Finite Group Databasebeta

← C2×#10593931 #11903393

Subgroups — C2×#10593931 #11903393

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×#876C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C2×#63915C211yesmaximal, characteristic
5C2×#63913C211yesmaximal, characteristic
6C2×#63893C211yesmaximal, characteristic, complemented
7C2×#63879C211yesmaximal, characteristic
8C2×#63878C211yesmaximal, characteristic, complemented
9C2×#63862C211yesmaximal, characteristic, complemented
10C2×#63861C211yesmaximal, characteristic, complemented
11C2×#63859C211yesmaximal, characteristic, complemented
12C2×#63851C211yesmaximal, characteristic, complemented
13C2×#63840C211yesmaximal, characteristic, complemented
14C2×#63838C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10593931C2116yesmaximal, direct product factor
17C2×#5702—31nomaximal
18C2×#5533—31nomaximal
19C22×#634C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C4×#634C2218yescomplemented
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#876C2218yescomplemented
44C3×#872C2218yescomplemented
45C2×#3724C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×Dic32C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63915C2218yes—
58#63913C2218yes—
59#63893C2218yescomplemented
60#63879C2218yes—
61#63878C2218yescomplemented
62#63862C2218yescomplemented
63#63861C2218yescomplemented
64#63859C2218yescomplemented
65#63851C2218yescomplemented
66#63840C2218yescomplemented
67#63838C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#117—31no—
71C2×C4×#67—31no—
72C2×#924—31no—
73#5702—316no—
74#5533—316no—
75C2×#898—31no—
76C2×#898—31no—
77C2×#897—31no—
78C2×#896—31no—
79C2×#892—31no—
80C2×#888—31no—
81C2×#888—31no—
82C2×#887—31no—
83C2×#887—31no—
84C2×#887—31no—
85C2×#885—31no—
86C2×#885—31no—
87C2×#885—31no—
88C2×#885—31no—
89C2×#67⋊C4—31no—
90C2×#879—31no—
91C2×#879—31no—
92C2×#879—31no—
93C2×#878—31no—
94C2×#877—31no—
95C2×#876—31no—
96C2×#876D311yescharacteristic, complemented
97C2×#872D311yescharacteristic, complemented
98C2×C4×Dic6—31no—
99C2×C4×Dic6—31no—
100C2×C4×Dic6—31no—
101C2×C4×Dic6—61no—
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
111C2×#634—24no—
112C2×#634C2314yes—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×C3×C4×D3—24no—
120C2×C3×C4×D3C2314yes—
121C2×#627—24no—
122C2×#627—24no—
123C2×#627C2314yes—
124C2×#627C2314yes—
125C2×#625—24no—
126C2×#625C2314yes—
127C2×D3×Dic3—24no—
128C2×D3×Dic3C2314yes—
129C32×C42C2314yes—
130C4⋊(C3⋊Dic3)C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133C4×C3⋊Dic3C2314yes—
134C4×C3⋊Dic3C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×C4×Dic3C2314yes—
146#3724C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150(C2×D3)⋊Dic3C2314yes—
151(C2×D3)⋊Dic3C2314yes—
152(C2×D3)⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155Dic32C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158C2×#556—91noSylow
159C23×C3×C4—31no—
160C22×#67—31no—
161C22×#67—31no—
162C23×Dic3—31no—
163C22×C4×D3—31no—
164C22×C4×D3C2×D311yescharacteristic
165C22×Dic6—31no—
166C22×Dic6—31no—
167C22×Dic6—31no—
168C22×Dic6—31no—
169C22×Dic6—31no—
170C22×Dic6—31no—
171C22×Dic6—61no—
172C3×#126—38no—
173C3×#117—38no—
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×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C42—21no—
185C2×C3×C42—31no—
186C2×C3×C42C2×D311yescharacteristic
187C2×C3×C42C2×D311yescharacteristic
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C4×#67—38no—
