Finite Group Databasebeta

← C2×#19148407 #26004922

Subgroups — C2×#19148407 #26004922

Order 11008.

7478 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148407C2132yesmaximal, direct product factor
2C2×Q8×Dic86C212yesmaximal, complemented
3C2×#14583627C212yesmaximal, complemented
4C2×#14583609C212yesmaximal, complemented
5C2×#14583607C214yesmaximal, complemented
6C2×Q8×D172C212yesmaximal, complemented
7C2×#14583562C214yesmaximal, complemented
8C2×#14583529C214yesmaximal, complemented
9C2×#14583527C212yesmaximal, complemented
10C2×#14583454C212yesmaximal, complemented
11C22×#13063325C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×D43C212yesmaximal, complemented
13C2×#14583379C212yesmaximal
14C2×C4×#10621898C211yesmaximal, characteristic
15C2×C43×#533C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×Dic86C2212yes—
18C22×Q8×D43C2214yes—
19Q8×Dic86C22132yescomplemented
20#14583627C22132yescomplemented
21#14583609C22132yescomplemented
22#14583607C22164yescomplemented
23Q8×D172C22132yescomplemented
24#14583562C22164yescomplemented
25#14583529C22164yescomplemented
26#14583527C22132yescomplemented
27#14583454C22132yescomplemented
28C2×#13063325C2212yes—
29C2×#13063325C2214yes—
30C2×#13063325C2212yes—
31C2×#13063325C2212yes—
32C2×#13063325C2212yes—
33C2×#13063325C22116yescomplemented
34C2×#13063324C2218yes—
35C2×#13063324C2214yes—
36C2×#13063324C2214yes—
37C2×#13063323C2214yes—
38C4⋊Q8×D43C22132yescomplemented
39C2×#13063317C2214yes—
40C2×#13063316C2214yes—
41C2×#13063315C2218yes—
42C2×#13063305C2214yes—
43C2×#13063305C2218yes—
44C2×#13063303C2218yes—
45C2×#13063302C2218yes—
46C2×#13063301C2214yes—
47#14583379C22132yes—
48C4×#10621898C22116yes—
49C2×Q8×Dic43C2214yes—
50C2×C4×Dic86C2214yes—
51C2×C4×Dic86C2211yescharacteristic
52C2×C4×Dic86C2211yescharacteristic
53C2×#13063290C2214yes—
54C2×C4×D172C2214yes—
55C2×C4×D172C2211yescharacteristic
56C2×C4×D172C2211yescharacteristic
57C2×C4×C22⋊D43C2212yes—
58C2×C4×C22⋊D43C2212yes—
59C2×(C22⋊D43)⋊C4C2218yes—
60C2×#13063284C2211yescharacteristic
61C2×#13063283C2214yes—
62C2×#13063282C2212yes—
63C22×C4⋊Dic43C2212yes—
64C22×C4⋊Dic43C2212yes—
65C2×C4⋊C4×D43C2214yes—
66C2×C4⋊C4×D43C2214yes—
67C2×C42×D43C2212yes—
68C43×#533C22116yescomplemented
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4⋊Q8×C43C2211yescharacteristic
71C2×#125×C43C2212yes—
72C2×C22⋊Q8×C43C2212yes—
73C2×C22⋊Q8×C43C2212yes—
74C2×C4×Q8×C43C2212yes—
