Finite Group Databasebeta

← C2×#10594088 #11900621

Subgroups — C2×#10594088 #11900621

Order 1152.

2629 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64094C211yesmaximal, characteristic, complemented
2C2×C3×#883C211yesmaximal, characteristic, complemented
3C2×C3×#877C211yesmaximal, characteristic, complemented
4C2×Dic3×#67C211yesmaximal, characteristic, complemented
5C2×#63971C211yesmaximal, characteristic
6C2×#63956C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8C2×#63896C211yesmaximal, characteristic, complemented
9C2×#63880C211yesmaximal, characteristic, complemented
10C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
11C2×#63870C211yesmaximal, characteristic, complemented
12C2×#63850C211yesmaximal, characteristic, complemented
13C2×#63848C211yesmaximal, characteristic, complemented
14C2×#63844C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594088C2116yesmaximal, direct product factor
17C2×#5649—31nomaximal
18C2×#5528—31nomaximal
19C22×#638C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64094C2218yescomplemented
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#883C2218yescomplemented
44C3×#877C2218yescomplemented
45Dic3×#67C2218yescomplemented
46#63971C2218yes—
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56#63956C2218yescomplemented
57C2×Dic32C2211yescharacteristic
58C2×Dic32C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60#63952C2218yescomplemented
61#63896C2218yescomplemented
62#63880C2218yescomplemented
63C4×D3×Dic3C2218yescomplemented
64#63870C2218yescomplemented
65#63850C2218yescomplemented
66#63848C2218yescomplemented
67#63844C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#117—31no—
71C2×#939—31no—
72C2×D4×Dic3—31no—
73C2×#929—31no—
74C2×C4×#67—31no—
75C2×C4×#67—31no—
76C22×C4×Dic3—31no—
77#5649—316no—
78#5528—316no—
79C2×#898—31no—
80C2×#898—31no—
81C2×#896—31no—
82C2×#894—31no—
83C2×#892—31no—
84C2×#889—31no—
85C2×#889—31no—
86C2×#887—31no—
87C2×#885—31no—
88C2×#885—31no—
89C2×#885—61no—
90C2×#884—31no—
91C2×#883D311yescharacteristic, complemented
92C2×#67⋊C4—31no—
93C2×#67⋊C4—31no—
94C2×#879—31no—
95C2×#879—31no—
96C2×#878—31no—
97C2×#877D311yescharacteristic, complemented
98C2×C4×D12—31no—
99C2×#872—31no—
100C2×C42×D3—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C2×#638—24no—
108C2×#638C2314yes—
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×#634—24no—
113C2×#634C2314yes—
114C2×C3×#67—24no—
115C2×C3×#67C2314yes—
116C22×C3×Dic3—24no—
117C22×C3×Dic3C2314yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×C4×D3—24no—
126C2×C3×C4×D3C2314yes—
127C2×#626—24no—
128C2×#626C2314yes—
129C2×#624—24no—
130C2×#624C2314yes—
131C2×D3×Dic3—24no—
132C2×D3×Dic3—24no—
133C2×D3×Dic3C2314yes—
134C2×D3×Dic3C2314yes—
135C32×C22⋊C4C2314yes—
136#3757C2314yes—
137#3752C2314yes—
138#3752C2314yes—
139C4×C3⋊Dic3C2314yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×C4⋊Dic3C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×C4×Dic3C2314yes—
148C3×C4×Dic3C2314yes—
149#3724C2314yes—
150#3724C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156#3722C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158Dic32C2314yes—
159Dic32C2314yes—
160Dic32C2314yes—
161C2×#529—91noSylow
162C22×C3×D4—31no—
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—61no—
169C22×#67C2×D311yescharacteristic
170C23×Dic3—31no—
171C23×Dic3—31no—
172C23×Dic3C2×D311yescharacteristic
173C22×D12—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3C2×D311yescharacteristic
179C22×Dic6—31no—
180C22×Dic6—31no—
181C22×Dic6—61no—
182C3×#123—38no—
183C3×#117—38no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C22⋊C4—21no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4C2×D311yescharacteristic
193C2×C3×C22⋊C4C2×D311yescharacteristic
194C2×C3×C42—31no—
195C2×C3×C42—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—61no—
200C2×#217C2×D311yescharacteristic
