Finite Group Databasebeta

← C2×#19137304 #25255382

Subgroups — C2×#19137304 #25255382

Order 11008.

3566 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063311C211yesmaximal, characteristic
2C22×C4×Dic86C211yesmaximal, characteristic, complemented
3C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
4#19137304C2116yesmaximal, direct product factor
5C2×#14582803C211yesmaximal, characteristic, complemented
6C2×#14582799C211yesmaximal, characteristic
7C2×#14582791C211yesmaximal, characteristic, complemented
8C2×#14582790C211yesmaximal, characteristic, complemented
9C2×#14582787C211yesmaximal, characteristic, complemented
10C2×#14582774C211yesmaximal, characteristic, complemented
11C2×#14582773C211yesmaximal, characteristic, complemented
12C2×#14582771C211yesmaximal, characteristic, complemented
13C2×#14582770C211yesmaximal, characteristic, complemented
14C2×#14582768C211yesmaximal, characteristic, complemented
15C2×#14582744C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063311C4116yescomplemented
22C2×#13063311C2218yes—
23C2×C4×Dic86—28no—
24C2×C4×Dic86C2218yescomplemented
25C2×(C22⋊D43)⋊C4—28no—
26C2×(C22⋊D43)⋊C4C2218yes—
27C22×C4⋊Dic43C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×C22⋊Dic43C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43C22×C4×Dic43C2211yescharacteristic
44C22×C4×Dic43C2211yescharacteristic
45#14582803C2218yescomplemented
46#14582799C2218yes—
47#14582791C2218yescomplemented
48#14582790C2218yescomplemented
49#14582787C2218yescomplemented
50#14582774C2218yescomplemented
51#14582773C2218yescomplemented
52#14582771C2218yescomplemented
53#14582770C2218yescomplemented
54#14582768C2218yescomplemented
55#14582744C2218yescomplemented
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C42×C43C2211yescharacteristic
67C43×#388C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C22×Dic86—24no—
72C22×Dic86—24no—
73C22×Dic86C2×C418yescomplemented
74C22×Dic86C2314yes—
75C22×C22⋊D43—24no—
76C22×C22⋊D43—24no—
77C22×C22⋊D43C2×C418yes—
78C22×C22⋊D43C2314yes—
79C23×Dic43—24no—
80C23×Dic43—42no—
81C23×Dic43—42no—
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2314yes—
89C23×Dic43C2311yescharacteristic
90C22×C4×D43—24no—
91C22×C4×D43—42no—
92C22×C4×D43—42no—
93C22×C4×D43C2314yes—
94#13063311C2×C4164yescomplemented
95C4×Dic86—232no—
96(C22⋊D43)⋊C4—232no—
97C2×C4⋊Dic43—24no—
98C2×C4⋊Dic43—42no—
99C2×C4⋊Dic43C2314yes—
100C2×C4⋊Dic43C2314yes—
101C2×Dic43⋊C4—24no—
102C2×Dic43⋊C4—24no—
103C2×Dic43⋊C4—24no—
104C2×Dic43⋊C4—42no—
105C2×Dic43⋊C4—42no—
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2314yes—
111C2×C22⋊Dic43—42no—
112C2×C22⋊Dic43C2×C418yescomplemented
113C2×C22⋊Dic43C2314yes—
114C2×C22⋊Dic43C2314yes—
115C2×(C2×D43)⋊C4—24no—
116C2×(C2×D43)⋊C4—42no—
117C2×(C2×D43)⋊C4—42no—
118C2×(C2×D43)⋊C4C2×C418yescomplemented
119C2×(C2×D43)⋊C4C2×C418yescomplemented
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×C4×Dic43—24no—
126C2×C4×Dic43—24no—
127C2×C4×Dic43C2×C418yescomplemented
128C2×C4×Dic43D418yes—
129C2×C4×Dic43C2314yes—
130C2×C4×Dic43C2314yes—
131C2×C4×Dic43C2314yes—