75C2×C4×Q8×C43C2212yes—
76C2×#117×C43C2212yes—
77C22×C42×C43C2211yescharacteristic
78C2×#10621898Q8116yescomplemented
79C2×#10621898C2318yes—
80C22×Dic86—48no—
81C22×Dic86C2314yes—
82C22×Dic86C23116yes—
83C22×Dic86C2318yes—
84C22×Dic86C2314yes—
85C22×Dic86C2311yescharacteristic
86C2×Q8×D43—416no—
87C2×Q8×D43C23132yes—
88C22×D172C2311yescharacteristic
89C22×C22⋊D43C2312yes—
90C23×Dic43C2314yes—
91C22×C4×D43C2312yes—
92C22×C4×D43C2312yes—
93C22×C4×D43C2318yes—
94C22×C4×D43C2312yes—
95#13063325C23116yes—
96#13063325C23132yes—
97#13063325C23116yes—
98#13063325C23116yes—
99#13063325C23116yes—
100#13063324C23164yes—
101#13063324C23132yes—
102#13063324C23132yes—
103#13063323C23132yes—
104#13063317C23132yes—
105#13063316C23132yes—
106#13063315C23164yes—
107#13063305C23132yes—
108#13063305C23164yes—
109#13063303C23164yes—
110#13063302C23164yes—
111#13063301C23132yes—
112Q8×Dic43C23132yes—
113C4×Dic86C2318yes—
114C4×Dic86C2318yes—
115C4×Dic86C23132yes—
116#13063290C23132yes—
117C4×D172C2318yes—
118C4×D172C23132yes—
119C4×D172C2318yes—
120C4×C22⋊D43C23116yes—
121C4×C22⋊D43C23116yes—
122(C22⋊D43)⋊C4C23164yes—
123#13063284C2318yes—
124#13063283C23132yes—
125#13063282C23116yes—
126C2×C4⋊Dic43C2314yes—
127C2×C4⋊Dic43C2314yes—
128C2×C4⋊Dic43C23116yes—
129C2×C4⋊Dic43C2314yes—
130C2×C4⋊Dic43C23116yes—
131C2×C4⋊Dic43C2314yes—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2318yes—
135C2×Dic43⋊C4C2318yes—
136C2×Dic43⋊C4C2318yes—
137C2×Dic43⋊C4C2312yes—
138C2×Dic43⋊C4C2312yes—
139C2×Dic43⋊C4C2318yes—
140C4⋊C4×D43C23132yes—
141C4⋊C4×D43C23132yes—
142C2×C22⋊Dic43C2312yes—
143C2×(C2×D43)⋊C4C2312yes—
144C2×(C2×D43)⋊C4C2312yes—
145C2×(C2×D43)⋊C4C2318yes—
146C2×C4×Dic43C2312yes—
147C2×C4×Dic43C2312yes—
148C2×C4×Dic43C2312yes—
149C2×C4×Dic43C2318yes—
150C42×D43C23116yes—
151C22×Q8×C43C2312yes—
152C22×Q8×C43C2312yes—
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C4⋊Q8×C43C2318yes—
157C4⋊Q8×C43C2318yes—
158#125×C43C23116yes—
159C22⋊Q8×C43C23116yes—
160C22⋊Q8×C43C23116yes—
161C4×Q8×C43C23116yes—
162C4×Q8×C43C23116yes—
163#117×C43C23116yes—
164C2×C4⋊C4×C43C2312yes—
165C2×C4⋊C4×C43C2312yes—
166C2×C4⋊C4×C43C2314yes—
167C2×C4⋊C4×C43C2314yes—
168C2×C4⋊C4×C43C2312yes—
169C2×C4⋊C4×C43C2312yes—
170C2×C22⋊C4×C43C2314yes—
171C2×C42×C43C2311yescharacteristic
172C2×C42×C43C2311yescharacteristic
173C2×C42×C43C2311yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C2×C42×C43C2318yes—
176C2×C42×C43C2314yes—
