C4C22×C4×D4314yes—
749C2×C4C22×C4×D4314yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—232no—
757C22—864no—
758C22—864no—
759C22—864no—
760C22—1722no—
761C22—1722no—
762C22—1722no—
763C22—1722no—
764C22—17216no—
765C22C2×#1306328318yes—
766C22C2×#1306328314yes—
767C22#1458337114yes—
768C22#1458337814yes—
769C22#1458348414yes—
770C22#1458348914yes—
771C22#1458349314yes—
772C22#1458349814yes—
773C22C23×C4×D4311yescharacteristic
774C22C22×#1062190011yescharacteristic
775C22C22×#1062190211yescharacteristic
776C22C2×#1306337011yescharacteristic
777C22C2×#1306337011yescharacteristic
778C22C2×#1306337111yescharacteristic
779C22C2×#1306337211yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—864no—
787C4—864no—
788C4—864no—
789C4—1722no—
790C4—1722no—
791C4—1722no—
792C4—1722no—
793C2—28no—
794C2—1724no—
795C2#1913722318yesdirect product factor
796C2C22×#1306328311yescharacteristic
797C2C2×#1458337111yescharacteristic
798C2C2×#1458337811yescharacteristic
799C2C2×#1458348411yescharacteristic
800C2C2×#1458348911yescharacteristic
801C2C2×#1458349311yescharacteristic
802C2C2×#1458349811yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×#2318
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #19137223C2direct (N × H)
3. C2×#14582791C2semidirect
4. C2×#14582789C2semidirect
5. C2×#14582786C2semidirect
6. C2×#14582780C2semidirect
9. C2×#14582774C2semidirect
10. C2×#14582766C2semidirect
11. C2×#14582764C2semidirect
12. C2×#14582761C2semidirect
13. C2×#14582756C2semidirect
14. C2×C22⋊C4×Dic43C2semidirect
15. C22×C43⋊#95C2semidirect
16. C2×C43×#385C2semidirect
21. C2×(C22⋊D43)⋊C4C4semidirect
35. #14582791C22semidirect
36. #14582789C22semidirect
37. #14582786C22semidirect
38. #14582780C22semidirect
41. #14582774C22semidirect
42. #14582766C22semidirect
43. #14582764C22semidirect
44. #14582761C22semidirect
45. #14582756C22semidirect
46. C22⋊C4×Dic43C22semidirect
59. C2×C43⋊#95C22semidirect
65. C43×#385C22semidirect
90. C22×C4×D43C2×C4semidirect
92. (C22⋊D43)⋊C4C2×C4semidirect
97. C2×Dic43⋊C4C2×C4semidirect
105. C2×(C2×D43)⋊C4C2×C4semidirect
113. C2×C4×Dic43C2×C4semidirect
238. C2×C4×D43C22×C4semidirect
248. (C2×D43)⋊C4C22×C4semidirect
251. Dic43⋊C4C22×C4semidirect
254. C4×Dic43C22×C4semidirect
401. C2×#385D43semidirect
409. C2×C43#2318semidirect
448. #385C2×D43semidirect
469. C43C2×#2318semidirect
795. C2#19137223direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
#191372232
C2×#145827912
C2×#145827892
C2×#145827862
C2×#145827802
C2×#145827782
C2×#145827762
C2×#145827742
C2×#145827662
C2×#145827642
C2×#145827612
C2×#145827562
C2×C22⋊C4×Dic432
C22×C43⋊#952
C2×C43×#3852
C2×#231843