132C2×C4×Dic43C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C25×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43—42no—
147C2×C4⋊C4×C43C2314yes—
148C2×C22⋊C4×C43—24no—
149C2×C22⋊C4×C43—42no—
150C2×C22⋊C4×C43C2×C418yescomplemented
151C2×C22⋊C4×C43C2314yes—
152C2×C22⋊C4×C43C2314yes—
153C2×C22⋊C4×C43C2314yes—
154C2×C42×C43—24no—
155C2×C42×C43C2314yes—
156#95×C43C2314yes—
157#95×C43C2314yes—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43C22×C414yes—
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—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—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43C22×C414yes—
191C22×C4×C43C22×C414yes—
192C22×C4×C43C2×D414yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C2×C22⋊D43—232no—
200C2×C22⋊D43—28no—
201C2×C22⋊D43—28no—
202C2×C22⋊D43C22×C4116yes—
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—22no—
219C22×Dic43—44no—
220C22×Dic43—44no—
221C22×Dic43—416no—
222C22×Dic43C22×C414yes—
223C22×Dic43C22×C414yes—
224C22×Dic43C22×C414yes—
225C22×Dic43C2×D414yes—
226C22×Dic43C2×D414yes—
227C22×Dic43#4114yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C2×C4×D43—28no—
236C2×C4×D43—44no—
237C2×C4×D43—44no—
238C2×C4×D43—416no—
239C2×Dic86—232no—
240C2×Dic86—28no—
241C2×Dic86—28no—
242C2×Dic86C22×C4116yescomplemented
243C4⋊C4×C43—44no—
244C22⋊C4×C43—28no—
245C22⋊C4×C43—44no—
246C22⋊C4×C43C22×C4116yescomplemented
247C42×C43—28no—
248C22⋊Dic43—44no—
249C22⋊Dic43C22×C4116yescomplemented
250(C2×D43)⋊C4—28no—
251(C2×D43)⋊C4—44no—
252(C2×D43)⋊C4—44no—
253(C2×D43)⋊C4C22×C4116yescomplemented
254(C2×D43)⋊C4C22×C4116yescomplemented
255C4⋊Dic43—28no—
256C4⋊Dic43—44no—
257Dic43⋊C4—28no—
258Dic43⋊C4—28no—
259Dic43⋊C4—28no—
260Dic43⋊C4—44no—
261Dic43⋊C4—44no—
262C4×Dic43—28no—
263C4×Dic43—28no—
264C4×Dic43C22×C4116yescomplemented
265C4×Dic43C2×D4116yes—
266C23×C43—28no—
267C23×C43—28no—
268C23×C43—28no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—44no—
276C23×C43—44no—
277C23×C43—44no—
278C23×C43—44no—
279C23×C43C23×C414yes—
280C23×C43C23×C412yes—
281C23×C43C22×D412yes—
282C23×C43C2×#4112yes—
283C23×C43H(5,𝔽2)12yes—
284C23×C43H(5,𝔽2)12yes—
285C23×C432−1+412yes—
286C23×C432−1+412yes—
287C23×C43C2511yescharacteristic
288C22×D43—28no—
289C22×D43—28no—
290C22×D43—28no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—44no—
298C22×D43—44no—
299C22×D43—44no—
300C22×D43—44no—
301C22×D43C23×C414yes—
302C2×C4×C43—28no—
303C2×C4×C43—28no—
304C2×C4×C43—28no—
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—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—44no—
321C2×C4×C43—44no—
322C2×C4×C43—44no—
323C2×C4×C43C23×C414yes—
324C2×C4×C43C23×C414yes—
325C2×C4×C43C22×D414yes—
326C22⋊D43—232no—
327C2×Dic43—28no—
328C2×Dic43—28no—
329C2×Dic43—28no—
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—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—416no—
346C2×Dic43—44no—
347C2×Dic43—44no—
348C2×Dic43—44no—
349C2×Dic43C4×D4116yes—
350C2×Dic43C23×C414yes—
351C2×Dic43C23×C414yes—
352C2×Dic43C23×C414yes—
353C2×Dic43C22×D414yes—
354C2×Dic43C22×D414yes—
355C2×Dic43C2×#4114yes—
356C4×D43—416no—
357Dic86—232no—