177C24×C43C2411yescharacteristic
178C23×D43C2412yes—
179C2×Q8×C43—28no—
180C2×Q8×C43—28no—
181C2×Q8×C43C2418yes—
182C2×Q8×C43C2418yes—
183C22×C4×C43—24no—
184C22×C4×C43—24no—
185C22×C4×C43C2×Q818yescomplemented
186C22×C4×C43C2411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C22×C4×C43C2414yes—
189C22×C4×C43C2414yes—
190C22×C4×C43C2414yes—
191C22×C4×C43C2414yes—
192C22×C4×C43C2411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C22×C4×C43C2414yes—
195C22×C4×C43C2411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43C2×Q8116yescomplemented
198C2×C22⋊D43C2418yes—
199C22×Dic43—48no—
200C22×Dic43C2412yes—
201C22×Dic43C2412yes—
202C22×Dic43C2418yes—
203C22×Dic43C24116yes—
204C22×Dic43C2412yes—
205Q8×D43—464no—
206#10621898C2×Q8164yescomplemented
207C2×D172C2×Q818yescomplemented
208C2×D172C2414yes—
209C2×C4×D43—28no—
210C2×C4×D43—28no—
211C2×C4×D43—416no—
212C2×C4×D43C2×Q8116yescomplemented
213C2×C4×D43C2418yes—
214C2×C4×D43C2418yes—
215C2×C4×D43C24132yes—
216C2×C4×D43C2418yes—
217C2×Dic86—216no—
218C2×Dic86—432no—
219C2×Dic86—416no—
220C2×Dic86—48no—
221C2×Dic86C2×Q818yescomplemented
222C2×Dic86C24116yes—
223C2×Dic86C24132yes—
224C2×Dic86C24116yes—
225C2×Dic86C2414yes—
226C4⋊C4×C43C2418yes—
227C4⋊C4×C43C2418yes—
228C4⋊C4×C43C24116yes—
229C4⋊C4×C43C24116yes—
230C4⋊C4×C43C2418yes—
231C4⋊C4×C43C2418yes—
232C22⋊C4×C43C24116yes—
233C42×C43C2414yes—
234C42×C43C2414yes—
235C42×C43C2414yes—
236C42×C43C2414yes—
237C42×C43C24116yes—
238C22⋊Dic43C2418yes—
239(C2×D43)⋊C4C2418yes—
240(C2×D43)⋊C4C2418yes—
241(C2×D43)⋊C4C24132yes—
242C4⋊Dic43C24116yes—
243C4⋊Dic43C24116yes—
244C4⋊Dic43C24116yes—
245C4⋊Dic43C24116yes—
246C4⋊Dic43C2414yes—
247C4⋊Dic43C2414yes—
248C4⋊Dic43C24132yes—
249Dic43⋊C4C24132yes—
250Dic43⋊C4C24132yes—
251Dic43⋊C4C2418yes—
252Dic43⋊C4C2418yes—
253Dic43⋊C4C24132yes—
254C4×Dic43C2418yes—
255C4×Dic43C2418yes—
256C4×Dic43C2418yes—
257C4×Dic43C24132yes—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43C22×Q814yes—
261C23×C43C2512yes—
262C23×C43C2511yescharacteristic
263C22×D43—24no—
264C22×D43—24no—
265C22×D43C22×Q818yes—
266C22×D43C2514yes—
267Q8×C43—216no—
268Q8×C43—216no—
269C2×C4×C43—22no—
270C2×C4×C43—28no—
271C2×C4×C43—22no—
272C2×C4×C43—28no—
273C2×C4×C43—28no—
274C2×C4×C43—28no—
275C2×C4×C43C22×Q814yes—
276C2×C4×C43C22×Q814yes—
277C2×C4×C43C22×Q8116yescomplemented
278C2×C4×C43H(5,𝔽2)14yes—
279C2×C4×C432−1+414yes—
280C2×C4×C43C2518yes—
281C2×C4×C43C2518yes—
282C2×C4×C43C2512yes—
