Finite Group Databasebeta

← C2×#19138076 #25264306

Subgroups — C2×#19138076 #25264306

Order 11008.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063308C211yesmaximal, characteristic
2C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
3#19138076C2116yesmaximal, direct product factor
4C2×#14582840C211yesmaximal, characteristic, complemented
5C2×#14582833C211yesmaximal, characteristic, complemented
6C2×#14582828C211yesmaximal, characteristic, complemented
7C2×#14582826C211yesmaximal, characteristic, complemented
8C2×#14582782C211yesmaximal, characteristic, complemented
9C2×#14582781C211yesmaximal, characteristic, complemented
10C2×#14582776C211yesmaximal, characteristic
11C2×#14582774C211yesmaximal, characteristic, complemented
12C2×#14582773C211yesmaximal, characteristic, complemented
13C2×#14582761C211yesmaximal, characteristic, complemented
14C2×#14582757C211yesmaximal, characteristic, complemented
15C22×C43⋊#95C211yesmaximal, characteristic, complemented
16C2×C43×#381C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063308—28no—
22C2×#13063308C2218yes—
23C2×(C22⋊D43)⋊C4—28no—
24C2×(C22⋊D43)⋊C4C2218yes—
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39#14582840C2218yescomplemented
40#14582833C2218yescomplemented
41#14582828C2218yescomplemented
42#14582826C2218yescomplemented
43#14582782C2218yescomplemented
44#14582781C2218yescomplemented
45#14582776C2218yes—
46#14582774C2218yescomplemented
47#14582773C2218yescomplemented
48#14582761C2218yescomplemented
49#14582757C2218yescomplemented
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⋊#95C2211yescharacteristic
60C2×C43⋊#95C2218yescomplemented
61C24×C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C43×#381C2218yescomplemented
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C22×C22⋊D43—24no—
71C22×C22⋊D43—24no—
72C22×C22⋊D43D418yes—
73C22×C22⋊D43C2314yes—
74C23×Dic43—24no—
75C23×Dic43—24no—
76C23×Dic43—24no—
77C23×Dic43—24no—
78C23×Dic43—42no—
79C23×Dic43—42no—
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2314yes—
85C23×Dic43C2314yes—
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C22×C4×D43—24no—
90C22×C4×D43—24no—
91C22×C4×D43—42no—
92C22×C4×D43C2314yes—
93#13063308—232no—
94(C22⋊D43)⋊C4—232no—
95C2×C4⋊Dic43—24no—
96C2×C4⋊Dic43—42no—
97C2×C4⋊Dic43C2314yes—
98C2×C4⋊Dic43C2314yes—
99C2×Dic43⋊C4—24no—
100C2×Dic43⋊C4—24no—
101C2×Dic43⋊C4—24no—
102C2×Dic43⋊C4—24no—
103C2×Dic43⋊C4—42no—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×C22⋊Dic43—24no—
110C2×C22⋊Dic43C2314yes—
111C2×(C2×D43)⋊C4—24no—
112C2×(C2×D43)⋊C4—24no—
113C2×(C2×D43)⋊C4—24no—
114C2×(C2×D43)⋊C4—24no—
115C2×(C2×D43)⋊C4—42no—
116C2×(C2×D43)⋊C4C2314yes—
117C2×(C2×D43)⋊C4C2314yes—
118C2×(C2×D43)⋊C4C2314yes—
119C2×(C2×D43)⋊C4C2314yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×C4×Dic43—24no—
122C2×C4×Dic43C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C25×C43C2311yescharacteristic
134C23×C4×C43—24no—
135C23×C4×C43—24no—
136C23×C4×C43—24no—
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2314yes—
144C2×C22⋊C4×C43—24no—
145C2×C22⋊C4×C43—24no—
146C2×C22⋊C4×C43C2314yes—
147C2×C22⋊C4×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150#95×C43C2314yes—
151#95×C43C2314yes—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43C2×D414yes—
157C24×C43#4114yes—
158C24×C43#4114yes—
159C24×C43C2412yes—
160C24×C43C2411yescharacteristic
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43C2×D414yes—
168C23×D43C2412yes—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—28no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—28no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—28no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—416no—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C2×C22⋊D43—232no—