358C2×#2326—431nomaximal, Sylow
359C22×C43—24no—
360C22×C43—24no—
361C22×C43—24no—
362C22×C43—416no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43C2×C4×D414yes—
368C22×C43#52014yes—
369C22×C43#52014yes—
370C22×C43#53514yes—
371C22×C43#53614yes—
372C22×C43#54214yes—
373C22×C43#54214yes—
374C22×C43C24×C411yescharacteristic
375C22×C43C23×D411yescharacteristic
376C22×C43C22×#4111yescharacteristic
377C22×C43C2×H(5,𝔽2)11yescharacteristic
378C22×C43C2×H(5,𝔽2)11yescharacteristic
379C22×C43C2×2−1+411yescharacteristic
380C22×C43C2×2−1+411yescharacteristic
381C2×D43—24no—
382C2×D43—24no—
383C2×D43—24no—
384C2×D43—416no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C4×C43—24no—
390C4×C43—24no—
391C4×C43—24no—
392C4×C43—42no—
393C4×C43—42no—
394C4×C43—42no—
395Dic43—24no—
396Dic43—24no—
397Dic43—24no—
398Dic43—42no—
399Dic43—42no—
400Dic43—42no—
401Dic43C2×C4×D418yes—
402C22×#124—431no—
403C22×C4×Q8—431no—
404C22×C4×D4—431no—
405#2326—4316no—
406C2×#391—431no—
407C2×#390—431no—
408C2×#388—431no—
409C2×#388—431no—
410C2×#388—431no—
411C2×#388D4311yescharacteristic, complemented
412C2×#385—431no—
413C2×#385—431no—
414C2×#385—431no—
415C2×#385—431no—
416C2×#384—431no—
417C2×#376—431no—
418C2×C43—44no—
419C2×C43#232618yescomplemented
420C2×C43C22×C4×D411yescharacteristic
421C2×C43C2×#52011yescharacteristic
422C2×C43C2×#52011yescharacteristic
423C2×C43C2×#53511yescharacteristic
424C2×C43C2×#53611yescharacteristic
425C2×C43C2×#54211yescharacteristic
426C2×C43C2×#54211yescharacteristic
427D43—44no—
428C23×Q8—431no—
429C23×D4—431no—
430C24×C4—431no—
431C24×C4—431no—
432C2×#124—438no—
433C2×#124—4316no—
434C2×C4×Q8—438no—
435C2×C4×Q8—868no—
436C2×C4×D4—438no—
437C2×C4×D4—868no—
438C22×C4⋊C4—431no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444C22×C4⋊C4—431no—
445C22×C4⋊C4C2×D4311yescharacteristic
446C22×C22⋊C4—431no—
447C22×C22⋊C4—431no—
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4—431no—
451C22×C22⋊C4—431no—
452C22×C22⋊C4—431no—
453C22×C22⋊C4C2×D4311yescharacteristic
454C22×C22⋊C4C2×D4311yescharacteristic
455C22×C22⋊C4C2×D4311yescharacteristic
456C22×C42—431no—
457C22×C42—431no—
458C22×C42—431no—
459C22×C42—431no—
460C22×C42C2×D4311yescharacteristic
461#391—438no—
462#390—438no—
463#388—438no—
464#388—438no—
465#388—438no—
466#388C2×D4318yescomplemented
467#385—438no—
468#385—438no—
469#385—438no—
470#385—438no—
471#384—438no—
472#376—438no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95C2×D4311yescharacteristic
480C2×#95C2×D4311yescharacteristic
481C43C2×#232611yescharacteristic, complemented, Sylow
482C25—431no—
483C25C22×D4311yescharacteristic
484C22×Q8—438no—
485C22×Q8—434no—
486C22×Q8—864no—
487C22×Q8—864no—
488C22×D4—438no—
489C22×D4—434no—
490C22×D4—864no—
491C22×D4—864no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—431no—
497C23×C4—431no—
498C23×C4—431no—
499C23×C4—434no—
500C23×C4—434no—
501C23×C4—864no—
502C23×C4—864no—
503C23×C4—1722no—
504C23×C4—1722no—
505C23×C4—1722no—
506C23×C4—1722no—
507C23×C4C22×D4311yescharacteristic
508C23×C4C22×D4311yescharacteristic
509C23×C4C22×D4311yescharacteristic