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)⋊C4C2×D311yescharacteristic
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—61no—
210#924—38no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—61no—
221C2×Dic3⋊C4—61no—
222C2×Dic3⋊C4C2×D311yescharacteristic
223C2×Dic3⋊C4C2×D311yescharacteristic
224C2×Dic3⋊C4C2×D311yescharacteristic
225C2×Dic3⋊C4C2×D311yescharacteristic
226C2×Dic3⋊C4C2×D311yescharacteristic
227C2×C4×Dic3—31no—
228C2×C4×Dic3—31no—
229C2×C4×Dic3—31no—
230C2×C4×Dic3—31no—
231C2×C4×Dic3—31no—
232C2×C4×Dic3—31no—
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—31no—
236C2×C4×Dic3—31no—
237C2×C4×Dic3—61no—
238C2×C4×Dic3—61no—
239C2×C4×Dic3C2×D311yescharacteristic
240#898—38no—
241#898—38no—
242#897—38no—
243#896—38no—
244#892—38no—
245#888—38no—
246#888—38no—
247#887—38no—
248#887—38no—
249#887—38no—
250#885—38no—
251#885—38no—
252#885—38no—
253#885—38no—
254#67⋊C4—38no—
255#879—38no—
256#879—38no—
257#879—38no—
258#878—38no—
259#877—38no—
260#876—38no—
261#876C2×D318yescomplemented
262#872C2×D318yescomplemented
263C4×Dic6—38no—
264C4×Dic6—38no—
265C4×Dic6—38no—
266C4×Dic6—68no—
267C23×C32C2411yescharacteristic
268C22×C3×D3—22no—
269C22×C3×D3—22no—
270C22×C3×D3—22no—
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3C2412yes—
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⋊Dic3#4114yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C2×C3⋊Dic3C2412yes—
289C2×C3⋊Dic3C2412yes—
290#634—28no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3#4114yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C3×C4×D3—28no—
304#627—28no—
305#627—28no—
306#625—28no—
307D3×Dic3—28no—
308#556—916no—
309C2×C4⋊Q8—91no—
310C2×#126—31no—
311C2×#126—91no—
312C2×#126—91no—
313C2×#126—91no—
314C2×#124—91no—
315C2×#124—91no—
316C2×C22⋊Q8—91no—
317C2×C22⋊Q8—91no—
318C2×C4×Q8—91no—
319C2×C4×Q8—91no—
320C2×C4×Q8—91no—
321C2×C4×D4—91no—
322C2×#117—31no—
323C2×#117—91no—
324C24×C3—31no—
325C24×C3—31no—
326C23×D3C22×D311yescharacteristic
327C23×D3C22×D311yescharacteristic
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—34no—
338C22×C3×C4—64no—
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—34no—
347C2×#67—64no—
348C2×#67—64no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—34no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—64no—
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C2×C4×D3—24no—
370C2×C4×D3—34no—
371C2×C4×D3—64no—
372C2×C4×D3C22×D314yes—
373C2×Dic6—34no—
374C2×Dic6—34no—
375C2×Dic6—34no—
376C2×Dic6—34no—
377C2×Dic6—34no—
378C2×Dic6—34no—
379C2×Dic6—64no—
380C2×Dic6—64no—
381C2×Dic6—64no—
382C2×Dic6—64no—
383C2×Dic6—64no—
384C2×Dic6—64no—
385C2×Dic6—68no—
386C2×Dic6—64no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C42—24no—
398C3×C42—34no—
399C3×C42C22×D314yes—
400C3×C42C22×D314yes—
401#217—34no—
402#217—34no—
403#217—34no—
404#217—34no—
405#217—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)⋊C4C22×D314yes—
412(C2×D3)⋊C4C22×D314yes—
413(C2×D3)⋊C4C22×D314yes—
414(C2×D3)⋊C4C22×D314yes—
415(C2×D3)⋊C4C22×D314yes—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—64no—
422Dic3⋊C4—34no—
423Dic3⋊C4—34no—
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—64no—
432Dic3⋊C4—64no—
433Dic3⋊C4C22×D314yes—
434Dic3⋊C4C22×D314yes—
435Dic3⋊C4C22×D314yes—
436Dic3⋊C4C22×D314yes—
437Dic3⋊C4C22×D314yes—
438C4×Dic3—34no—
439C4×Dic3—34no—
440C4×Dic3—34no—
441C4×Dic3—34no—
442C4×Dic3—34no—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—64no—
449C4×Dic3—64no—