283C2×C4×C43C2512yes—
284C2×C4×C43C2512yes—
285C2×C4×C43C2512yes—
286C2×C4×C43C2512yes—
287C2×C4×C43C2512yes—
288C22⋊D43C22×Q8132yescomplemented
289C2×Dic43—216no—
290C2×Dic43—24no—
291C2×Dic43—24no—
292C2×Dic43—416no—
293C2×Dic43C22×Q818yes—
294C2×Dic43C2514yes—
295C2×Dic43C2514yes—
296C2×Dic43C25116yes—
297C2×Dic43C2514yes—
298D172C22×Q8116yescomplemented
299C4×D43—216no—
300C4×D43—216no—
301C4×D43—432no—
302C4×D43C22×Q8132yescomplemented
303Dic86—232no—
304Dic86—416no—
305Dic86—432no—
306Dic86C22×Q8116yescomplemented
307C2×#3503—431nomaximal, Sylow
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—28no—
311C22×C43C23×Q814yes—
312C22×C43C23×Q812yes—
313C22×C43C2×H(5,𝔽2)12yes—
314C22×C43C2×2−1+412yes—
315C22×C43C2611yescharacteristic
316C2×D43—24no—
317C2×D43—24no—
318C2×D43—216no—
319C2×D43C23×Q818yes—
320C4×C43—22no—
321C4×C43—28no—
322C4×C43—22no—
323C4×C43—28no—
324C4×C43C23×Q814yes—
325C4×C43C23×Q814yes—
326C4×C43C2×H(5,𝔽2)14yes—
327C4×C43C2×2−1+414yes—
328Dic43—216no—
329Dic43—24no—
330Dic43—24no—
331Dic43C23×Q818yes—
332#3503—4332no—
333C2×Q82—432no—
334C2×#557—432no—
335C2×#554—434no—
336C2×#554—432no—
337C2×D4×Q8—434no—
338C2×D4×Q8—432no—
339C2×#544—434no—
340C2×#544—432no—
341C2×#533—432no—
342C2×#533D4311yescharacteristic, complemented
343C22×C4⋊Q8—431no—
344C22×C4⋊Q8—432no—
345C2×#520—432no—
346C2×C4×#41—431no—
347C2×C43—24no—
348C2×C43#350314yescomplemented
349C2×C43C24×Q811yescharacteristic
350C2×C43C22×H(5,𝔽2)11yescharacteristic
351C2×C43C22×2−1+411yescharacteristic
352D43—28no—
353C22×#41—431no—
354C23×Q8—434no—
355C23×Q8—432no—
356Q82—4332no—
357#557—4332no—
358#554—4364no—
359#554—4332no—
360D4×Q8—4364no—
361D4×Q8—4332no—
362#544—4364no—
363#544—4332no—
364#533—4332no—
365#533C2×D43116yescomplemented
366C2×C4⋊Q8—434no—
367C2×C4⋊Q8—4332no—
368C2×C4⋊Q8—434no—
369C2×C4⋊Q8—434no—
370C2×C4⋊Q8—438no—
371C2×C4⋊Q8—432no—
372C2×C4⋊Q8—432no—
373C2×C4⋊Q8—432no—
374C2×C4⋊Q8—432no—
375C2×C4⋊Q8—4316no—
376C2×C4⋊Q8—434no—
377C2×C4⋊Q8C2×D4311yescharacteristic
378C2×C4⋊Q8C2×D4311yescharacteristic
379C2×#125—434no—
380C2×#125—438no—
381C2×#125—434no—
382C2×#125C2×D4312yes—
383C2×C22⋊Q8—434no—
384C2×C22⋊Q8—438no—
385C2×C22⋊Q8—434no—
386C2×C22⋊Q8—438no—
387C2×C22⋊Q8—438no—
388C2×C22⋊Q8C2×D4312yes—
389C2×C22⋊Q8C2×D4312yes—
390#520—4332no—
391C4×#41—4316no—
392C2×C4×Q8—434no—
393C2×C4×Q8—434no—
394C2×C4×Q8—431no—
395C2×C4×Q8—431no—
396C2×C4×Q8—434no—
397C2×C4×Q8C2×D4312yes—
