Finite Group Databasebeta

← C2×#19137031 #25254929

Subgroups — C2×#19137031 #25254929

Order 11008.

4134 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×#13063283C211yesmaximal, characteristic, complemented
3C23×C4×Dic43C211yesmaximal, characteristic, complemented
4#19137031C2116yesmaximal, direct product factor
5C2×#14582791C211yesmaximal, characteristic, complemented
6C2×#14582789C211yesmaximal, characteristic, complemented
7C2×#14582786C211yesmaximal, characteristic, complemented
8C2×#14582780C211yesmaximal, characteristic, complemented
9C2×#14582778C211yesmaximal, characteristic
10C2×#14582776C211yesmaximal, characteristic
11C2×#14582774C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C2×#14582746C211yesmaximal, characteristic, complemented
15C2×#14582744C211yesmaximal, 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—
23C2×#13063283—28no—
24C2×#13063283C2218yescomplemented
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43—28no—
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2218yescomplemented
43#14582791C2218yescomplemented
44#14582789C2218yescomplemented
45#14582786C2218yescomplemented
46#14582780C2218yescomplemented
47#14582778C2218yes—
48#14582776C2218yes—
49#14582774C2218yescomplemented
50C4⋊C4×Dic43C2218yescomplemented
51C22⋊C4×Dic43C2218yescomplemented
52#14582746C2218yescomplemented
53#14582744C2218yescomplemented
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C24×C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C43×#385C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C22×C22⋊D43—24no—
72C22×C22⋊D43—24no—
73C22×C22⋊D43C2×C418yes—
74C22×C22⋊D43C2314yes—
75C23×Dic43—24no—
76C23×Dic43—24no—
77C23×Dic43—24no—
78C23×Dic43—24no—
79C23×Dic43—24no—
80C23×Dic43C2×C418yes—
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2314yes—
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2314yes—
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C22×C4×D43—24no—
91C22×C4×D43—24no—
92C22×C4×D43C2×C418yescomplemented
93C22×C4×D43C2314yes—
94(C22⋊D43)⋊C4C2×C4164yescomplemented
95#13063283—232no—
96C2×C4⋊Dic43—24no—
97C2×C4⋊Dic43—24no—
98C2×C4⋊Dic43C2314yes—
99C2×C4⋊Dic43C2314yes—
100C2×Dic43⋊C4C2×C418yescomplemented
101C2×Dic43⋊C4C2314yes—
102C2×C22⋊Dic43—24no—
103C2×C22⋊Dic43C2314yes—
104C2×(C2×D43)⋊C4—24no—
105C2×(C2×D43)⋊C4—24no—
106C2×(C2×D43)⋊C4—24no—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4C2×C418yescomplemented
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×C4×Dic43—24no—
115C2×C4×Dic43—24no—
116C2×C4×Dic43—24no—
117C2×C4×Dic43—24no—
118C2×C4×Dic43—24no—
119C2×C4×Dic43—232no—
120C2×C4×Dic43C2×C418yescomplemented
121C2×C4×Dic43D418yescomplemented
122C2×C4×Dic43C2314yes—
123C2×C4×Dic43C2314yes—
124C2×C4×Dic43C2314yes—
125C2×C4×Dic43C2314yes—
126C2×C4×Dic43C2314yes—
127C2×C4×Dic43C2314yes—
128C2×C4×Dic43C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C25×C43C2311yescharacteristic
138C23×C4×C43—24no—
139C23×C4×C43—24no—
140C23×C4×C43—24no—
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2314yes—
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43—24no—
149C2×C4⋊C4×C43—24no—
150C2×C4⋊C4×C43C2314yes—
151C2×C4⋊C4×C43C2314yes—
152C2×C22⋊C4×C43—24no—
153C2×C22⋊C4×C43C2×C418yes—
154C2×C22⋊C4×C43C2314yes—
155C2×C22⋊C4×C43C2314yes—
