Finite Group Databasebeta

← C2×#10594400 #11901919

Subgroups — C2×#10594400 #11901919

Order 1152.

2321 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64105C211yesmaximal, characteristic
2C2×C3×#889C211yesmaximal, characteristic, complemented
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C2×#63895C211yesmaximal, characteristic
5C2×#63888C211yesmaximal, characteristic
6C2×#63883C211yesmaximal, characteristic
7C2×#63871C211yesmaximal, characteristic
8C2×#63867C211yesmaximal, characteristic, complemented
9C2×#63866C211yesmaximal, characteristic, complemented
10C2×#63846C211yesmaximal, characteristic, complemented
11C2×#63846C211yesmaximal, characteristic, complemented
12C2×#63840C211yesmaximal, characteristic, complemented
13C2×#63839C211yesmaximal, characteristic, complemented
14C2×#63836C211yesmaximal, characteristic
15C2×#63836C211yesmaximal, characteristic
16#10594400C2116yesmaximal, direct product factor
17C2×#5729—31nomaximal
18C2×#5689—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31#64105C2218yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×#889C2218yescomplemented
43C3×#888C2218yescomplemented
44C2×#3724C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63895C2218yes—
58#63888C2218yes—
59#63883C2218yes—
60#63871C2218yes—
61#63867C2218yescomplemented
62#63866C2218yescomplemented
63#63846C2218yescomplemented
64#63846C2218yescomplemented
65#63840C2218yescomplemented
66#63839C2218yescomplemented
67#63836C2218yes—
68#63836C2218yes—
69C2×C3×C4⋊Q8—31no—
70C2×C3×#125—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×#944—31no—
74C2×#944—31no—
75#5729—316no—
76#5689—316no—
77C2×#897—31no—
78C2×#897—31no—
79C2×#896—31no—
80C2×#896—31no—
81C2×#896—31no—
82C2×#896—31no—
83C2×#896—61no—
84C2×#892—31no—
85C2×#892—31no—
86C2×D3×C4⋊C4—31no—
87C2×D3×C4⋊C4—31no—
88C2×#890—31no—
89C2×#890—31no—
90C2×#889—31no—
91C2×#889—31no—
92C2×#889—31no—
93C2×#889D311yescharacteristic, complemented
94C2×#888—31no—
95C2×#888—31no—
96C2×#888—31no—
97C2×#888D311yescharacteristic, complemented
98C2×#872—31no—
99C2×#872—31no—
100C2×#870—31no—
101C2×#869—31no—
102C23×C3⋊D3C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C2×C4×C3⋊D3—42no—
110C2×C4×C3⋊D3C2314yes—
111C2×#634—42no—
112C2×#634C2314yes—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×Dic6—42no—
122C2×C3×Dic6—42no—
123C2×C3×Dic6C2314yes—
124C2×C3×Dic6C2314yes—
125C2×#627—42no—
126C2×#627C2314yes—
127C2×#624—42no—
128C2×#624Q818yescomplemented
129C2×#624C2314yes—
130C2×#624C2314yes—
131C32×C4⋊C4C2314yes—
132#3752C2314yes—
133#3752C2314yes—
134#3750C2314yes—
135#3750C2314yes—
136C3×C4⋊Dic3C2314yes—
137C3×C4⋊Dic3C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×C4×Dic3C2314yes—
145C3×C4×Dic3C2314yes—
146#3724C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156#3722C2314yes—
157Dic32C2314yes—
158Dic32C2314yes—
159C2×#544—91noSylow
160C22×C3×Q8—31no—
161C22×C3×Q8—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C22×C4×D3—61no—
169C22×Dic6—31no—
170C22×Dic6—31no—
171C22×Dic6—31no—
172C22×Dic6—31no—
173C22×Dic6—61no—
174C22×Dic6C2×D311yescharacteristic
175C22×Dic6C2×D311yescharacteristic
176C3×C4⋊Q8—38no—
177C3×#125—38no—
178C2×C3×C4⋊C4—21no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4C2×D311yescharacteristic
188C2×C3×C4⋊C4C2×D311yescharacteristic
189C2×C3×C42—31no—
190C2×C3×C42—31no—
191#946—38no—
192#946—38no—
193#944—38no—
194#944—38no—
