Finite Group Databasebeta

← C2×#10594319 #11901600

Subgroups — C2×#10594319 #11901600

Order 1152.

2121 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64098C211yesmaximal, characteristic, complemented
2C2×C3×#896C211yesmaximal, characteristic
3C2×C3×#890C211yesmaximal, characteristic, complemented
4C2×#63862C211yesmaximal, characteristic
5C2×#63859C211yesmaximal, characteristic
6C2×#63858C211yesmaximal, characteristic
7C2×#63858C211yesmaximal, characteristic
8C2×#63851C211yesmaximal, characteristic
9C2×#63846C211yesmaximal, characteristic, complemented
10C2×#63846C211yesmaximal, characteristic, complemented
11C2×#63845C211yesmaximal, characteristic, complemented
12C2×#63843C211yesmaximal, characteristic, complemented
13C2×#63841C211yesmaximal, characteristic
14C2×#63839C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594319C2116yesmaximal, direct product factor
17C2×#5696—31nomaximal
18C2×#5625—31nomaximal
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29#64098C2218yescomplemented
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C3×#896C2218yes—
41C3×#890C2218yescomplemented
42C2×#3724C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
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×Dic32C2211yescharacteristic
54C2×Dic32C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63862C2218yes—
58#63859C2218yes—
59#63858C2218yes—
60#63858C2218yes—
61#63851C2218yes—
62#63846C2218yescomplemented
63#63846C2218yescomplemented
64#63845C2218yescomplemented
65#63843C2218yescomplemented
66#63841C2218yes—
67#63839C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#125—31no—
70C2×C3×C22⋊Q8—31no—
71C2×Q8×Dic3—31no—
72C2×#944—31no—
73C2×#926—31no—
74C2×#924—31no—
75#5696—316no—
76#5625—316no—
77C2×#898—31no—
78C2×#898—31no—
79C2×#898—31no—
80C2×#896—31no—
81C2×#896D311yescharacteristic
82C2×#892—31no—
83C2×#890—31no—
84C2×#890—31no—
85C2×#890—31no—
86C2×#890D311yescharacteristic, complemented
87C2×#889—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#889—31no—
91C2×#889—31no—
92C2×#889—61no—
93C2×#888—31no—
94C2×#887—31no—
95C2×#887—31no—
96C2×#879—31no—
97C2×#879—31no—
98C2×#879—31no—
99C2×#879—31no—
100C2×#876—31no—
101C2×C4×Dic6—31no—
102C23×C3×D3C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
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×C3×C4×D3—24no—
118C2×C3×C4×D3C2314yes—
119C2×C3×Dic6—24no—
120C2×C3×Dic6C2314yes—
121C2×#627—24no—
122C2×#627C2314yes—
123C32×C4⋊C4C2314yes—
124C4⋊(C3⋊Dic3)C2314yes—
125#3750C2314yes—
126#3750C2314yes—
127#3750C2314yes—
128#3750C2314yes—
129C4×C3⋊Dic3C2314yes—
130C3×(C2×D3)⋊C4C2314yes—
131C3×(C2×D3)⋊C4C2314yes—
132C3×C4⋊Dic3C2314yes—
133C3×C4⋊Dic3C2314yes—
134C3×C4⋊Dic3C2314yes—
135C3×Dic3⋊C4C2314yes—
136C3×Dic3⋊C4C2314yes—
137C3×Dic3⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×C4×Dic3C2314yes—
140#3724C2314yes—
141Dic3⋊Dic3C2314yes—
142Dic3⋊Dic3C2314yes—
143Dic3⋊Dic3C2314yes—
144Dic3⋊Dic3C2314yes—
145Dic3⋊Dic3C2314yes—
146Dic3⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2314yes—
148(C2×D3)⋊Dic3C2314yes—
149(C2×D3)⋊Dic3C2314yes—
150(C2×D3)⋊Dic3C2314yes—
151Dic32C2314yes—
152Dic32C2314yes—
153Dic32C2314yes—
154Dic32C2314yes—
155C2×#541—91noSylow
156C22×C3×Q8—31no—
157C23×C3×C4—31no—
158C22×C4×D3C2×D311yescharacteristic
159C22×Dic6—31no—
160C22×Dic6—31no—
161C22×Dic6C2×D311yescharacteristic
162C3×#125—38no—
163C3×C22⋊Q8—38no—
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4C2×D311yescharacteristic