398C2×C4×Q8C2×D4312yes—
399C2×C4×D4—432no—
400C2×C4×D4—432no—
401C2×C4×D4—438no—
402C2×C4×D4—431no—
403C2×C4×D4—431no—
404C2×C4×D4—434no—
405C2×#117—431no—
406C2×#117—434no—
407C2×#117—432no—
408C2×#117C2×D4312yes—
409C22×C4⋊C4—432no—
410C22×C4⋊C4—432no—
411C22×C4⋊C4—434no—
412C22×C4⋊C4—434no—
413C22×C42—432no—
414C22×C42C2×D4311yescharacteristic
415C43C2×#350311yescharacteristic, complemented, Sylow
416C2×#41—4316no—
417C2×#41—438no—
418C22×Q8—4332no—
419C22×Q8—431no—
420C22×Q8—434no—
421C22×Q8—438no—
422C22×Q8—434no—
423C22×Q8—4316no—
424C22×Q8—1728no—
425C22×Q8—17216no—
426C22×Q8C22×D4312yes—
427C22×Q8C22×D4312yes—
428C22×D4—432no—
429C22×D4—431no—
430C23×C4—432no—
431C23×C4—434no—
432C23×C4—432no—
433C23×C4—432no—
434C23×C4—438no—
435C23×C4C22×D4311yescharacteristic
436C23×C4C22×D4311yescharacteristic
437C23×C4C22×D4311yescharacteristic
438C4⋊Q8—4332no—
439C4⋊Q8—4332no—
440C4⋊Q8—4332no—
441C4⋊Q8—4364no—
442C4⋊Q8—4316no—
443C4⋊Q8—4316no—
444C4⋊Q8—4316no—
445C4⋊Q8—4316no—
446C4⋊Q8—4332no—
447C4⋊Q8C22×D4318yes—
448C4⋊Q8C22×D4318yes—
449#125—4332no—
450#125—4364no—
451#125—4332no—
452#125C22×D43116yes—
453C22⋊Q8—4332no—
454C22⋊Q8—4332no—
455C22⋊Q8—4364no—
456C22⋊Q8—4364no—
457C22⋊Q8—4364no—
458C22⋊Q8C22×D43116yes—
459C22⋊Q8C22×D43116yes—
460C4×Q8—4332no—
461C4×Q8—4332no—
462C4×Q8—438no—
463C4×Q8—438no—
464C4×Q8—4332no—
465C4×Q8C22×D43116yes—
466C4×Q8C22×D43116yes—
467C4×D4—4316no—
468C4×D4—4316no—
469C4×D4—4364no—
470C4×D4—438no—
471C4×D4—438no—
472C4×D4—4332no—
473#117—438no—
474#117—4332no—
475#117—4316no—
476#117C22×D43116yes—
477C2×C4⋊C4—434no—
478C2×C4⋊C4—434no—
479C2×C4⋊C4—438no—
480C2×C4⋊C4—434no—
481C2×C4⋊C4—4316no—
482C2×C4⋊C4—438no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—4316no—
485C2×C4⋊C4—432no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—432no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—438no—
490C2×C4⋊C4—438no—
491C2×C4⋊C4—4332no—
492C2×C4⋊C4—4332no—
493C2×C4⋊C4C22×D4312yes—
494C2×C4⋊C4C22×D4312yes—
495C2×C4⋊C4C22×D4312yes—
496C2×C4⋊C4C22×D4312yes—
497C2×C4⋊C4C22×D4314yes—
498C2×C4⋊C4C22×D4314yes—
499C2×C22⋊C4—432no—
500C2×C22⋊C4—432no—
501C2×C22⋊C4—432no—
502C2×C22⋊C4—438no—
503C2×C22⋊C4C22×D4314yes—
504C2×C42—432no—
505C2×C42—438no—
506C2×C42—432no—
507C2×C42—432no—
508C2×C42—4316no—
509C2×C42C22×D4311yescharacteristic
510C2×C42C22×D4314yes—
511C2×C42C22×D4311yescharacteristic
512C2×C42C22×D4311yescharacteristic
513C2×C42C22×D4318yes—