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—31no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3C2×D311yescharacteristic
214C2×C4⋊Dic3C2×D311yescharacteristic
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
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⋊C4—61no—
231C2×Dic3⋊C4C2×D311yescharacteristic
232C2×Dic3⋊C4C2×D311yescharacteristic
233C2×Dic3⋊C4C2×D311yescharacteristic
234C2×Dic3⋊C4C2×D311yescharacteristic
235C2×Dic3⋊C4C2×D311yescharacteristic
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×C4×Dic3—31no—
238C2×C4×Dic3—31no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3C2×D311yescharacteristic
242C2×C4×Dic3C2×D311yescharacteristic
243#897—38no—
244#897—38no—
245#896—38no—
246#896—38no—
247#896—38no—
248#896—38no—
249#896—68no—
250#892—38no—
251#892—38no—
252D3×C4⋊C4—38no—
253D3×C4⋊C4—38no—
254#890—38no—
255#890—38no—
256#889—38no—
257#889—38no—
258#889—38no—
259#889C2×D318yescomplemented
260#888—38no—
261#888—38no—
262#888—38no—
263#888C2×D318yescomplemented
264#872—38no—
265#872—38no—
266#870—38no—
267#869—38no—
268C23×C32C2411yescharacteristic
269C22×C3⋊D3—22no—
270C22×C3⋊D3—22no—
271C22×C3⋊D3C2×Q814yes—
272C22×C3⋊D3C2412yes—
273C2×C32×C4—22no—
274C2×C32×C4—22no—
275C2×C32×C4—22no—
276C2×C32×C4C2412yes—
277C2×C32×C4C2412yes—
278C2×C32×C4C2412yes—
279C2×C3⋊Dic3—22no—
280C2×C3⋊Dic3—22no—
281C2×C3⋊Dic3—22no—
282C2×C3⋊Dic3C2412yes—
283C2×C3⋊Dic3C2412yes—
284C2×C3⋊Dic3C2412yes—
285C4×C3⋊D3—44no—
286#634—44no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3C2×Q814yes—
294C2×C3×Dic3C2×Q814yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C3×Dic6—44no—
304C3×Dic6—44no—
305#627—44no—
306#624—44no—
307#624C2×Q8116yescomplemented
308#544—916no—
309C2×C4⋊Q8—31no—
310C2×C4⋊Q8—91no—
311C2×C4⋊Q8—91no—
312C2×C4⋊Q8—91no—
313C2×#125—31no—
314C2×#125—91no—
315C2×#125—91no—
316C2×#125—91no—
317C2×C22⋊Q8—91no—
318C2×C22⋊Q8—91no—
319C2×C22⋊Q8—91no—
320C2×C22⋊Q8—91no—
321C2×#117—91no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C23×D3—31no—
325C23×D3—31no—
326C23×D3—61no—
327C2×C3×Q8—34no—
328C2×C3×Q8—34no—
329C2×C3×Q8—122no—
330C2×C3×Q8—122no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C2×C4×D3—38no—
366C2×C4×D3—38no—
367C2×C4×D3—34no—
368C2×C4×D3—34no—
369C2×C4×D3—34no—
370C2×C4×D3—34no—
371C2×C4×D3—34no—
372C2×C4×D3—34no—
373C2×C4×D3—64no—
374C2×C4×D3—122no—
375C2×C4×D3—122no—
376C2×C4×D3—122no—
377C2×C4×D3—122no—
378C2×C4×D3—124no—
379C2×Dic6—34no—
380C2×Dic6—34no—
381C2×Dic6—34no—
382C2×Dic6—34no—
383C2×Dic6—42no—
384C2×Dic6—42no—
385C2×Dic6—64no—
386C2×Dic6—122no—
387C2×Dic6—122no—
388C2×Dic6—122no—
389C2×Dic6—122no—
390C2×Dic6—124no—
391C2×Dic6C22×D314yes—
392C2×Dic6C22×D314yes—
393C3×C4⋊C4—24no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—34no—
401C3×C4⋊C4—34no—
402C3×C4⋊C4C22×D314yes—
403C3×C4⋊C4C22×D314yes—
404C3×C42—34no—
405C3×C42—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—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—34no—
424C4⋊Dic3C22×D314yes—
425C4⋊Dic3C22×D314yes—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
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—64no—
441Dic3⋊C4—64no—
442Dic3⋊C4C22×D314yes—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D314yes—
445Dic3⋊C4C22×D314yes—
446Dic3⋊C4C22×D314yes—
447Dic3⋊C4C22×D314yes—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3—34no—
451C4×Dic3—34no—
452C4×Dic3C22×D314yes—
453C4×Dic3C22×D314yes—
454C22×C32C22×Q812yes—
455C22×C32H(5,𝔽2)12yes—
456C22×C322−1+412yes—