173C2×C3×C4⋊C4C2×D311yescharacteristic
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C42—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181Q8×Dic3—38no—
182#944—38no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189#926—38no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—61no—
199C2×C4⋊Dic3C2×D311yescharacteristic
200C2×C4⋊Dic3C2×D311yescharacteristic
201C2×C4⋊Dic3C2×D311yescharacteristic
202#924—38no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
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—61no—
220C2×Dic3⋊C4—61no—
221C2×Dic3⋊C4—61no—
222C2×Dic3⋊C4—61no—
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×Dic3C2×D311yescharacteristic
239#898—38no—
240#898—38no—
241#898—38no—
242#896—38no—
243#896C2×D318yes—
244#892—38no—
245#890—38no—
246#890—38no—
247#890—38no—
248#890C2×D318yescomplemented
249#889—38no—
250#889—38no—
251#889—38no—
252#889—38no—
253#889—38no—
254#889—68no—
255#888—38no—
256#887—38no—
257#887—38no—
258#879—38no—
259#879—38no—
260#879—38no—
261#879—38no—
262#876—38no—
263C4×Dic6—38no—
264C23×C32C2411yescharacteristic
265C22×C3×D3—22no—
266C22×C3×D3—22no—
267C22×C3×D3—22no—
268C22×C3×D3C2412yes—
269C2×C32×C4—22no—
270C2×C32×C4—22no—
271C2×C32×C4—22no—
272C2×C32×C4C2412yes—
273C2×C32×C4C2412yes—
274C2×C32×C4C2412yes—
275C2×C3⋊Dic3—22no—
276C2×C3⋊Dic3—22no—
277C2×C3⋊Dic3—22no—
278C2×C3⋊Dic3—22no—
279C2×C3⋊Dic3C2412yes—
280C2×C3⋊Dic3C2412yes—
281C2×C3⋊Dic3C2412yes—
282C2×C3⋊Dic3C2412yes—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3#4114yes—
290C2×C3×Dic3C2412yes—
291C2×C3×Dic3C2412yes—
292C2×C3×Dic3C2412yes—
293C2×C3×Dic3C2412yes—
294C2×C3×Dic3C2412yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2412yes—
297C3×C4×D3—28no—
298C3×Dic6—28no—
299#627—28no—
300#541—916no—
301C2×C4⋊Q8—91no—
302C2×#126—91no—
303C2×#126—91no—
304C2×#126—91no—
305C2×#126—91no—
306C2×#125—31no—
307C2×#125—91no—
308C2×#125—91no—
309C2×#125—91no—
310C2×#125—91no—
311C2×C22⋊Q8—31no—
312C2×C22⋊Q8—91no—
313C2×C4×Q8—91no—
314C2×C4×Q8—91no—
315C2×#117—91no—
316C24×C3—31no—
317C23×D3C22×D311yescharacteristic
318C2×C3×Q8—34no—
319C2×C3×Q8—64no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—34no—
331C22×C3×C4—64no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C2×C4×D3—24no—
358C2×C4×D3C22×D314yes—
359C2×Dic6—24no—
360C2×Dic6—34no—
361C2×Dic6—34no—
362C2×Dic6—64no—
363C2×Dic6—64no—
364C2×Dic6C22×D314yes—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—34no—
367C3×C4⋊C4—34no—
368C3×C4⋊C4—34no—
369C3×C4⋊C4—34no—
370C3×C4⋊C4—34no—
371C3×C4⋊C4—34no—
372C3×C4⋊C4—34no—
373C3×C4⋊C4C22×D314yes—
374C3×C4⋊C4C22×D314yes—
375C3×C22⋊C4—34no—
376C3×C22⋊C4—34no—
377C3×C42—34no—
378#217—34no—
379#217—34no—
380#217—34no—
381#217—34no—
382(C2×D3)⋊C4—34no—
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—34no—
386(C2×D3)⋊C4C22×D314yes—
387(C2×D3)⋊C4C22×D314yes—
388C4⋊Dic3—34no—
389C4⋊Dic3—34no—
390C4⋊Dic3—34no—
391C4⋊Dic3—34no—
392C4⋊Dic3—34no—
393C4⋊Dic3—34no—
394C4⋊Dic3—34no—
395C4⋊Dic3—34no—
396C4⋊Dic3—64no—
397C4⋊Dic3C22×D314yes—
398C4⋊Dic3C22×D314yes—
399C4⋊Dic3C22×D314yes—
400Dic3⋊C4—34no—
401Dic3⋊C4—34no—
402Dic3⋊C4—34no—
403Dic3⋊C4—34no—
404Dic3⋊C4—34no—
405Dic3⋊C4—34no—
406Dic3⋊C4—34no—
407Dic3⋊C4—34no—
408Dic3⋊C4—34no—
409Dic3⋊C4—34no—
410Dic3⋊C4—34no—
411Dic3⋊C4—34no—
412Dic3⋊C4—34no—
413Dic3⋊C4—34no—
414Dic3⋊C4—34no—
415Dic3⋊C4—34no—
416Dic3⋊C4—64no—
417Dic3⋊C4—64no—
418Dic3⋊C4—64no—
419Dic3⋊C4—64no—