201C2×#217C2×D311yescharacteristic
202#939—38no—
203D4×Dic3—38no—
204#929—38no—
205C4×#67—38no—
206C4×#67—38no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—61no—
217C2×(C2×D3)⋊C4—61no—
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4C2×D311yescharacteristic
233C2×Dic3⋊C4C2×D311yescharacteristic
234C2×Dic3⋊C4C2×D311yescharacteristic
235C2×C4×Dic3—31no—
236C2×C4×Dic3—31no—
237C2×C4×Dic3—31no—
238C2×C4×Dic3—31no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3—38no—
244C2×C4×Dic3—61no—
245C2×C4×Dic3C2×D311yescharacteristic
246C2×C4×Dic3C2×D311yescharacteristic
247#898—38no—
248#898—38no—
249#896—38no—
250#894—38no—
251#892—38no—
252#889—38no—
253#889—38no—
254#887—38no—
255#885—38no—
256#885—38no—
257#885—68no—
258#884—38no—
259#883C2×D318yescomplemented
260#67⋊C4—38no—
261#67⋊C4—38no—
262#879—38no—
263#879—38no—
264#878—38no—
265#877C2×D318yescomplemented
266C4×D12—38no—
267#872—38no—
268C42×D3—38no—
269C4×Dic6—38no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2412yes—
274C23×C32C2411yescharacteristic
275C22×C3⋊D3—22no—
276C22×C3⋊D3—22no—
277C22×C3⋊D3—22no—
278C22×C3⋊D3C2412yes—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3#4114yes—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4C2412yes—
286C2×C32×C4C2412yes—
287#638—28no—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3#4114yes—
291C2×C3⋊Dic3C2412yes—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294#634—28no—
295C3×#67—28no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—28no—
303C2×C3×Dic3#4114yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C3×C4×D3—28no—
312#626—28no—
313#624—28no—
314D3×Dic3—28no—
315D3×Dic3—28no—
316#529—916no—
317C2×#126—91no—
318C2×#126—91no—
319C2×#125—91no—
320C2×#124—91no—
321C2×#123—31no—
322C2×#123—91no—
323C2×C22⋊Q8—91no—
324C2×#121—91no—
325C2×C4×Q8—91no—
326C2×C4×D4—91no—
327C2×C4×D4—91no—
328C2×C4×D4—91no—
329C2×#117—31no—
330C2×#117—91no—
331C22×C42—91no—
332C24×C3—21no—
333C24×C3—31no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C23×D3—31no—
337C23×D3—31no—
338C23×D3—61no—
339C23×D3C22×D311yescharacteristic
340C2×C3×D4—34no—
341C2×C3×D4—64no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C22×C3×C4—64no—
354C22×C3×C4—64no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—24no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—64no—
364C2×#67—64no—
365C2×#67—64no—
366C2×#67—64no—
367C2×#67—124no—
368C2×#67C22×D314yes—
369C22×Dic3—24no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—34no—
377C22×Dic3—34no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—64no—
382C22×Dic3—64no—
383C22×Dic3C22×D314yes—
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C2×D12—34no—
392C2×D12—64no—
393C2×C4×D3—24no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—34no—
397C2×C4×D3—34no—
398C2×C4×D3—64no—
399C2×C4×D3—64no—
400C2×C4×D3—64no—
401C2×C4×D3—64no—
402C2×C4×D3C22×D314yes—
403C2×Dic6—34no—
404C2×Dic6—34no—
405C2×Dic6—64no—
406C2×Dic6—64no—
407C2×Dic6—64no—
408C2×Dic6—124no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4—34no—
413C3×C22⋊C4—24no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4C22×D314yes—
418C3×C22⋊C4C22×D314yes—
419C3×C42—34no—
420C3×C42—34no—
421#217—34no—
422#217—34no—
423#217—34no—
424#217—64no—
425#217C22×D314yes—
426#217C22×D314yes—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—64no—
437(C2×D3)⋊C4—64no—
438(C2×D3)⋊C4C22×D314yes—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3C22×D314yes—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4C22×D314yes—
453Dic3⋊C4C22×D314yes—
454Dic3⋊C4C22×D314yes—
455C4×Dic3—34no—
456C4×Dic3—34no—
457C4×Dic3—34no—
458C4×Dic3—34no—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—64no—
464C4×Dic3C22×D314yes—
465C4×Dic3C22×D314yes—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—44no—
470C22×C32C2×#4112yes—
471C22×C32C2×#4112yes—
