Finite Group Databasebeta

← C2×#10594506 #11910343

Subgroups — C2×#10594506 #11910343

Order 1152.

2171 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64107C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#890C211yesmaximal, characteristic, complemented
4C2×#63919C211yesmaximal, characteristic, complemented
5C2×#63918C211yesmaximal, characteristic, complemented
6C2×#63899C211yesmaximal, characteristic, complemented
7C2×#63895C211yesmaximal, characteristic, complemented
8C2×#63895C211yesmaximal, characteristic, complemented
9C2×#63893C211yesmaximal, characteristic, complemented
10C2×#63890C211yesmaximal, characteristic
11C2×#63868C211yesmaximal, characteristic, complemented
12C2×#63867C211yesmaximal, characteristic, complemented
13C2×#63862C211yesmaximal, characteristic, complemented
14C2×#63854C211yesmaximal, characteristic
15C2×#63852C211yesmaximal, characteristic
16#10594506C2116yesmaximal, direct product factor
17C2×#5712—31nomaximal
18C2×#5699—31nomaximal
19C22×#627C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32#64107C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C3×#898C2218yescomplemented
46C3×#890C2218yescomplemented
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63919C2218yescomplemented
58#63918C2218yescomplemented
59#63899C2218yescomplemented
60#63895C2218yescomplemented
61#63895C2218yescomplemented
62#63893C2218yescomplemented
63#63890C2218yes—
64#63868C2218yescomplemented
65#63867C2218yescomplemented
66#63862C2218yescomplemented
67#63854C2218yes—
68#63852C2218yes—
69C2×C3×#126—31no—
70C2×C3×#125—31no—
71#5712—316no—
72#5699—316no—
73C2×#898—31no—
74C2×#898—31no—
75C2×#898—31no—
76C2×#898—31no—
77C2×#898—61no—
78C2×#898D311yescharacteristic, complemented
79C2×#897—31no—
80C2×#897—31no—
81C2×#897—31no—
82C2×#896—31no—
83C2×#896—31no—
84C2×#896—31no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#890D311yescharacteristic, complemented
88C2×#889—31no—
89C2×#888—31no—
90C2×#888—31no—
91C2×#888—31no—
92C2×#886—31no—
93C2×#885—31no—
94C2×#883—31no—
95C2×#879—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#876—31no—
99C2×#875—31no—
100C2×#870—31no—
101C2×#869—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×#627—42no—
118C2×#627—42no—
119C2×#627—42no—
120C2×#627C2314yes—
121C2×#627C2314yes—
122C2×#627C2314yes—
123C2×#626—42no—
124C2×#626C2314yes—
125C2×#624—42no—
126C2×#624C2314yes—
127C2×D3×Dic3—42no—
128C2×D3×Dic3C2314yes—
129C32×C4⋊C4C2314yes—
130#3752C2314yes—
131#3752C2314yes—
132#3752C2314yes—
133C4⋊(C3⋊Dic3)C2314yes—
134#3750C2314yes—
135C4×C3⋊Dic3C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×C4⋊Dic3C2314yes—
140C3×C4⋊Dic3C2314yes—
141C3×C4⋊Dic3C2314yes—
142C3×C4⋊Dic3C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×C4×Dic3C2314yes—
147C3×C4×Dic3C2314yes—
148#3724C2314yes—
149#3724C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154#3722C2314yes—
155#3722C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158C2×#563—91noSylow
159C22×#67—31no—
160C23×Dic3—31no—
161C22×D12—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×Dic6—31no—
166C22×Dic6—31no—
167C22×Dic6—31no—
168C22×Dic6—31no—
169C22×Dic6—31no—
170C22×Dic6—31no—
171C3×#126—38no—
172C3×#125—38no—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4C2×D311yescharacteristic
182C2×C3×C4⋊C4C2×D311yescharacteristic
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C42—31no—