450C4×Dic3C22×D314yes—
451C22×C32C2×#4112yes—
452C22×C32C2×#4112yes—
453C22×C322−1+412yes—
454C22×C32C2511yescharacteristic
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—44no—
462C2×C3×D3—44no—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—22no—
468C3⋊Dic3—22no—
469C3⋊Dic3C2×#4114yes—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3C2×#4114yes—
476C22×Q8—91no—
477C22×Q8—91no—
478C22×Q8—91no—
479C22×D4—91no—
480C23×C4—31no—
481C23×C4—91no—
482C4⋊Q8—98no—
483#126—38no—
484#126—98no—
485#126—98no—
486#126—98no—
487#124—98no—
488#124—98no—
489C22⋊Q8—98no—
490C22⋊Q8—98no—
491C4×Q8—98no—
492C4×Q8—98no—
493C4×Q8—98no—
494C4×D4—98no—
495#117—38no—
496#117—98no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—91no—
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×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—31no—
513C2×C22⋊C4—31no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C42—31no—
520C2×C42—91no—
521C2×C42—91no—
522C2×C42—91no—
523C2×C42—91no—
524C2×C42—91no—
525C2×C42D3211yescharacteristic
526C23×C3—21no—
527C23×C3—32no—
528C23×C3—32no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3—62no—
533C23×C3—62no—
534C23×C3—62no—
535C23×C3C23×D311yescharacteristic
536C23×C3C23×D311yescharacteristic
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3C23×D312yes—
544C22×D3C23×D312yes—
545C2×C3×C4—24no—
546C2×C3×C4—24no—
547C2×C3×C4—22no—
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—34no—
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—42no—
564C2×C3×C4—68no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—62no—
569C2×C3×C4—62no—
570C2×C3×C4C23×D312yes—
571C2×C3×C4C23×D312yes—
572C2×C3×C4C23×D312yes—
573C2×C3×C4C23×D312yes—
574C2×C3×C4C23×D312yes—
575C2×C3×C4C23×D312yes—
576#67—68no—
577#67—68no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—34no—
584C2×Dic3—34no—
585C2×Dic3—32no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—64no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—64no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—68no—
606C2×Dic3—122no—
607C2×Dic3—122no—
608C2×Dic3#23514yes—
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D312yes—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614C2×Dic3C23×D312yes—
615C4×D3—28no—
616C4×D3—68no—
617Dic6—68no—
618Dic6—68no—
619Dic6—68no—
620Dic6—68no—
621Dic6—68no—
622Dic6—616no—
623Dic6—68no—
624C2×C32#55614yescomplemented
625C2×C32C22×#4111yescharacteristic
626C2×C32C22×#4111yescharacteristic
627C2×C32C2×2−1+411yescharacteristic
628C3×D3—42no—
629C3×D3—42no—
630C24—31no—
631C24—31no—
632C2×Q8—94no—
633C2×Q8—94no—
634C2×Q8—94no—
635C2×Q8—184no—
636C2×Q8—184no—
637C2×Q8—184no—
638C2×D4—94no—
639C2×D4—184no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—34no—
647C22×C4—64no—
648C22×C4—94no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—91no—
653C22×C4—184no—
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—94no—
663C4⋊C4—94no—
664C4⋊C4—94no—
665C4⋊C4—94no—
666C4⋊C4—94no—
667C4⋊C4—94no—
668C4⋊C4—94no—
669C22⋊C4—34no—
670C22⋊C4—34no—
671C22⋊C4—34no—
672C22⋊C4—34no—
673C22⋊C4—34no—
674C22⋊C4—94no—
675C22⋊C4—94no—
676C22⋊C4—94no—
677C22⋊C4—94no—
678C22⋊C4—94no—
679C42—34no—
680C42—94no—
681C42—94no—
682C42—94no—
683C42—94no—
684C42—94no—
685C42C2×D3214yes—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—21no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—62no—
696C22×C3—124no—
697C22×C3—124no—
698C22×C3C2×#23512yes—
699C22×C3D3×#4112yes—
700C22×C3D3×#4112yes—