514C2×C42C22×D4311yescharacteristic
515C24—432no—
516C24C23×D4311yescharacteristic
517#41—4364no—
518C2×Q8—28no—
519C2×Q8—28no—
520C2×Q8—438no—
521C2×Q8—434no—
522C2×Q8—4316no—
523C2×Q8—4332no—
524C2×Q8—4316no—
525C2×Q8—8616no—
526C2×Q8—1728no—
527C2×Q8—17216no—
528C2×Q8—17232no—
529C2×Q8—17264no—
530C2×Q8C23×D4318yes—
531C2×Q8C23×D4318yes—
532C2×D4—4316no—
533C2×D4—438no—
534C2×D4—438no—
535C2×D4—434no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—432no—
539C22×C4—4316no—
540C22×C4—438no—
541C22×C4—432no—
542C22×C4—432no—
543C22×C4—438no—
544C22×C4—4316no—
545C22×C4—438no—
546C22×C4—438no—
547C22×C4—4332no—
548C22×C4—868no—
549C22×C4—868no—
550C22×C4—17216no—
551C22×C4—1728no—
552C22×C4Q8×D4318yescomplemented
553C22×C4C23×D4314yes—
554C22×C4C23×D4314yes—
555C22×C4C23×D4314yes—
556C22×C4C23×D4311yescharacteristic
557C22×C4C23×D4311yescharacteristic
558C22×C4C23×D4314yes—
559C22×C4C23×D4311yescharacteristic
560C22×C4C23×D4311yescharacteristic
561C22×C4C23×D4314yes—
562C22×C4C23×D4311yescharacteristic
563C22×C4C23×D4311yescharacteristic
564C4⋊C4—4316no—
565C4⋊C4—4316no—
566C4⋊C4—4332no—
567C4⋊C4—4316no—
568C4⋊C4—4332no—
569C4⋊C4—4316no—
570C4⋊C4—438no—
571C4⋊C4—434no—
572C4⋊C4—438no—
573C4⋊C4—434no—
574C4⋊C4—4332no—
575C4⋊C4—4332no—
576C4⋊C4C23×D4318yes—
577C4⋊C4C23×D4318yes—
578C4⋊C4C23×D4318yes—
579C4⋊C4C23×D4318yes—
580C4⋊C4C23×D43116yes—
581C4⋊C4C23×D43116yes—
582C22⋊C4—438no—
583C22⋊C4—438no—
584C22⋊C4—438no—
585C22⋊C4—4332no—
586C22⋊C4C23×D43116yes—
587C42—438no—
588C42—438no—
589C42—438no—
590C42—4332no—
591C42C23×D4314yes—
592C42C23×D4314yes—
593C42C23×D4314yes—
594C42C23×D4314yes—
595C42C23×D43116yes—
596C23—22no—
597C23—22no—
598C23—438no—
599C23—434no—
600C23—864no—
601C23—864no—
602C23C2×Q8×D4314yes—
603C23C24×D4312yes—
604C23C24×D4311yescharacteristic
605Q8—216no—
606Q8—216no—
607Q8—4316no—
608Q8—8632no—
609Q8—17216no—
610Q8—17232no—
611D4—4332no—
612D4—4316no—
613C2×C4—22no—
614C2×C4—28no—
615C2×C4—22no—
616C2×C4—28no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—438no—
620C2×C4—434no—
621C2×C4—4332no—
622C2×C4—434no—
623C2×C4—434no—
624C2×C4—4316no—
625C2×C4—864no—
626C2×C4—8616no—
627C2×C4—864no—
628C2×C4—8616no—
629C2×C4—8616no—
630C2×C4—17232no—
631C2×C4—17216no—
632C2×C4C2×Q8×D4314yes—
633C2×C4C2×Q8×D4314yes—
634C2×C4C2×Q8×D43116yescomplemented
635C2×C4#1306337114yes—
636C2×C4#1306337214yes—
637C2×C4C24×D4318yes—
638C2×C4C24×D4312yes—