457C22×C32C2511yescharacteristic
458C2×C3⋊D3—28no—
459C2×C3⋊D3—22no—
460C2×C3⋊D3—22no—
461C2×C3⋊D3C22×Q814yes—
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×Dic3C22×Q814yes—
475C3×Dic3C22×Q814yes—
476C22×Q8—31no—
477C22×Q8—31no—
478C22×Q8—91no—
479C22×Q8—91no—
480C23×C4—91no—
481C23×C4—91no—
482C23×C4—91no—
483C4⋊Q8—38no—
484C4⋊Q8—98no—
485C4⋊Q8—98no—
486C4⋊Q8—98no—
487#125—38no—
488#125—98no—
489#125—98no—
490#125—98no—
491C22⋊Q8—98no—
492C22⋊Q8—98no—
493C22⋊Q8—98no—
494C22⋊Q8—98no—
495#117—98no—
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—31no—
503C2×C4⋊C4—31no—
504C2×C4⋊C4—31no—
505C2×C4⋊C4—98no—
506C2×C4⋊C4—91no—
507C2×C4⋊C4—91no—
508C2×C4⋊C4—91no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—91no—
511C2×C4⋊C4—91no—
512C2×C4⋊C4—91no—
513C2×C4⋊C4—91no—
514C2×C4⋊C4—91no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4D3211yescharacteristic
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—
525C2×C42—91no—
526C23×C3—21no—
527C23×C3C23×D311yescharacteristic
528C23×C3C23×D311yescharacteristic
529C22×D3—34no—
530C22×D3—34no—
531C22×D3—32no—
532C22×D3—32no—
533C22×D3—64no—
534C22×D3—62no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—122no—
540C22×D3—122no—
541C3×Q8—124no—
542C3×Q8—124no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—34no—
553C2×C3×C4—34no—
554C2×C3×C4—32no—
555C2×C3×C4—32no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—32no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—42no—
563C2×C3×C4—42no—
564C2×C3×C4—42no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—62no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4C23×D312yes—
572C2×C3×C4C23×D312yes—
573C2×C3×C4C23×D312yes—
574C2×C3×C4C23×D312yes—
575C2×C3×C4C23×D312yes—
576C2×C3×C4C23×D312yes—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—32no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—62no—
590C2×Dic3—62no—
591C2×Dic3—62no—
592C2×Dic3—64no—
593C2×Dic3—62no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—122no—
600C2×Dic3—122no—
601C2×Dic3D3×Q814yes—
602C2×Dic3D3×Q814yes—
603C2×Dic3C23×D312yes—
604C2×Dic3C23×D312yes—
605C2×Dic3C23×D312yes—
606C2×Dic3C23×D312yes—
607C2×Dic3C23×D312yes—
608C2×Dic3C23×D312yes—
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D312yes—
611C4×D3—316no—
612C4×D3—316no—
613C4×D3—124no—
614C4×D3—124no—
615C4×D3—124no—
616C4×D3—124no—
617C4×D3—128no—
618Dic6—44no—
619Dic6—44no—
620Dic6—124no—
621Dic6—124no—
622Dic6—124no—
623Dic6—124no—
624Dic6—128no—
625C2×C32#54414yescomplemented
626C2×C32C23×Q811yescharacteristic
627C2×C32C2×H(5,𝔽2)11yescharacteristic
628C2×C32C2×2−1+411yescharacteristic
629C3⋊D3—24no—
630C24—91no—
631C2×Q8—34no—
632C2×Q8—34no—
633C2×Q8—94no—
634C2×Q8—94no—
635C2×Q8—122no—
636C2×Q8—122no—
637C2×Q8—362no—
638C2×Q8—362no—
639C22×C4—31no—
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—98no—
649C22×C4—94no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—91no—
653C22×C4—94no—
654C22×C4—362no—
655C22×C4—362no—
656C22×C4C2×D3211yescharacteristic
657C22×C4C2×D3211yescharacteristic
658C22×C4C2×D3211yescharacteristic
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4—34no—
666C4⋊C4—34no—
667C4⋊C4—94no—
668C4⋊C4—94no—
669C4⋊C4—94no—
670C4⋊C4—94no—
671C4⋊C4—94no—
672C4⋊C4—94no—
673C4⋊C4—94no—
674C4⋊C4—94no—
675C4⋊C4—94no—
676C4⋊C4—94no—
677C4⋊C4—94no—
678C4⋊C4C2×D3214yes—
679C22⋊C4—94no—
680C22⋊C4—94no—
681C22⋊C4—94no—
682C22⋊C4—94no—
683C42—34no—
684C42—34no—
685C42—94no—