420Dic3⋊C4C22×D314yes—
421Dic3⋊C4C22×D314yes—
422Dic3⋊C4C22×D314yes—
423Dic3⋊C4C22×D314yes—
424C4×Dic3—34no—
425C4×Dic3—34no—
426C4×Dic3—34no—
427C4×Dic3—34no—
428C4×Dic3—34no—
429C4×Dic3—34no—
430C4×Dic3—34no—
431C4×Dic3—34no—
432C4×Dic3—34no—
433C4×Dic3—34no—
434C4×Dic3—64no—
435C4×Dic3C22×D314yes—
436C22×C32C2×#4112yes—
437C22×C322−1+412yes—
438C22×C322−1+412yes—
439C22×C32C2511yescharacteristic
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—44no—
444C32×C4—22no—
445C32×C4—22no—
446C32×C4—22no—
447C3⋊Dic3—22no—
448C3⋊Dic3—22no—
449C3⋊Dic3—22no—
450C3⋊Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—22no—
457C3×Dic3C2×#4114yes—
458C22×Q8—31no—
459C22×Q8—91no—
460C23×C4—31no—
461C4⋊Q8—98no—
462#126—98no—
463#126—98no—
464#126—98no—
465#126—98no—
466#125—38no—
467#125—98no—
468#125—98no—
469#125—98no—
470#125—98no—
471C22⋊Q8—38no—
472C22⋊Q8—98no—
473C4×Q8—98no—
474C4×Q8—98no—
475#117—98no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—31no—
478C2×C4⋊C4—31no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—91no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4D3211yescharacteristic
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C42—31no—
503C2×C42—91no—
504C2×C42—91no—
505C2×C42—91no—
506C2×C42—91no—
507C2×C42—91no—
508C23×C3—21no—
509C23×C3—32no—
510C23×C3—62no—
511C23×C3—62no—
512C23×C3—62no—
513C23×C3C23×D311yescharacteristic
514C23×C3C23×D311yescharacteristic
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3C23×D312yes—
519C3×Q8—68no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—34no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—42no—
538C2×C3×C4—42no—
539C2×C3×C4—42no—
540C2×C3×C4—68no—
541C2×C3×C4—62no—
542C2×C3×C4—62no—
543C2×C3×C4—62no—
544C2×C3×C4—62no—
545C2×C3×C4—62no—
546C2×C3×C4—62no—
547C2×C3×C4C23×D312yes—
548C2×C3×C4C23×D312yes—
549C2×C3×C4C23×D312yes—
550C2×C3×C4C23×D312yes—
551C2×C3×C4C23×D312yes—
552C2×C3×C4C23×D312yes—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—32no—
560C2×Dic3—32no—
561C2×Dic3—32no—
562C2×Dic3—32no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—62no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—62no—
571C2×Dic3—64no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—62no—
575C2×Dic3—62no—
576C2×Dic3—62no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—62no—
580C2×Dic3—122no—
581C2×Dic3—122no—
582C2×Dic3—122no—
583C2×Dic3#23714yes—
584C2×Dic3C23×D312yes—
585C2×Dic3C23×D312yes—
586C2×Dic3C23×D312yes—
587C2×Dic3C23×D312yes—
588C2×Dic3C23×D312yes—
589C2×Dic3C23×D312yes—
590C2×Dic3C23×D312yes—
591C4×D3—28no—
592Dic6—28no—
593Dic6—68no—
594Dic6—68no—
595C2×C32#54114yescomplemented
596C2×C32C22×#4111yescharacteristic
597C2×C32C2×2−1+411yescharacteristic
598C2×C32C2×2−1+411yescharacteristic
599C3×D3—42no—
600C24—31no—
601C2×Q8—34no—
602C2×Q8—64no—
603C2×Q8—94no—
604C2×Q8—184no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—34no—
613C22×C4—64no—
614C22×C4—91no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4C2×D3211yescharacteristic
619C22×C4C2×D3211yescharacteristic
620C22×C4C2×D3211yescharacteristic
621C4⋊C4—34no—
622C4⋊C4—34no—
623C4⋊C4—34no—
624C4⋊C4—34no—
625C4⋊C4—34no—
626C4⋊C4—34no—
627C4⋊C4—34no—
628C4⋊C4—94no—
629C4⋊C4—94no—
630C4⋊C4—94no—
631C4⋊C4—94no—
632C4⋊C4—94no—
633C4⋊C4—94no—
634C4⋊C4—94no—
635C4⋊C4—94no—
636C4⋊C4—94no—
637C4⋊C4—94no—
638C4⋊C4—94no—
639C4⋊C4—94no—
640C4⋊C4C2×D3214yes—
641C22⋊C4—34no—
642C22⋊C4—34no—
643C22⋊C4—94no—