639C2×C4C24×D4312yes—
640C2×C4C24×D4318yes—
641C2×C4C24×D4312yes—
642C2×C4C24×D4312yes—
643C2×C4C24×D4312yes—
644C2×C4C24×D4312yes—
645C22—22no—
646C22—22no—
647C22—28no—
648C22—438no—
649C22—864no—
650C22—864no—
651C22—8616no—
652C22C22×Q8×D4314yes—
653C22C22×Q8×D4312yes—
654C22C2×#1306337112yes—
655C22C2×#1306337212yes—
656C22C25×D4311yescharacteristic
657C4—22no—
658C4—28no—
659C4—22no—
660C4—28no—
661C4—438no—
662C4—864no—
663C4—8616no—
664C4—864no—
665C4C22×Q8×D4314yes—
666C4C22×Q8×D4314yes—
667C4C2×#1306337114yes—
668C4C2×#1306337214yes—
669C2—24no—
670C2—868no—
671C2#1914840714yesdirect product factor
672C2C23×Q8×D4311yescharacteristic
673C2C22×#1306337111yescharacteristic
674C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#533C2
socleC23×C43C25
prime radicalC22×#10621898C22
hypercenterC2×#533D43
hypocenterC43C2×#3503
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #19148407C2direct (N × H)
2. C2×Q8×Dic86C2semidirect
3. C2×#14583627C2semidirect
4. C2×#14583609C2semidirect
5. C2×#14583607C2semidirect
6. C2×Q8×D172C2semidirect
7. C2×#14583562C2semidirect
8. C2×#14583529C2semidirect
9. C2×#14583527C2semidirect
10. C2×#14583454C2semidirect
11. C22×#13063325C2semidirect
12. C2×C4⋊Q8×D43C2semidirect
15. C2×C43×#533C2semidirect
19. Q8×Dic86C22semidirect
20. #14583627C22semidirect
21. #14583609C22semidirect
22. #14583607C22semidirect
23. Q8×D172C22semidirect
24. #14583562C22semidirect
25. #14583529C22semidirect
26. #14583527C22semidirect
27. #14583454C22semidirect
33. C2×#13063325C22semidirect
38. C4⋊Q8×D43C22semidirect
68. C43×#533C22semidirect
78. C2×#10621898Q8semidirect
185. C22×C4×C43C2×Q8semidirect
197. C2×C22⋊D43C2×Q8semidirect
206. #10621898C2×Q8semidirect
207. C2×D172C2×Q8semidirect
212. C2×C4×D43C2×Q8semidirect
221. C2×Dic86C2×Q8semidirect
277. C2×C4×C43C22×Q8semidirect
288. C22⋊D43C22×Q8semidirect
298. D172C22×Q8semidirect
302. C4×D43C22×Q8semidirect
306. Dic86C22×Q8semidirect
342. C2×#533D43semidirect
348. C2×C43#3503semidirect
365. #533C2×D43semidirect
415. C43C2×#3503semidirect
552. C22×C4Q8×D43semidirect
634. C2×C4C2×Q8×D43semidirect
671. C2#19148407direct (N × H)

Maximal subgroups

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

subgroupindex
#191484072
C2×Q8×Dic862
C2×#145836272
C2×#145836092
C2×#145836072
C2×Q8×D1722
C2×#145835622
C2×#145835292
C2×#145835272
C2×#145834542
C22×#130633252
C2×C4⋊Q8×D432
C2×#145833792
C2×C4×#106218982
C2×C43×#5332
C2×#350343