472C22×C32C2×#4112yes—
473C22×C32C2511yescharacteristic
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—44no—
478C2×C3×D3—28no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3C2×#4114yes—
482C32×C4—22no—
483C32×C4—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3⋊Dic3C2×#4114yes—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3C2×#4114yes—
494C22×Q8—91no—
495C22×D4—31no—
496C22×D4—91no—
497C22×D4—91no—
498C23×C4—31no—
499C23×C4—31no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4—91no—
503#126—98no—
504#126—98no—
505#125—98no—
506#124—98no—
507#123—38no—
508#123—98no—
509C22⋊Q8—98no—
510#121—98no—
511C4×Q8—98no—
512C4×D4—98no—
513C4×D4—98no—
514C4×D4—98no—
515#117—38no—
516#117—98no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4D3211yescharacteristic
537C2×C42—31no—
538C2×C42—31no—
539C2×C42—98no—
540C2×C42—91no—
541C2×C42—91no—
542C2×C42—91no—
543C2×C42—91no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—21no—
552C23×C3—34no—
553C23×C3—32no—
554C23×C3—42no—
555C23×C3—42no—
556C23×C3—42no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3C23×D312yes—
560C23×C3C23×D312yes—
561C23×C3C23×D311yescharacteristic
562C23×C3C23×D311yescharacteristic
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—32no—
566C22×D3—32no—
567C22×D3—62no—
568C22×D3—62no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—62no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3#23714yes—
578C22×D3C23×D312yes—
579C3×D4—68no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—34no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—42no—
595C2×C3×C4—42no—
596C2×C3×C4—68no—
597C2×C3×C4—68no—
598C2×C3×C4—62no—
599C2×C3×C4—62no—
600C2×C3×C4—62no—
601C2×C3×C4—62no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4C23×D312yes—
605C2×C3×C4C23×D312yes—
606C2×C3×C4C23×D312yes—
607C2×C3×C4C23×D312yes—
608#67—28no—
609#67—68no—
610#67—68no—
611#67—68no—
612#67—128no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—28no—
620C2×Dic3—34no—
621C2×Dic3—34no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—32no—
627C2×Dic3—32no—
628C2×Dic3—64no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—68no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—62no—
637C2×Dic3—68no—
638C2×Dic3—122no—
639C2×Dic3—122no—
640C2×Dic3#23514yes—
641C2×Dic3C23×D312yes—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D312yes—
645C2×Dic3C23×D312yes—
646C2×Dic3C23×D312yes—
647C2×Dic3C23×D312yes—
648D12—68no—
649C4×D3—28no—
650C4×D3—68no—
651C4×D3—68no—
652C4×D3—68no—
653C4×D3—68no—
654Dic6—68no—
655Dic6—68no—
656Dic6—128no—
657C2×C32—42no—
658C2×C32#52914yescomplemented
659C2×C32C22×#4111yescharacteristic
660C2×C32C22×#4111yescharacteristic
661C2×C32C22×#4111yescharacteristic
662C3⋊D3—42no—
663C3×D3—24no—
664C24—31no—
665C24—91no—
666C24C2×D3211yescharacteristic
667C2×Q8—94no—
668C2×Q8—184no—
669C2×D4—34no—
670C2×D4—64no—
671C2×D4—94no—
672C2×D4—94no—
673C2×D4—184no—
674C2×D4—184no—
675C22×C4—31no—
676C22×C4—34no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—34no—
684C22×C4—64no—
685C22×C4—64no—
686C22×C4—94no—
687C22×C4—94no—
688C22×C4—94no—
689C22×C4—91no—
690C22×C4—91no—
691C22×C4—91no—
692C22×C4—184no—
693C22×C4—184no—
694C22×C4—184no—
695C22×C4C2×D3211yescharacteristic
696C22×C4C2×D3211yescharacteristic
697C4⋊C4—34no—
698C4⋊C4—34no—
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—94no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—34no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4C2×D3214yes—
717C42—34no—
718C42—34no—
719C42—94no—
720C42—94no—
721C42—94no—
722C42—94no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—21no—
733C22×C3—34no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—44no—
738C22×C3—44no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—68no—
742C22×C3—84no—
743C22×C3C2×#23512yes—
744C22×C3C2×#23712yes—
745C22×C3D3×#4112yes—