187C2×C3×C42—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—61no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—61no—
215C2×C4⋊Dic3C2×D311yescharacteristic
216C2×C4⋊Dic3C2×D311yescharacteristic
217C2×C4⋊Dic3C2×D311yescharacteristic
218C2×C4⋊Dic3C2×D311yescharacteristic
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—31no—
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—61no—
230C2×Dic3⋊C4C2×D311yescharacteristic
231C2×Dic3⋊C4C2×D311yescharacteristic
232C2×Dic3⋊C4C2×D311yescharacteristic
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—61no—
236C2×C4×Dic3C2×D311yescharacteristic
237C2×C4×Dic3C2×D311yescharacteristic
238#898—38no—
239#898—38no—
240#898—38no—
241#898—38no—
242#898—68no—
243#898C2×D318yescomplemented
244#897—38no—
245#897—38no—
246#897—38no—
247#896—38no—
248#896—38no—
249#896—38no—
250#894—38no—
251#894—38no—
252#890C2×D318yescomplemented
253#889—38no—
254#888—38no—
255#888—38no—
256#888—38no—
257#886—38no—
258#885—38no—
259#883—38no—
260#879—38no—
261#878—38no—
262#878—38no—
263#876—38no—
264#875—38no—
265#870—38no—
266#869—38no—
267C23×C32C2411yescharacteristic
268C22×C3⋊D3—22no—
269C22×C3⋊D3—22no—
270C22×C3⋊D3—22no—
271C22×C3⋊D3C2412yes—
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3C2412yes—
276C2×C32×C4—22no—
277C2×C32×C4—22no—
278C2×C32×C4—22no—
279C2×C32×C4C2412yes—
280C2×C32×C4C2412yes—
281C2×C32×C4C2412yes—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3—22no—
284C2×C3⋊Dic3—22no—
285C2×C3⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302#627—44no—
303#627—44no—
304#627—44no—
305#626—44no—
306#624—44no—
307D3×Dic3—44no—
308#563—916no—
309C2×C4⋊Q8—91no—
310C2×C4⋊Q8—91no—
311C2×#126—31no—
312C2×#126—91no—
313C2×#126—91no—
314C2×#126—91no—
315C2×#125—31no—
316C2×#125—91no—
317C2×#124—91no—
318C2×#123—91no—
319C2×#123—91no—
320C2×C22⋊Q8—91no—
321C2×C22⋊Q8—91no—
322C2×C22⋊Q8—91no—
323C2×C22⋊Q8—91no—
324C24×C3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—61no—
328C23×D3C22×D311yescharacteristic
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67—34no—
346C2×#67—122no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—34no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—122no—
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C2×D12—34no—
366C2×D12—122no—
367C2×C4×D3—34no—
368C2×C4×D3—34no—
369C2×C4×D3—34no—
370C2×C4×D3—122no—
371C2×C4×D3—122no—
372C2×C4×D3—122no—
373C2×Dic6—34no—
374C2×Dic6—34no—
375C2×Dic6—34no—
376C2×Dic6—34no—
377C2×Dic6—34no—
378C2×Dic6—34no—
379C2×Dic6—122no—
380C2×Dic6—122no—
381C2×Dic6—122no—
382C2×Dic6—122no—
383C2×Dic6—122no—
384C2×Dic6—122no—
385C3×C4⋊C4—24no—
386C3×C4⋊C4—34no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4C22×D314yes—
394C3×C4⋊C4C22×D314yes—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4—34no—
398C3×C42—34no—
399C3×C42—34no—
400#217—34no—
401#217—34no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—64no—
415(C2×D3)⋊C4—64no—
416(C2×D3)⋊C4—64no—
417(C2×D3)⋊C4C22×D314yes—
418(C2×D3)⋊C4C22×D314yes—
419(C2×D3)⋊C4C22×D314yes—
420C4⋊Dic3—34no—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—34no—
424C4⋊Dic3—34no—
425C4⋊Dic3—34no—
426C4⋊Dic3—64no—
427C4⋊Dic3C22×D314yes—
428C4⋊Dic3C22×D314yes—
429C4⋊Dic3C22×D314yes—
430C4⋊Dic3C22×D314yes—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
441Dic3⋊C4—64no—
442Dic3⋊C4C22×D314yes—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D314yes—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—64no—