510C23×C4C22×D4311yescharacteristic
511C23×C4C22×D4311yescharacteristic
512C23×C4C22×D4311yescharacteristic
513#124—4364no—
514C4×Q8—8632no—
515C4×D4—8632no—
516C2×C4⋊C4—42no—
517C2×C4⋊C4—434no—
518C2×C4⋊C4—434no—
519C2×C4⋊C4—434no—
520C2×C4⋊C4—434no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—864no—
525C2×C4⋊C4—864no—
526C2×C4⋊C4—864no—
527C2×C4⋊C4—864no—
528C2×C4⋊C4—1722no—
529C2×C4⋊C4—1722no—
530C2×C4⋊C4—1722no—
531C2×C4⋊C4C22×D4314yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—438no—
535C2×C22⋊C4—434no—
536C2×C22⋊C4—438no—
537C2×C22⋊C4—438no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—434no—
540C2×C22⋊C4—434no—
541C2×C22⋊C4—434no—
542C2×C22⋊C4—434no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—864no—
545C2×C22⋊C4—1722no—
546C2×C22⋊C4—1722no—
547C2×C22⋊C4—1722no—
548C2×C22⋊C4C4×D4318yescomplemented
549C2×C22⋊C4C22×D4314yes—
550C2×C22⋊C4C22×D4314yes—
551C2×C22⋊C4C22×D4314yes—
552C2×C42—24no—
553C2×C42—438no—
554C2×C42—438no—
555C2×C42—434no—
556C2×C42—434no—
557C2×C42—434no—
558C2×C42—434no—
559C2×C42—864no—
560C2×C42—864no—
561C2×C42C22×D4314yes—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95C22×D4314yes—
569#95C22×D4314yes—
570C24—22no—
571C24—22no—
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—
585C24C23×D4312yes—
586C24C23×D4311yescharacteristic
587C2×Q8—4316no—
588C2×Q8—868no—
589C2×Q8—8632no—
590C2×Q8—868no—
591C2×D4—4316no—
592C2×D4—868no—
593C2×D4—8632no—
594C2×D4—868no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—434no—
611C22×C4—434no—
612C22×C4—434no—
613C22×C4—432no—
614C22×C4—434no—
615C22×C4—434no—
616C22×C4—434no—
617C22×C4—432no—
618C22×C4—432no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—868no—
624C22×C4—868no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—1724no—
641C22×C4—1724no—
642C22×C4—17216no—
643C22×C4—1724no—
644C22×C4—1724no—
645C22×C4—17216no—
646C22×C4C2×C4×D4314yes—
647C22×C4C2×C4×D4314yes—
648C22×C4D4×D4314yes—
649C22×C4C23×D4312yes—
650C22×C4C23×D4312yes—
651C22×C4C23×D4312yes—
652C22×C4C23×D4312yes—
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C4⋊C4—44no—
656C4⋊C4—868no—
657C4⋊C4—868no—
658C4⋊C4—868no—
659C4⋊C4—868no—
660C4⋊C4—1724no—
661C4⋊C4—1724no—
662C4⋊C4—1724no—
663C22⋊C4—28no—
664C22⋊C4—44no—
665C22⋊C4—4316no—
666C22⋊C4—4316no—
667C22⋊C4—4316no—
668C22⋊C4—868no—
669C22⋊C4—1724no—
670C22⋊C4—1724no—
671C22⋊C4—1724no—
672C22⋊C4C2×C4×D43116yescomplemented
673C42—28no—
674C42—4316no—
675C42—4316no—
676C42—868no—
677C42—868no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
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—
705C23C22×C4×D4314yes—
706C23C22×C4×D4312yes—
707C23C2×D4×D4312yes—
708C23#41×D4312yes—
709C23#1306337012yes—
710C23#1306337112yes—
711C23#1306337212yes—
712C23#1306337212yes—
713C23C24×D4311yescharacteristic
714Q8—8632no—
715D4—8632no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
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—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—4316no—
738C2×C4—434no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—434no—
742C2×C4—434no—
743C2×C4—434no—