156#95×C43C2314yes—
157#95×C43C2314yes—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43C22×C414yes—
163C24×C43#4114yes—
164C24×C43#4114yes—
165C24×C43C2412yes—
166C24×C43C2411yescharacteristic
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43—22no—
172C23×D43—22no—
173C23×D43C22×C414yes—
174C23×D43C2412yes—
175C22×C4×C43—232no—
176C22×C4×C43—28no—
177C22×C4×C43—28no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—28no—
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—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43C22×C414yes—
194C22×C4×C43C22×C414yes—
195C22×C4×C43C2×D414yes—
196C22×C4×C43#4114yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2412yes—
203C2×C22⋊D43—232no—
204C2×C22⋊D43—28no—
205C2×C22⋊D43—28no—
206C2×C22⋊D43C22×C4116yes—
207C22×Dic43—232no—
208C22×Dic43—232no—
209C22×Dic43—28no—
210C22×Dic43—28no—
211C22×Dic43—28no—
212C22×Dic43—28no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—28no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43—22no—
224C22×Dic43—22no—
225C22×Dic43—22no—
226C22×Dic43—22no—
227C22×Dic43—22no—
228C22×Dic43C22×C414yes—
229C22×Dic43C22×C414yes—
230C22×Dic43C22×C4116yes—
231C22×Dic43C22×C414yes—
232C22×Dic43C2×D414yes—
233C22×Dic43C2×D414yes—
234C22×Dic43#4114yes—
235C22×Dic43#4114yes—
236C22×Dic43C2412yes—
237C22×Dic43C2412yes—
238C22×Dic43C2412yes—
239C22×Dic43C2412yes—
240C22×Dic43C2412yes—
241C22×Dic43C2412yes—
242C22×Dic43C2412yes—
243C2×C4×D43—232no—
244C2×C4×D43—28no—
245C2×C4×D43—28no—
246C2×C4×D43C22×C4116yescomplemented
247C4⋊C4×C43—28no—
248C4⋊C4×C43—28no—
249C22⋊C4×C43—28no—
250C22⋊C4×C43C22×C4116yes—
251C22⋊Dic43—28no—
252(C2×D43)⋊C4—28no—
253(C2×D43)⋊C4—28no—
254(C2×D43)⋊C4—28no—
255(C2×D43)⋊C4—28no—
256(C2×D43)⋊C4C22×C4116yescomplemented
257C4⋊Dic43—28no—
258C4⋊Dic43—28no—
259Dic43⋊C4C22×C4116yescomplemented
260C4×Dic43—28no—
261C4×Dic43—28no—
262C4×Dic43—28no—
263C4×Dic43—28no—
264C4×Dic43—28no—
265C4×Dic43C22×C4116yescomplemented
266C4×Dic43C2×D4116yescomplemented
267C23×C43—28no—
268C23×C43—28no—
269C23×C43—28no—
270C23×C43—28no—
271C23×C43—28no—
272C23×C43—28no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43#117116yescomplemented
278C23×C43C23×C414yes—
279C23×C43C23×C412yes—
280C23×C43C22×D412yes—
281C23×C43C2×#4112yes—
282C23×C43C2×#4112yes—
283C23×C43C2×#4114yes—
284C23×C43C2×#4112yes—
285C23×C43C2×#4112yes—
286C23×C43C2×#4114yes—
287C23×C43C2×#4112yes—
288C23×C43C2511yescharacteristic
289C22×D43—28no—
290C22×D43—28no—
291C22×D43—28no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—44no—
299C22×D43—44no—
300C22×D43—44no—
301C22×D43—44no—
302C22×D43C23×C414yes—
303C2×C4×C43—232no—
304C2×C4×C43—28no—
305C2×C4×C43—28no—
306C2×C4×C43—28no—
307C2×C4×C43—28no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—44no—
323C2×C4×C43—44no—
324C2×C4×C43C23×C414yes—
325C2×C4×C43C23×C414yes—
326C2×C4×C43C22×D414yes—
327C2×C4×C43C2×#4114yes—
328C22⋊D43—232no—
329C2×Dic43—232no—
330C2×Dic43—28no—
331C2×Dic43—28no—
332C2×Dic43—28no—
333C2×Dic43—28no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—232no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—44no—
350C2×Dic43—44no—
351C2×Dic43C4×D4116yes—
352C2×Dic43C23×C414yes—
353C2×Dic43C23×C414yes—
354C2×Dic43C23×C414yes—
355C2×Dic43C22×D414yes—