198C2×C22⋊D43—28no—
199C2×C22⋊D43—28no—
200C2×C22⋊D43C2×D4116yes—
201C22×Dic43—28no—
202C22×Dic43—28no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—28no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—28no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43—44no—
224C22×Dic43—44no—
225C22×Dic43—416no—
226C22×Dic43—416no—
227C22×Dic43C2×D414yes—
228C22×Dic43#4114yes—
229C22×Dic43#4114yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C22×Dic43C2412yes—
236C22×Dic43C2412yes—
237C2×C4×D43—28no—
238C2×C4×D43—28no—
239C2×C4×D43—44no—
240C2×C4×D43—416no—
241C22⋊C4×C43—28no—
242C22⋊C4×C43—28no—
243C22⋊Dic43—28no—
244(C2×D43)⋊C4—28no—
245(C2×D43)⋊C4—28no—
246(C2×D43)⋊C4—28no—
247(C2×D43)⋊C4—28no—
248(C2×D43)⋊C4—44no—
249C4⋊Dic43—28no—
250C4⋊Dic43—44no—
251Dic43⋊C4—28no—
252Dic43⋊C4—28no—
253Dic43⋊C4—28no—
254Dic43⋊C4—28no—
255Dic43⋊C4—44no—
256C4×Dic43—28no—
257C23×C43—28no—
258C23×C43—28no—
259C23×C43—28no—
260C23×C43—28no—
261C23×C43—28no—
262C23×C43—28no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43#123116yes—
268C23×C43C22×D414yes—
269C23×C43C22×D412yes—
270C23×C43C2×#4112yes—
271C23×C43C2×#4112yes—
272C23×C43C2×#4114yes—
273C23×C43C2×#4112yes—
274C23×C43C2×#4114yes—
275C23×C43C2×#4112yes—
276C23×C43H(5,𝔽2)12yes—
277C23×C432−1+412yes—
278C23×C43C2511yescharacteristic
279C22×D43—28no—
280C22×D43—28no—
281C22×D43—28no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43—44no—
291C22×D43—44no—
292C22×D43C22×D414yes—
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—22no—
310C2×C4×C43—22no—
311C2×C4×C43—416no—
312C2×C4×C43—44no—
313C2×C4×C43—44no—
314C2×C4×C43—44no—
315C2×C4×C43—44no—
316C2×C4×C43—44no—
317C2×C4×C43—44no—
318C22⋊D43—232no—
319C2×Dic43—28no—
320C2×Dic43—28no—
321C2×Dic43—28no—
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—22no—
339C2×Dic43—22no—
340C2×Dic43—416no—
341C2×Dic43—416no—
342C2×Dic43—44no—
343C2×Dic43—44no—
344C2×Dic43—44no—
345C2×Dic43—44no—
346C2×Dic43C22×D414yes—
347C2×Dic43C2×#4114yes—
348C2×Dic43C2×#4114yes—
349C4×D43—416no—
350C2×#2419—431nomaximal, Sylow
351C22×C43—24no—
352C22×C43—232no—
353C22×C43—24no—
354C22×C43—24no—
355C22×C43—24no—
356C22×C43—24no—
357C22×C43—24no—
358C22×C43C2×#12318yes—
359C22×C43C2×#12314yes—
360C22×C43#52914yes—
361C22×C43#53914yes—
362C22×C43#54614yes—
363C22×C43#54714yes—
364C22×C43#55114yes—
365C22×C43#55214yes—
366C22×C43C23×D411yescharacteristic
367C22×C43C22×#4111yescharacteristic
368C22×C43C22×#4111yescharacteristic
369C22×C43C22×#4111yescharacteristic
370C22×C43C22×#4111yescharacteristic
371C22×C43C2×H(5,𝔽2)11yescharacteristic
372C22×C43C2×2−1+411yescharacteristic
373C2×D43—24no—
374C2×D43—24no—
375C2×D43—24no—
376C2×D43—42no—
377C2×D43—416no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43—42no—
387Dic43—24no—
388Dic43—24no—
389Dic43—24no—
390Dic43—42no—
391Dic43—42no—
392Dic43—42no—
393Dic43—42no—
394C22×#123—431no—
395C22×C4×D4—431no—
396#2419—4316no—
397C2×#400—431no—
398C2×#398—431no—
399C2×#397—431no—
400C2×#397—431no—
401C2×#387—431no—
402C2×#387—431no—
403C2×#386—431no—
404C2×#385—431no—
405C2×#385—431no—
406C2×#381—431no—
407C2×#381D4311yescharacteristic, complemented
408C2×#380—431no—
409C22×#95—431no—
410C2×C43—28no—
411C2×C43#241918yescomplemented
412C2×C43C22×#12311yescharacteristic
413C2×C43C2×#52911yescharacteristic
414C2×C43C2×#53911yescharacteristic
415C2×C43C2×#54611yescharacteristic
416C2×C43C2×#54711yescharacteristic
417C2×C43C2×#55111yescharacteristic
418C2×C43C2×#55211yescharacteristic
419D43—44no—
420C23×D4—431no—
421C24×C4—431no—