744C2×C4—868no—
745C2×C4—868no—
746C2×C4—862no—
747C2×C4—868no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
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—17216no—
763C2×C4—17216no—
764C2×C4—1724no—
765C2×C4—1724no—
766C2×C4—1724no—
767C2×C4C22×C4×D4314yes—
768C2×C4C22×C4×D4314yes—
769C2×C4C2×D4×D4314yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—416no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—864no—
779C22—864no—
780C22—864no—
781C22—17216no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22—1722no—
786C22C4×D4×D4314yes—
787C22#1458337814yes—
788C22#1458337914yes—
789C22#1458346514yes—
790C22#1458347114yes—
791C22#1458351314yes—
792C22#1458351514yes—
793C22C23×C4×D4311yescharacteristic
794C22C22×D4×D4311yescharacteristic
795C22C2×#41×D4311yescharacteristic
796C22C2×#1306337011yescharacteristic
797C22C2×#1306337111yescharacteristic
798C22C2×#1306337211yescharacteristic
799C22C2×#1306337211yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—438no—
807C4—864no—
808C4—864no—
809C4—864no—
810C4—1722no—
811C4—1722no—
812C4—1722no—
813C2—44no—
814C2—1724no—
815C2#1913730418yesdirect product factor
816C2C2×C4×D4×D4311yescharacteristic
817C2C2×#1458337811yescharacteristic
818C2C2×#1458337911yescharacteristic
819C2C2×#1458346511yescharacteristic
820C2C2×#1458347111yescharacteristic
821C2C2×#1458351311yescharacteristic
822C2C2×#1458351511yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2326
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic86C2semidirect
4. #19137304C2direct (N × H)
5. C2×#14582803C2semidirect
7. C2×#14582791C2semidirect
8. C2×#14582790C2semidirect
9. C2×#14582787C2semidirect
10. C2×#14582774C2semidirect
11. C2×#14582773C2semidirect
12. C2×#14582771C2semidirect
13. C2×#14582770C2semidirect
14. C2×#14582768C2semidirect
15. C2×#14582744C2semidirect
16. C2×C43×#388C2semidirect
21. C2×#13063311C4semidirect
24. C2×C4×Dic86C22semidirect
45. #14582803C22semidirect
47. #14582791C22semidirect
48. #14582790C22semidirect
49. #14582787C22semidirect
50. #14582774C22semidirect
51. #14582773C22semidirect
52. #14582771C22semidirect
53. #14582770C22semidirect
54. #14582768C22semidirect
55. #14582744C22semidirect
67. C43×#388C22semidirect
73. C22×Dic86C2×C4semidirect
94. #13063311C2×C4semidirect
112. C2×C22⋊Dic43C2×C4semidirect
118. C2×(C2×D43)⋊C4C2×C4semidirect
119. C2×(C2×D43)⋊C4C2×C4semidirect
127. C2×C4×Dic43C2×C4semidirect
150. C2×C22⋊C4×C43C2×C4semidirect
242. C2×Dic86C22×C4semidirect
246. C22⋊C4×C43C22×C4semidirect
249. C22⋊Dic43C22×C4semidirect
253. (C2×D43)⋊C4C22×C4semidirect
254. (C2×D43)⋊C4C22×C4semidirect
264. C4×Dic43C22×C4semidirect
411. C2×#388D43semidirect
419. C2×C43#2326semidirect
466. #388C2×D43semidirect
481. C43C2×#2326semidirect
548. C2×C22⋊C4C4×D43semidirect
672. C22⋊C4C2×C4×D43semidirect
815. C2#19137304direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633112
C22×C4×Dic862
C22×(C22⋊D43)⋊C42
#191373042
C2×#145828032
C2×#145827992
C2×#145827912
C2×#145827902
C2×#145827872
C2×#145827742
C2×#145827732
C2×#145827712
C2×#145827702
C2×#145827682
C2×#145827442
C2×C43×#3882
C2×#232643