746C22×C3D3×#4112yes—
747C22×C3D3×#4112yes—
748C22×C3D3×#4112yes—
749C22×C3C24×D311yescharacteristic
750C22×C3C24×D311yescharacteristic
751C2×D3—28no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—122no—
763C2×D3—124no—
764C2×D3—124no—
765C2×D3—244no—
766C2×D3C2×#23714yes—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—34no—
772C3×C4—42no—
773C3×C4—42no—
774C3×C4—62no—
775C3×C4—62no—
776C3×C4—62no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—62no—
780Dic3—22no—
781Dic3—22no—
782Dic3—22no—
783Dic3—22no—
784Dic3—22no—
785Dic3—22no—
786Dic3—34no—
787Dic3—34no—
788Dic3—64no—
789Dic3—62no—
790Dic3—62no—
791Dic3—62no—
792Dic3—62no—
793Dic3—122no—
794Dic3—122no—
795Dic3C2×#23514yes—
796C32C2×#52911yescharacteristic, complemented, Sylow
797C23—22no—
798C23—22no—
799C23—22no—
800C23—34no—
801C23—32no—
802C23—62no—
803C23—62no—
804C23—92no—
805C23—182no—
806C23—182no—
807C23—182no—
808C23C22×D3212yes—
809C23C22×D3211yescharacteristic
810Q8—188no—
811D4—68no—
812D4—188no—
813D4—188no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—34no—
817C2×C4—32no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—68no—
825C2×C4—68no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—94no—
833C2×C4—92no—
834C2×C4—92no—
835C2×C4—92no—
836C2×C4—188no—
837C2×C4—188no—
838C2×C4—188no—
839C2×C4—182no—
840C2×C4—182no—
841C2×C4C22×D3212yes—
842C2×C4C22×D3212yes—
843C2×C3—24no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—42no—
848C2×C3—42no—
849C2×C3—64no—
850C2×C3—82no—
851C2×C3#552814yescomplemented
852C2×C3#564914yescomplemented
853C2×C3C22×#23511yescharacteristic
854C2×C3C22×#23711yescharacteristic
855C2×C3C2×D3×#4111yescharacteristic
856C2×C3C2×D3×#4111yescharacteristic
857C2×C3C2×D3×#4111yescharacteristic
858C2×C3C2×D3×#4111yescharacteristic
859D3—24no—
860D3—122no—
861D3—122no—
862D3—242no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—34no—
867C22—44no—
868C22—68no—
869C22—62no—
870C22—62no—
871C22—182no—
872C22—182no—
873C22—182no—
874C22—364no—
875C22D3×#23512yes—
876C22D3×#23712yes—
877C22#6431212yes—
878C22C23×D3211yescharacteristic
879C4—22no—
880C4—22no—
881C4—34no—
882C4—62no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—62no—
888C4—94no—
889C4—182no—
890C4—182no—
891C3—21no—
892C3C2×#552811yescharacteristic, complemented
893C3C2×#564911yescharacteristic, complemented
894C2—42no—
895C2—64no—
896C2—362no—
897C2#1059408814yesdirect product factor
898C2C2×D3×#23511yescharacteristic
899C2C2×D3×#23711yescharacteristic
900C2C2×#6431211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63971C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64094C2semidirect
2. C2×C3×#883C2semidirect
3. C2×C3×#877C2semidirect
4. C2×Dic3×#67C2semidirect
6. C2×#63956C2semidirect
7. C2×#63952C2semidirect
8. C2×#63896C2semidirect
9. C2×#63880C2semidirect
10. C2×C4×D3×Dic3C2semidirect
11. C2×#63870C2semidirect
12. C2×#63850C2semidirect
13. C2×#63848C2semidirect
14. C2×#63844C2semidirect
15. C2×#63836C2semidirect
16. #10594088C2direct (N × H)
33. #64094C22semidirect
43. C3×#883C22semidirect
44. C3×#877C22semidirect
45. Dic3×#67C22semidirect
56. #63956C22semidirect
60. #63952C22semidirect
61. #63896C22semidirect
62. #63880C22semidirect
63. C4×D3×Dic3C22semidirect
64. #63870C22semidirect
65. #63850C22semidirect
66. #63848C22semidirect
67. #63844C22semidirect
68. #63836C22semidirect
91. C2×#883D3semidirect
97. C2×#877D3semidirect
259. #883C2×D3semidirect
265. #877C2×D3semidirect
658. C2×C32#529semidirect
796. C32C2×#529semidirect
851. C2×C3#5528semidirect
852. C2×C3#5649semidirect
892. C3C2×#5528semidirect
893. C3C2×#5649semidirect
897. C2#10594088direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640942
C2×C3×#8832
C2×C3×#8772
C2×Dic3×#672
C2×#639712
C2×#639562
C2×#639522
C2×#638962
C2×#638802
C2×C4×D3×Dic32
C2×#638702
C2×#638502
C2×#638482
C2×#638442
C2×#638362
#105940882
C2×#56493
C2×#55283