356C2×Dic43C22×D414yes—
357C2×Dic43C2×#4114yes—
358C2×Dic43C2×#4114yes—
359C4×D43—232no—
360C2×#2290—431nomaximal, Sylow
361C22×C43—24no—
362C22×C43—24no—
363C22×C43—24no—
364C22×C43—24no—
365C22×C43—24no—
366C22×C43—24no—
367C22×C43—232no—
368C22×C43C2×#11714yes—
369C22×C43C2×#11718yescomplemented
370C22×C43C2×C4×D414yes—
371C22×C43C4×#4114yes—
372C22×C43#52514yes—
373C22×C43#52514yes—
374C22×C43#52914yes—
375C22×C43#52914yes—
376C22×C43C24×C411yescharacteristic
377C22×C43C23×D411yescharacteristic
378C22×C43C22×#4111yescharacteristic
379C22×C43C22×#4111yescharacteristic
380C22×C43C22×#4111yescharacteristic
381C22×C43C22×#4111yescharacteristic
382C22×C43C22×#4111yescharacteristic
383C2×D43—24no—
384C2×D43—24no—
385C2×D43—24no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—416no—
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—24no—
394C4×C43—24no—
395C4×C43—42no—
396C4×C43—42no—
397Dic43—24no—
398Dic43—24no—
399Dic43—24no—
400Dic43—24no—
401Dic43—42no—
402Dic43—42no—
403Dic43C2×C4×D418yes—
404C22×C4×D4—431no—
405C22×#117—431no—
406C23×C42—431no—
407#2290—4316no—
408C2×#388—431no—
409C2×#388—431no—
410C2×#387—431no—
411C2×#387—431no—
412C2×#386—431no—
413C2×#386—431no—
414C2×#385—431no—
415C2×#385D4311yescharacteristic, complemented
416C2×C4×C4⋊C4—431no—
417C2×C4×C22⋊C4—431no—
418C2×C4×C22⋊C4—431no—
419C2×#376—431no—
420C2×C43—28no—
421C2×C43#229018yescomplemented
422C2×C43C22×#11711yescharacteristic
423C2×C43C22×C4×D411yescharacteristic
424C2×C43C2×C4×#4111yescharacteristic
425C2×C43C2×#52511yescharacteristic
426C2×C43C2×#52511yescharacteristic
427C2×C43C2×#52911yescharacteristic
428C2×C43C2×#52911yescharacteristic
429D43—44no—
430C23×D4—431no—
431C24×C4—431no—
432C24×C4—431no—
433C24×C4—431no—
434C24×C4C2×D4311yescharacteristic
435C2×C4×D4—438no—
436C2×C4×D4—4316no—
437C2×#117—438no—
438C2×#117—868no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4C2×D4311yescharacteristic
443C22×C4⋊C4C2×D4311yescharacteristic
444C22×C22⋊C4—431no—
445C22×C22⋊C4—431no—
446C22×C22⋊C4—431no—
447C22×C22⋊C4—431no—
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4C2×D4311yescharacteristic
451C22×C22⋊C4C2×D4311yescharacteristic
452C22×C42—431no—
453C22×C42—431no—
454C22×C42—431no—
455C22×C42—431no—
456C22×C42—431no—
457C22×C42—431no—
458C22×C42—431no—
459C22×C42—438no—
460C22×C42—868no—
461#388—438no—
462#388—438no—
463#387—438no—
464#387—438no—
465#386—438no—
466#386—438no—
467#385—438no—
468#385C2×D4318yescomplemented
469C4×C4⋊C4—438no—
470C4×C22⋊C4—438no—
471C4×C22⋊C4—438no—
472#376—438no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95—431no—
480C2×#95—431no—
481C2×#95C2×D4311yescharacteristic
482C2×#95C2×D4311yescharacteristic
483C43C2×#229011yescharacteristic, complemented, Sylow
484C25—431no—
485C25C22×D4311yescharacteristic
486C22×D4—438no—
487C22×D4—434no—
488C22×D4—864no—
489C22×D4—864no—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—431no—
494C23×C4—438no—
495C23×C4—434no—
496C23×C4—431no—
497C23×C4—431no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—438no—
501C23×C4—434no—
502C23×C4—434no—
503C23×C4—431no—
504C23×C4—431no—
505C23×C4—864no—
506C23×C4—864no—
507C23×C4—864no—
508C23×C4—864no—
509C23×C4—864no—
510C23×C4—864no—
511C23×C4—864no—
512C23×C4C22×D4314yes—
513C23×C4C22×D4311yescharacteristic