448C4×Dic3C22×D314yes—
449C4×Dic3C22×D314yes—
450C22×C32H(5,𝔽2)12yes—
451C22×C322−1+412yes—
452C22×C322−1+412yes—
453C22×C32C2511yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—44no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—44no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C22×Q8—91no—
476C22×Q8—91no—
477C22×Q8—91no—
478C22×D4—91no—
479C23×C4—91no—
480C23×C4—91no—
481C4⋊Q8—98no—
482C4⋊Q8—98no—
483#126—38no—
484#126—98no—
485#126—98no—
486#126—98no—
487#125—38no—
488#125—98no—
489#124—98no—
490#123—98no—
491#123—98no—
492C22⋊Q8—98no—
493C22⋊Q8—98no—
494C22⋊Q8—98no—
495C22⋊Q8—98no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—31no—
503C2×C4⋊C4—91no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—91no—
507C2×C4⋊C4—91no—
508C2×C4⋊C4—91no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—91no—
511C2×C4⋊C4D3211yescharacteristic
512C2×C22⋊C4—31no—
513C2×C22⋊C4—31no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522C2×C42—31no—
523C2×C42—31no—
524C2×C42—91no—
525C23×C3—21no—
526C23×C3—32no—
527C23×C3—62no—
528C23×C3—62no—
529C23×C3—62no—
530C23×C3C23×D311yescharacteristic
531C23×C3C23×D311yescharacteristic
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—32no—
536C22×D3—32no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3C23×D312yes—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—32no—
558C2×C3×C4—32no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—42no—
565C2×C3×C4—42no—
566C2×C3×C4—42no—
567C2×C3×C4—62no—
568C2×C3×C4—62no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4C23×D312yes—
575C2×C3×C4C23×D312yes—
576C2×C3×C4C23×D312yes—
577C2×C3×C4C23×D312yes—
578C2×C3×C4C23×D312yes—
579C2×C3×C4C23×D312yes—
580#67—124no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—122no—
604C2×Dic3—122no—
605C2×Dic3—122no—
606C2×Dic3—124no—
607C2×Dic3C23×D312yes—
608C2×Dic3C23×D312yes—
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D312yes—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614D12—124no—
615C4×D3—124no—
616C4×D3—124no—
617C4×D3—124no—
618Dic6—124no—
619Dic6—124no—
620Dic6—124no—
621Dic6—124no—
622Dic6—124no—
623Dic6—124no—
624C2×C32#56314yescomplemented
625C2×C32C2×H(5,𝔽2)11yescharacteristic
626C2×C32C2×2−1+411yescharacteristic
627C2×C32C2×2−1+411yescharacteristic
628C3⋊D3—42no—
629C3×D3—42no—
630C24—31no—
631C24—91no—
632C2×Q8—94no—
633C2×Q8—94no—
634C2×Q8—94no—
635C2×Q8—362no—
636C2×Q8—362no—
637C2×Q8—362no—
638C2×D4—94no—
639C2×D4—362no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—94no—
648C22×C4—94no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—362no—
653C22×C4—362no—
654C22×C4C2×D3211yescharacteristic
655C22×C4C2×D3211yescharacteristic
656C22×C4C2×D3211yescharacteristic
657C4⋊C4—34no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—34no—
664C4⋊C4—94no—
665C4⋊C4—94no—
666C4⋊C4—94no—
667C4⋊C4—94no—
668C4⋊C4—94no—
669C4⋊C4—94no—
670C4⋊C4—94no—
671C4⋊C4—94no—
672C4⋊C4C2×D3214yes—
673C22⋊C4—34no—
674C22⋊C4—34no—
675C22⋊C4—34no—
676C22⋊C4—94no—
677C22⋊C4—94no—
678C22⋊C4—94no—
679C22⋊C4—94no—
680C22⋊C4—94no—
681C22⋊C4—94no—
682C22⋊C4—94no—
683C42—34no—
684C42—34no—
685C42—94no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—21no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—124no—
694C22×C3#100712yes—
695C22×C3#100912yes—
696C22×C3#100912yes—
697C22×C3#101012yes—
698C22×C3#101012yes—
699C22×C3#101012yes—