422C24×C4—431no—
423C24×C4—431no—
424C24×C4C2×D4311yescharacteristic
425C2×#123—438no—
426C2×#123—868no—
427C2×C4×D4—438no—
428C2×C4×D4—868no—
429C22×C4⋊C4—431no—
430C22×C4⋊C4—431no—
431C22×C4⋊C4—431no—
432C22×C4⋊C4—431no—
433C22×C4⋊C4—431no—
434C22×C4⋊C4—431no—
435C22×C4⋊C4—431no—
436C22×C22⋊C4—431no—
437C22×C22⋊C4—431no—
438C22×C22⋊C4—431no—
439C22×C22⋊C4—431no—
440C22×C22⋊C4—431no—
441C22×C22⋊C4—431no—
442C22×C22⋊C4C2×D4311yescharacteristic
443C22×C22⋊C4C2×D4311yescharacteristic
444C22×C42—431no—
445#400—438no—
446#398—438no—
447#397—438no—
448#397—438no—
449#387—438no—
450#387—438no—
451#386—438no—
452#385—438no—
453#385—438no—
454#381—438no—
455#381C2×D4318yescomplemented
456#380—438no—
457C2×#95—431no—
458C2×#95—431no—
459C2×#95—431no—
460C2×#95—431no—
461C2×#95—431no—
462C2×#95—431no—
463C2×#95—431no—
464C2×#95—438no—
465C2×#95—431no—
466C2×#95—431no—
467C2×#95—431no—
468C2×#95C2×D4311yescharacteristic
469C2×#95C2×D4311yescharacteristic
470C2×#95C2×D4311yescharacteristic
471C2×#95C2×D4311yescharacteristic
472C43C2×#241911yescharacteristic, complemented, Sylow
473C25—431no—
474C25C22×D4311yescharacteristic
475C22×D4—438no—
476C22×D4—434no—
477C22×D4—864no—
478C22×D4—864no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—434no—
490C23×C4—434no—
491C23×C4—434no—
492C23×C4—864no—
493C23×C4—864no—
494C23×C4—864no—
495C23×C4—864no—
496C23×C4—864no—
497C23×C4—864no—
498C23×C4—1722no—
499C23×C4—1722no—
500C23×C4—1722no—
501C23×C4C22×D4314yes—
502C23×C4C22×D4311yescharacteristic
503C23×C4C22×D4311yescharacteristic
504C23×C4C22×D4311yescharacteristic
505C23×C4C22×D4311yescharacteristic
506C23×C4C22×D4311yescharacteristic
507C23×C4C22×D4311yescharacteristic
508#123—8632no—
509C4×D4—8632no—
510C2×C4⋊C4—434no—
511C2×C4⋊C4—434no—
512C2×C4⋊C4—434no—
513C2×C4⋊C4—434no—
514C2×C4⋊C4—434no—
515C2×C4⋊C4—434no—
516C2×C4⋊C4—434no—
517C2×C4⋊C4—864no—
518C2×C4⋊C4—864no—
519C2×C4⋊C4—864no—
520C2×C4⋊C4—864no—
521C2×C4⋊C4—864no—
522C2×C4⋊C4—1722no—
523C2×C4⋊C4—1722no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—434no—
527C2×C22⋊C4—434no—
528C2×C22⋊C4—434no—
529C2×C22⋊C4—434no—
530C2×C22⋊C4—434no—
531C2×C22⋊C4—434no—
532C2×C22⋊C4—864no—
533C2×C22⋊C4—864no—
534C2×C22⋊C4—864no—
535C2×C22⋊C4—864no—
536C2×C22⋊C4—864no—
537C2×C22⋊C4—1722no—
538C2×C22⋊C4C22×D4314yes—
539C2×C22⋊C4C22×D4314yes—
540C2×C42—434no—
541C2×C42—864no—
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#95—434no—
551#95—434no—
552#95C22×D4314yes—
553#95C22×D4314yes—
554#95C22×D4314yes—
555#95C22×D4314yes—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—434no—
561C24—432no—
562C24—862no—
563C24—862no—
564C24—862no—
565C24—862no—
566C24—862no—
567C24—862no—
568C24#1062189814yes—
569C24D4×D4314yes—
570C24#1062190014yes—
571C24C23×D4312yes—
572C24C23×D4311yescharacteristic
573C2×D4—4316no—
574C2×D4—8632no—
575C2×D4—868no—
576C2×D4—868no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—28no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—416no—
599C22×C4—434no—
600C22×C4—434no—
601C22×C4—434no—
602C22×C4—432no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—432no—
606C22×C4—432no—
607C22×C4—432no—
608C22×C4—432no—
609C22×C4—868no—
610C22×C4—868no—
611C22×C4—868no—
612C22×C4—868no—
613C22×C4—862no—
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—868no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—868no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—1724no—
634C22×C4—17216no—
635C22×C4—1724no—
636C22×C4—1724no—
637C22×C4—17216no—
638C22×C4—17216no—
639C22×C4C23×D4312yes—
640C22×C4C23×D4312yes—
641C22×C4C23×D4312yes—
642C22×C4C23×D4312yes—
643C22×C4C23×D4312yes—
644C22×C4C23×D4312yes—