644C22⋊C4—94no—
645C22⋊C4—94no—
646C22⋊C4—94no—
647C42—34no—
648C42—94no—
649C42—94no—
650C42—94no—
651C42—94no—
652C42—94no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3—62no—
660C22×C3—124no—
661C22×C3C2×#23712yes—
662C22×C3#100712yes—
663C22×C3#100712yes—
664C22×C3D3×#4112yes—
665C22×C3#101012yes—
666C22×C3#101012yes—
667C22×C3C24×D311yescharacteristic
668C22×C3C24×D311yescharacteristic
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—22no—
672C2×D3—44no—
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—34no—
680C3×C4—42no—
681C3×C4—42no—
682C3×C4—42no—
683C3×C4—62no—
684C3×C4—62no—
685C3×C4—62no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—62no—
689Dic3—22no—
690Dic3—22no—
691Dic3—22no—
692Dic3—22no—
693Dic3—22no—
694Dic3—22no—
695Dic3—64no—
696Dic3—62no—
697Dic3—62no—
698Dic3—62no—
699Dic3—62no—
700Dic3—62no—
701Dic3—62no—
702Dic3—62no—
703Dic3—62no—
704Dic3—122no—
705Dic3—122no—
706Dic3—122no—
707Dic3C2×#23714yes—
708C32C2×#54111yescharacteristic, complemented, Sylow
709C23—32no—
710C23—62no—
711C23—62no—
712C23—62no—
713C23C22×D3211yescharacteristic
714Q8—68no—
715Q8—188no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—34no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—32no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—68no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—92no—
735C2×C4—92no—
736C2×C4—92no—
737C2×C4—92no—
738C2×C4—182no—
739C2×C4—182no—
740C2×C4—182no—
741C2×C4—182no—
742C2×C4C22×D3212yes—
743C2×C4C22×D3212yes—
744C2×C4C22×D3212yes—
745C2×C3—24no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—122no—
750C2×C3#562514yescomplemented
751C2×C3#569614yescomplemented
752C2×C3C22×#23711yescharacteristic
753C2×C3C2×#100711yescharacteristic
754C2×C3C2×#100711yescharacteristic
755C2×C3C2×D3×#4111yescharacteristic
756C2×C3C2×#101011yescharacteristic
757C2×C3C2×#101011yescharacteristic
758D3—42no—
759C22—62no—
760C22—62no—
761C22—62no—
762C22—124no—
763C22#6429712yes—
764C22D3×#23712yes—
765C22#6431512yes—
766C22C23×D3211yescharacteristic
767C4—22no—
768C4—22no—
769C4—22no—
770C4—34no—
771C4—62no—
772C4—62no—
773C4—62no—
774C4—62no—
775C4—62no—
776C4—62no—
777C4—182no—
778C4—182no—
779C4—182no—
780C4—182no—
781C3—21no—
782C3C2×#562511yescharacteristic, complemented
783C3C2×#569611yescharacteristic, complemented
784C2—122no—
785C2#1059431914yesdirect product factor
786C2C2×#6429711yescharacteristic
787C2C2×D3×#23711yescharacteristic
788C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#541
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×#64098C2semidirect
3. C2×C3×#890C2semidirect
9. C2×#63846C2semidirect
10. C2×#63846C2semidirect
11. C2×#63845C2semidirect
12. C2×#63843C2semidirect
14. C2×#63839C2semidirect
15. C2×#63837C2semidirect
16. #10594319C2direct (N × H)
29. #64098C22semidirect
41. C3×#890C22semidirect
62. #63846C22semidirect
63. #63846C22semidirect
64. #63845C22semidirect
65. #63843C22semidirect
67. #63839C22semidirect
68. #63837C22semidirect
86. C2×#890D3semidirect
248. #890C2×D3semidirect
595. C2×C32#541semidirect
708. C32C2×#541semidirect
750. C2×C3#5625semidirect
751. C2×C3#5696semidirect
782. C3C2×#5625semidirect
783. C3C2×#5696semidirect
785. C2#10594319direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640982
C2×C3×#8962
C2×C3×#8902
C2×#638622
C2×#638592
C2×#638582
C2×#638512
C2×#638462
C2×#638452
C2×#638432
C2×#638412
C2×#638392
C2×#638372
#105943192
C2×#56963
C2×#56253