700C22×C3C24×D311yescharacteristic
701C22×C3C24×D311yescharacteristic
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—22no—
705C2×D3—44no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—122no—
713C2×D3—122no—
714C2×D3—122no—
715C2×D3—124no—
716C2×D3—124no—
717C2×D3—244no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—62no—
728C3×C4—62no—
729C3×C4—62no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734Dic3—22no—
735Dic3—22no—
736Dic3—22no—
737Dic3—22no—
738Dic3—22no—
739Dic3—22no—
740Dic3—22no—
741Dic3—62no—
742Dic3—62no—
743Dic3—62no—
744Dic3—62no—
745Dic3—62no—
746Dic3—62no—
747Dic3—122no—
748Dic3—122no—
749Dic3—122no—
750C32C2×#56311yescharacteristic, complemented, Sylow
751C23—32no—
752C23—62no—
753C23—62no—
754C23—62no—
755C23—92no—
756C23—182no—
757C23—182no—
758C23—182no—
759C23C22×D3211yescharacteristic
760Q8—364no—
761Q8—364no—
762Q8—364no—
763D4—364no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—92no—
782C2×C4—92no—
783C2×C4—92no—
784C2×C4—182no—
785C2×C4—182no—
786C2×C4—182no—
787C2×C4—364no—
788C2×C4—364no—
789C2×C4C22×D3212yes—
790C2×C4C22×D3212yes—
791C2×C4C22×D3212yes—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—24no—
796C2×C3—122no—
797C2×C3#569914yescomplemented
798C2×C3#571214yescomplemented
799C2×C3C2×#100711yescharacteristic
800C2×C3C2×#100911yescharacteristic
801C2×C3C2×#100911yescharacteristic
802C2×C3C2×#101011yescharacteristic
803C2×C3C2×#101011yescharacteristic
804C2×C3C2×#101011yescharacteristic
805D3—42no—
806D3—122no—
807D3—122no—
808D3—242no—
809C22—62no—
810C22—62no—
811C22—62no—
812C22—124no—
813C22—182no—
814C22—182no—
815C22—182no—
816C22—364no—
817C22#6429712yes—
818C22#6430912yes—
819C22#6432012yes—
820C22C23×D3211yescharacteristic
821C4—22no—
822C4—22no—
823C4—22no—
824C4—62no—
825C4—62no—
826C4—62no—
827C4—62no—
828C4—62no—
829C4—62no—
830C4—62no—
831C4—182no—
832C4—182no—
833C4—182no—
834C3—21no—
835C3C2×#569911yescharacteristic, complemented
836C3C2×#571211yescharacteristic, complemented
837C2—122no—
838C2—362no—
839C2#1059450614yesdirect product factor
840C2C2×#6429711yescharacteristic
841C2C2×#6430911yescharacteristic
842C2C2×#6432011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#563
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64107C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#890C2semidirect
4. C2×#63919C2semidirect
5. C2×#63918C2semidirect
6. C2×#63899C2semidirect
7. C2×#63895C2semidirect
8. C2×#63895C2semidirect
9. C2×#63893C2semidirect
11. C2×#63868C2semidirect
12. C2×#63867C2semidirect
13. C2×#63862C2semidirect
16. #10594506C2direct (N × H)
32. #64107C22semidirect
45. C3×#898C22semidirect
46. C3×#890C22semidirect
57. #63919C22semidirect
58. #63918C22semidirect
59. #63899C22semidirect
60. #63895C22semidirect
61. #63895C22semidirect
62. #63893C22semidirect
64. #63868C22semidirect
65. #63867C22semidirect
66. #63862C22semidirect
78. C2×#898D3semidirect
87. C2×#890D3semidirect
243. #898C2×D3semidirect
252. #890C2×D3semidirect
624. C2×C32#563semidirect
750. C32C2×#563semidirect
797. C2×C3#5699semidirect
798. C2×C3#5712semidirect
835. C3C2×#5699semidirect
836. C3C2×#5712semidirect
839. C2#10594506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641072
C2×C3×#8982
C2×C3×#8902
C2×#639192
C2×#639182
C2×#638992
C2×#638952
C2×#638932
C2×#638902
C2×#638682
C2×#638672
C2×#638622
C2×#638542
C2×#638522
#105945062
C2×#57123
C2×#56993