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C23×C4C22×D4311yescharacteristic
517C23×C4C22×D4311yescharacteristic
518C23×C4C22×D4311yescharacteristic
519C4×D4—4364no—
520#117—8632no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—438no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—434no—
526C2×C4⋊C4—434no—
527C2×C4⋊C4—864no—
528C2×C4⋊C4—864no—
529C2×C4⋊C4C22×D4314yes—
530C2×C4⋊C4C22×D4314yes—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—438no—
533C2×C22⋊C4—434no—
534C2×C22⋊C4—434no—
535C2×C22⋊C4—434no—
536C2×C22⋊C4—434no—
537C2×C22⋊C4—434no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—864no—
540C2×C22⋊C4—864no—
541C2×C22⋊C4—864no—
542C2×C22⋊C4—864no—
543C2×C22⋊C4—864no—
544C2×C22⋊C4C4×D4318yes—
545C2×C22⋊C4C22×D4314yes—
546C2×C22⋊C4C22×D4314yes—
547C2×C42—438no—
548C2×C42—438no—
549C2×C42—434no—
550C2×C42—434no—
551C2×C42—434no—
552C2×C42—434no—
553C2×C42—434no—
554C2×C42—434no—
555C2×C42—434no—
556C2×C42—8632no—
557C2×C42—864no—
558C2×C42—864no—
559C2×C42—864no—
560C2×C42—864no—
561C2×C42—864no—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95—434no—
569#95—434no—
570#95C22×D4314yes—
571#95C22×D4314yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—434no—
577C24—432no—
578C24—862no—
579C24—862no—
580C24—862no—
581C24—862no—
582C24—862no—
583C24—862no—
584C24C2×C4×D4314yes—
585C24#1062190014yes—
586C24#1062190214yes—
587C24C23×D4312yes—
588C24C23×D4311yescharacteristic
589C2×D4—4316no—
590C2×D4—8632no—
591C2×D4—868no—
592C2×D4—868no—
593C22×C4—232no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—28no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—434no—
612C22×C4—434no—
613C22×C4—434no—
614C22×C4—432no—
615C22×C4—434no—
616C22×C4—434no—
617C22×C4—4316no—
618C22×C4—434no—
619C22×C4—434no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—4316no—
625C22×C4—432no—
626C22×C4—432no—
627C22×C4—868no—
628C22×C4—8632no—
629C22×C4—868no—
630C22×C4—868no—
631C22×C4—868no—
632C22×C4—8632no—
633C22×C4—868no—
634C22×C4—868no—
635C22×C4—8632no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—862no—
641C22×C4—868no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4C2×C4×D4314yes—
652C22×C4C2×C4×D4314yes—
653C22×C4D4×D4314yes—
654C22×C4#1062190014yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C22×C4C23×D4312yes—
658C22×C4C23×D4312yes—
659C22×C4C23×D4312yes—
660C22×C4C23×D4312yes—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—4316no—
664C4⋊C4—868no—
665C4⋊C4—868no—
666C22⋊C4—28no—
667C22⋊C4—4316no—
668C22⋊C4—868no—
669C22⋊C4—868no—
670C22⋊C4—868no—
671C22⋊C4—868no—
672C22⋊C4—868no—
673C22⋊C4C2×C4×D43116yes—
674C42—4316no—
675C42—4316no—
676C42—868no—
677C42—868no—
678C42—868no—
679C42—868no—
680C42—868no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—434no—
692C23—868no—
693C23—868no—
694C23—868no—
695C23—862no—
696C23—862no—
697C23—862no—
698C23—862no—
699C23—862no—
700C23—862no—
701C23—1724no—
702C23—1724no—
703C23—1724no—
704C23—1724no—
705C23#13063283116yescomplemented
706C23C22×C4×D4314yes—
707C23C22×C4×D4312yes—
708C23C2×D4×D4312yes—
709C23#41×D4312yes—
710C23#41×D4312yes—
711C23C2×#1062190014yes—
712C23C2×#1062190012yes—
713C23C2×#1062190012yes—
714C23C2×#1062190214yes—
715C23C2×#1062190212yes—
716C23C24×D4311yescharacteristic