686C42—94no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—21no—
691C22×C3#100412yes—
692C22×C3C2×D3×Q812yes—
693C22×C3C2×D3×Q812yes—
694C22×C3#100712yes—
695C22×C3#100912yes—
696C22×C3#101012yes—
697C22×C3C24×D311yescharacteristic
698C22×C3C24×D311yescharacteristic
699C2×D3—34no—
700C2×D3—34no—
701C2×D3—64no—
702C2×D3—68no—
703C2×D3—62no—
704C2×D3—62no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—68no—
708C2×D3—122no—
709C2×D3—122no—
710C2×D3—128no—
711C3×C4—22no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—34no—
718C3×C4—34no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—42no—
722C3×C4—62no—
723C3×C4—62no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4—62no—
727C3×C4—62no—
728Dic3—22no—
729Dic3—22no—
730Dic3—22no—
731Dic3—22no—
732Dic3—22no—
733Dic3—22no—
734Dic3—64no—
735Dic3—62no—
736Dic3—62no—
737Dic3—62no—
738Dic3—62no—
739Dic3—62no—
740Dic3—62no—
741Dic3—122no—
742Dic3—122no—
743Dic3C2×D3×Q814yes—
744Dic3C2×D3×Q814yes—
745C32C2×#54411yescharacteristic, complemented, Sylow
746C23—94no—
747C23—92no—
748C23—182no—
749C23—182no—
750C23C22×D3211yescharacteristic
751Q8—124no—
752Q8—124no—
753Q8—364no—
754Q8—364no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—34no—
759C2×C4—34no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—916no—
775C2×C4—92no—
776C2×C4—92no—
777C2×C4—92no—
778C2×C4—182no—
779C2×C4—182no—
780C2×C4—182no—
781C2×C4—364no—
782C2×C4—364no—
783C2×C4C22×D3212yes—
784C2×C4C22×D3212yes—
785C2×C4C22×D3212yes—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—24no—
790C2×C3#568914yescomplemented
791C2×C3#572914yescomplemented
792C2×C3C2×#100411yescharacteristic
793C2×C3C22×D3×Q811yescharacteristic
794C2×C3C22×D3×Q811yescharacteristic
795C2×C3C2×#100711yescharacteristic
796C2×C3C2×#100911yescharacteristic
797C2×C3C2×#101011yescharacteristic
798D3—64no—
799D3—64no—
800D3—124no—
801C22—94no—
802C22—182no—
803C22—182no—
804C22—188no—
805C22#6429712yes—
806C22#6431412yes—
807C22D32×Q812yes—
808C22C23×D3211yescharacteristic
809C4—22no—
810C4—22no—
811C4—22no—
812C4—34no—
813C4—34no—
814C4—62no—
815C4—62no—
816C4—62no—
817C4—62no—
818C4—62no—
819C4—62no—
820C4—182no—
821C4—182no—
822C4—182no—
823C3—21no—
824C3C2×#568911yescharacteristic, complemented
825C3C2×#572911yescharacteristic, complemented
826C2—184no—
827C2#1059440014yesdirect product factor
828C2C2×#6429711yescharacteristic
829C2C2×#6431411yescharacteristic
830C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#889C2semidirect
3. C2×C3×#888C2semidirect
8. C2×#63867C2semidirect
9. C2×#63866C2semidirect
10. C2×#63846C2semidirect
11. C2×#63846C2semidirect
12. C2×#63840C2semidirect
13. C2×#63839C2semidirect
16. #10594400C2direct (N × H)
42. C3×#889C22semidirect
43. C3×#888C22semidirect
61. #63867C22semidirect
62. #63866C22semidirect
63. #63846C22semidirect
64. #63846C22semidirect
65. #63840C22semidirect
66. #63839C22semidirect
93. C2×#889D3semidirect
97. C2×#888D3semidirect
128. C2×#624Q8semidirect
259. #889C2×D3semidirect
263. #888C2×D3semidirect
307. #624C2×Q8semidirect
625. C2×C32#544semidirect
745. C32C2×#544semidirect
790. C2×C3#5689semidirect
791. C2×C3#5729semidirect
824. C3C2×#5689semidirect
825. C3C2×#5729semidirect
827. C2#10594400direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641052
C2×C3×#8892
C2×C3×#8882
C2×#638952
C2×#638882
C2×#638832
C2×#638712
C2×#638672
C2×#638662
C2×#638462
C2×#638402
C2×#638392
C2×#638362
#105944002
C2×#57293
C2×#56893