645C4⋊C4—868no—
646C4⋊C4—868no—
647C4⋊C4—868no—
648C4⋊C4—868no—
649C4⋊C4—868no—
650C4⋊C4—1724no—
651C4⋊C4—1724no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—868no—
655C22⋊C4—868no—
656C22⋊C4—868no—
657C22⋊C4—868no—
658C22⋊C4—868no—
659C22⋊C4—1724no—
660C42—868no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—434no—
672C23—868no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—868no—
680C23—868no—
681C23—1724no—
682C23—1724no—
683C23—1724no—
684C23—1724no—
685C23#13063307116yes—
686C23C2×D4×D4314yes—
687C23C2×D4×D4312yes—
688C23#41×D4312yes—
689C23#41×D4312yes—
690C23C2×#1062190014yes—
691C23C2×#1062190012yes—
692C23C2×#1062189814yes—
693C23C2×#1062189812yes—
694C23#1306337112yes—
695C23#1306337212yes—
696C23C24×D4311yescharacteristic
697D4—8632no—
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—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—416no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—434no—
724C2×C4—434no—
725C2×C4—434no—
726C2×C4—868no—
727C2×C4—868no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—868no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—17216no—
748C2×C4—17216no—
749C2×C4—17216no—
750C2×C4—1724no—
751C2×C4—1724no—
752C2×C4—1724no—
753C2×C4—1724no—
754C22—24no—
755C22—24no—
756C22—232no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—864no—
762C22—864no—
763C22—864no—
764C22—17216no—
765C22—1722no—
766C22—1722no—
767C22—1722no—
768C22—1722no—
769C22C2×#1306330718yes—
770C22C2×#1306330714yes—
771C22#1458342614yes—
772C22#1458349314yes—
773C22#1458354114yes—
774C22#1458354714yes—
775C22#1458357314yes—
776C22#1458358214yes—
777C22C22×D4×D4311yescharacteristic
778C22C2×#41×D4311yescharacteristic
779C22C2×#41×D4311yescharacteristic
780C22C22×#1062190011yescharacteristic
781C22C22×#1062189811yescharacteristic
782C22C2×#1306337111yescharacteristic
783C22C2×#1306337211yescharacteristic
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—864no—
791C4—864no—
792C4—864no—
793C4—1722no—
794C4—1722no—
795C4—1722no—
796C4—1722no—
797C2—28no—
798C2—1724no—
799C2#1913807618yesdirect product factor
800C2C22×#1306330711yescharacteristic
801C2C2×#1458342611yescharacteristic
802C2C2×#1458349311yescharacteristic
803C2C2×#1458354111yescharacteristic
804C2C2×#1458354711yescharacteristic
805C2C2×#1458357311yescharacteristic
806C2C2×#1458358211yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#381C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#381D43
hypocenterC43C2×#2419
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #19138076C2direct (N × H)
4. C2×#14582840C2semidirect
5. C2×#14582833C2semidirect
6. C2×#14582828C2semidirect
7. C2×#14582826C2semidirect
8. C2×#14582782C2semidirect
9. C2×#14582781C2semidirect
11. C2×#14582774C2semidirect
12. C2×#14582773C2semidirect
13. C2×#14582761C2semidirect
14. C2×#14582757C2semidirect
15. C22×C43⋊#95C2semidirect
16. C2×C43×#381C2semidirect
39. #14582840C22semidirect
40. #14582833C22semidirect
41. #14582828C22semidirect
42. #14582826C22semidirect
43. #14582782C22semidirect
44. #14582781C22semidirect
46. #14582774C22semidirect
47. #14582773C22semidirect
48. #14582761C22semidirect
49. #14582757C22semidirect
60. C2×C43⋊#95C22semidirect
64. C43×#381C22semidirect
407. C2×#381D43semidirect
411. C2×C43#2419semidirect
455. #381C2×D43semidirect
472. C43C2×#2419semidirect
799. C2#19138076direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633082
C22×(C22⋊D43)⋊C42
#191380762
C2×#145828402
C2×#145828332
C2×#145828282
C2×#145828262
C2×#145827822
C2×#145827812
C2×#145827762
C2×#145827742
C2×#145827732
C2×#145827612
C2×#145827572
C22×C43⋊#952
C2×C43×#3812
C2×#241943