717D4—8632no—
718C2×C4—232no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—4316no—
740C2×C4—434no—
741C2×C4—434no—
742C2×C4—434no—
743C2×C4—434no—
744C2×C4—434no—
745C2×C4—434no—
746C2×C4—434no—
747C2×C4—8632no—
748C2×C4—8632no—
749C2×C4—8632no—
750C2×C4—868no—
751C2×C4—868no—
752C2×C4—868no—
753C2×C4—868no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—1724no—
769C2×C4—1724no—
770C2×C4C22×C4×D4314yes—
771C2×C4C22×C4×D4314yes—
772C2×C4C2×D4×D4314yes—
773C2×C4C2×#1062190014yes—
774C22—232no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—864no—
782C22—864no—
783C22—864no—
784C22—17216no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22C2×#1306328314yes—
790C22C2×#1306328318yescomplemented
791C22C4×D4×D4314yes—
792C22C4×#1062190014yes—
793C22#1458340514yes—
794C22#1458341214yes—
795C22#1458342614yes—
796C22#1458343514yes—
797C22C23×C4×D4311yescharacteristic
798C22C22×D4×D4311yescharacteristic
799C22C2×#41×D4311yescharacteristic
800C22C2×#41×D4311yescharacteristic
801C22C22×#1062190011yescharacteristic
802C22C22×#1062190011yescharacteristic
803C22C22×#1062190211yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—438no—
811C4—864no—
812C4—864no—
813C4—864no—
814C4—864no—
815C4—1722no—
816C4—1722no—
817C2—28no—
818C2—1724no—
819C2#1913703118yesdirect product factor
820C2C22×#1306328311yescharacteristic
821C2C2×C4×D4×D4311yescharacteristic
822C2C2×C4×#1062190011yescharacteristic
823C2C2×#1458340511yescharacteristic
824C2C2×#1458341211yescharacteristic
825C2C2×#1458342611yescharacteristic
826C2C2×#1458343511yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×#2290
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#13063283C2semidirect
3. C23×C4×Dic43C2semidirect
4. #19137031C2direct (N × H)
5. C2×#14582791C2semidirect
6. C2×#14582789C2semidirect
7. C2×#14582786C2semidirect
8. C2×#14582780C2semidirect
11. C2×#14582774C2semidirect
12. C2×C4⋊C4×Dic43C2semidirect
13. C2×C22⋊C4×Dic43C2semidirect
14. C2×#14582746C2semidirect
15. C2×#14582744C2semidirect
16. C2×C43×#385C2semidirect
21. C2×(C22⋊D43)⋊C4C4semidirect
24. C2×#13063283C22semidirect
42. C22×C4×Dic43C22semidirect
43. #14582791C22semidirect
44. #14582789C22semidirect
45. #14582786C22semidirect
46. #14582780C22semidirect
49. #14582774C22semidirect
50. C4⋊C4×Dic43C22semidirect
51. C22⋊C4×Dic43C22semidirect
52. #14582746C22semidirect
53. #14582744C22semidirect
67. C43×#385C22semidirect
92. C22×C4×D43C2×C4semidirect
94. (C22⋊D43)⋊C4C2×C4semidirect
100. C2×Dic43⋊C4C2×C4semidirect
108. C2×(C2×D43)⋊C4C2×C4semidirect
120. C2×C4×Dic43C2×C4semidirect
121. C2×C4×Dic43D4semidirect
246. C2×C4×D43C22×C4semidirect
256. (C2×D43)⋊C4C22×C4semidirect
259. Dic43⋊C4C22×C4semidirect
265. C4×Dic43C22×C4semidirect
266. C4×Dic43C2×D4semidirect
277. C23×C43#117semidirect
369. C22×C43C2×#117semidirect
415. C2×#385D43semidirect
421. C2×C43#2290semidirect
468. #385C2×D43semidirect
483. C43C2×#2290semidirect
705. C23#13063283semidirect
790. C22C2×#13063283semidirect
819. C2#19137031direct (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
C22×#130632832
C23×C4×Dic432
#191370312
C2×#145827912
C2×#145827892
C2×#145827862
C2×#145827802
C2×#145827782
C2×#145827762
C2×#145827742
C2×C4⋊C4×Dic432
C2×C22⋊C4×Dic432
C2×#145827462
C2×#145827442
C2×C43×#3852
C2×#229043