701C22×C3D3×#4112yes—
702C22×C3#101012yes—
703C22×C3#101012yes—
704C22×C3C24×D311yescharacteristic
705C22×C3C24×D311yescharacteristic
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—44no—
713C2×D3—44no—
714C3×C4—24no—
715C3×C4—24no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—34no—
723C3×C4—42no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4—62no—
727C3×C4—62no—
728C3×C4—62no—
729Dic3—22no—
730Dic3—22no—
731Dic3—22no—
732Dic3—22no—
733Dic3—22no—
734Dic3—34no—
735Dic3—34no—
736Dic3—64no—
737Dic3—64no—
738Dic3—62no—
739Dic3—62no—
740Dic3—62no—
741Dic3—62no—
742Dic3—62no—
743Dic3—62no—
744Dic3—122no—
745Dic3—122no—
746Dic3C2×#23514yes—
747C32C2×#55611yescharacteristic, complemented, Sylow
748C23—32no—
749C23—32no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23C22×D3211yescharacteristic
757Q8—188no—
758Q8—188no—
759Q8—188no—
760D4—188no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—34no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—68no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—94no—
778C2×C4—92no—
779C2×C4—92no—
780C2×C4—92no—
781C2×C4—92no—
782C2×C4—188no—
783C2×C4—182no—
784C2×C4—182no—
785C2×C4—182no—
786C2×C4C22×D3212yes—
787C2×C4C22×D3212yes—
788C2×C4C22×D3212yes—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—24no—
793C2×C3—122no—
794C2×C3—122no—
795C2×C3#553314yescomplemented
796C2×C3#570214yescomplemented
797C2×C3C22×#23511yescharacteristic
798C2×C3C2×D3×#4111yescharacteristic
799C2×C3C2×D3×#4111yescharacteristic
800C2×C3C2×D3×#4111yescharacteristic
801C2×C3C2×#101011yescharacteristic
802C2×C3C2×#101011yescharacteristic
803D3—42no—
804D3—42no—
805C22—62no—
806C22—62no—
807C22—62no—
808C22—62no—
809C22—62no—
810C22—62no—
811C22—124no—
812C22—124no—
813C22#6429812yes—
814C22D3×#23512yes—
815C22#6430612yes—
816C22C23×D3211yescharacteristic
817C4—22no—
818C4—22no—
819C4—22no—
820C4—34no—
821C4—62no—
822C4—62no—
823C4—62no—
824C4—62no—
825C4—62no—
826C4—94no—
827C4—182no—
828C4—182no—
829C4—182no—
830C3—21no—
831C3C2×#553311yescharacteristic, complemented
832C3C2×#570211yescharacteristic, complemented
833C2—122no—
834C2—122no—
835C2#1059393114yesdirect product factor
836C2C2×#6429811yescharacteristic
837C2C2×D3×#23511yescharacteristic
838C2C2×#6430611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C42D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
2. C2×C3×#876C2semidirect
3. C2×C3×#872C2semidirect
6. C2×#63893C2semidirect
8. C2×#63878C2semidirect
9. C2×#63862C2semidirect
10. C2×#63861C2semidirect
11. C2×#63859C2semidirect
12. C2×#63851C2semidirect
13. C2×#63840C2semidirect
14. C2×#63838C2semidirect
15. C2×#63837C2semidirect
16. #10593931C2direct (N × H)
31. C4×#634C22semidirect
43. C3×#876C22semidirect
44. C3×#872C22semidirect
59. #63893C22semidirect
61. #63878C22semidirect
62. #63862C22semidirect
63. #63861C22semidirect
64. #63859C22semidirect
65. #63851C22semidirect
66. #63840C22semidirect
67. #63838C22semidirect
68. #63837C22semidirect
96. C2×#876D3semidirect
97. C2×#872D3semidirect
261. #876C2×D3semidirect
262. #872C2×D3semidirect
624. C2×C32#556semidirect
747. C32C2×#556semidirect
795. C2×C3#5533semidirect
796. C2×C3#5702semidirect
831. C3C2×#5533semidirect
832. C3C2×#5702semidirect
835. C2#10593931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×#8762
C2×C3×#8722
C2×#639152
C2×#639132
C2×#638932
C2×#638792
C2×#638782
C2×#638622
C2×#638612
C2×#638592
C2×#638512
C2×#638402
C2×#638382
C2×#638372
#105939312
C2×#57023
C2×#55333