Finite Group Databasebeta

← C2×#10594960 #11903046

Subgroups — C2×#10594960 #11903046

Order 1152.

2457 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic, complemented
2C2×C3×#929C211yesmaximal, characteristic
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C2×#63982C211yesmaximal, characteristic, complemented
5C2×#67⋊Dic3C211yesmaximal, characteristic
6C2×#63962C211yesmaximal, characteristic
7C2×#63957C211yesmaximal, characteristic, complemented
8#10594960C2116yesmaximal, direct product factor
9C2×#63899C211yesmaximal, characteristic, complemented
10C2×#63877C211yesmaximal, characteristic, complemented
11C2×#63867C211yesmaximal, characteristic, complemented
12C2×#63859C211yesmaximal, characteristic, complemented
13C2×#63858C211yesmaximal, characteristic, complemented
14C2×#63847C211yesmaximal, characteristic, complemented
15C2×#63846C211yesmaximal, characteristic, complemented
16C2×#63837C211yesmaximal, characteristic, complemented
17C2×#5650—31nomaximal
18C2×#5531—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2218yescomplemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C3×#929C2218yes—
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×#926C2218yescomplemented
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43#63982C2218yescomplemented
44#67⋊Dic3C2218yes—
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×#3724C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53#63962C2218yes—
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63957C2218yescomplemented
58C2×Dic32C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63899C2218yescomplemented
62#63877C2218yescomplemented
63#63867C2218yescomplemented
64#63859C2218yescomplemented
65#63858C2218yescomplemented
66#63847C2218yescomplemented
67#63846C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#117—31no—
71C2×#935—31no—
72C2×D4×Dic3—31no—
73C2×#929D311yescharacteristic
74C2×#926D311yescharacteristic, complemented
75C22×Dic3⋊C4—31no—
76C22×Dic3⋊C4—31no—
77C22×Dic3⋊C4—61no—
78#5650—316no—
79#5531—316no—
80C2×#898—31no—
81C2×#896—31no—
82C2×#890—31no—
83C2×#889—31no—
84C2×#889—31no—
85C2×#889—31no—
86C2×#889—31no—
87C2×#887—31no—
88C2×#886—31no—
89C2×#67⋊C4—31no—
90C2×#879—31no—
91C2×#879—31no—
92C2×#878—31no—
93C2×#878—31no—
94C2×#878—31no—
95C2×#877—31no—
96C2×#877—31no—
97C2×#877—31no—
98C2×#876—31no—
99C2×#872—31no—
100C2×#870—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4—24no—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2314yes—
108C22×C3⋊Dic3—24no—
109C22×C3⋊Dic3—24no—
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2314yes—
114C22×C3⋊Dic3C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C3×#67—24no—
117C2×C3×#67C2314yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×#627—24no—
126C2×#627C2314yes—
127C2×D3×Dic3—24no—
128C2×D3×Dic3C2314yes—
129#3750C2314yes—
130#3750C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133C3×#217C2314yes—
134C3×#217C2314yes—
135C3×#217C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×C4⋊Dic3C2314yes—
139C3×C4⋊Dic3C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×C4×Dic3C2314yes—
143C3×C4×Dic3C2314yes—
144#3724C2314yes—
145#3724C2314yes—
146#3724C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152(C2×D3)⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155Dic32C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158C2×#552—91noSylow
159C22×C3×D4—31no—
160C23×C3×C4—21no—
161C23×C3×C4C2×D311yescharacteristic
162C23×C3×C4C2×D311yescharacteristic
163C22×#67C2×D311yescharacteristic
164C23×Dic3—31no—
165C23×Dic3—31no—
166C23×Dic3—31no—
167C23×Dic3—31no—
168C23×Dic3—31no—
169C23×Dic3—61no—
170C23×Dic3—61no—
171C22×C4×D3—31no—
172C22×Dic6—31no—
173C22×Dic6—31no—
174C3×#123—38no—
175C3×#117—38no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C42—31no—
186C2×C3×C42—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217C2×D311yescharacteristic
191C2×#217C2×D311yescharacteristic
192C2×#217C2×D311yescharacteristic
193#935—38no—
194D4×Dic3—38no—
195#929C2×D318yes—
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
201#926C2×D318yescomplemented
202C2×C4⋊Dic3—31no—
203C2×C4⋊Dic3—31no—
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3C2×D311yescharacteristic
208C2×C4⋊Dic3C2×D311yescharacteristic
209C2×Dic3⋊C4—38no—
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—38no—
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—31no—
230C2×Dic3⋊C4—61no—
231C2×Dic3⋊C4—61no—
232C2×Dic3⋊C4—61no—
233C2×Dic3⋊C4—61no—
234C2×Dic3⋊C4—68no—
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×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3C2×D311yescharacteristic
244C2×C4×Dic3C2×D311yescharacteristic
245#898—38no—
246#896—38no—
247#890—38no—
248#889—38no—
249#889—38no—
250#889—38no—
251#889—38no—
252#887—38no—
253#886—38no—
254#67⋊C4—38no—
255#879—38no—
256#879—38no—
257#878—38no—
258#878—38no—
259#878—38no—
260#877—38no—
261#877—38no—
262#877—38no—
263#876—38no—
264#872—38no—
265#870—38no—
266C4×Dic6—38no—
267C23×C32—22no—
268C23×C32—22no—
269C23×C32#4114yes—
270C23×C32C2412yes—
271C23×C32C2411yescharacteristic
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3C2412yes—
276C2×C32×C4—28no—
277C2×C32×C4—22no—
278C2×C32×C4—22no—
279C2×C32×C4C2412yes—
280C2×C32×C4C2412yes—
281C2×C3⋊Dic3—22no—
282C2×C3⋊Dic3—28no—
283C2×C3⋊Dic3—28no—
284C2×C3⋊Dic3—22no—
285C2×C3⋊Dic3—22no—
286C2×C3⋊Dic3#4114yes—
287C2×C3⋊Dic3C2412yes—
288C2×C3⋊Dic3C2412yes—
289C2×C3⋊Dic3C2412yes—
290C2×C3⋊Dic3C2412yes—
291C3×#67—28no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306#627—28no—
307D3×Dic3—28no—
308#552—916no—
309C2×#126—91no—
310C2×#126—91no—
311C2×#125—91no—
312C2×#125—91no—
313C2×#125—91no—
314C2×#123—31no—
315C2×#123—91no—
316C2×C22⋊Q8—91no—
317C2×C22⋊Q8—91no—
318C2×C4×Q8—91no—
319C2×C4×D4—91no—
320C2×#117—31no—
321C2×#117—91no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C24×C3—21no—
325C24×C3—31no—
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C23×D3C22×D311yescharacteristic
329C2×C3×D4—34no—
330C2×C3×D4—64no—
331C22×C3×C4—24no—
332C22×C3×C4—24no—
333C22×C3×C4—24no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
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×C4—31no—
343C22×C3×C4—44no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D314yes—
349C22×C3×C4C22×D314yes—
350C2×#67—24no—
351C2×#67C22×D314yes—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—34no—
355C22×Dic3—34no—
356C22×Dic3—34no—
357C22×Dic3—34no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—34no—
365C22×Dic3—61no—
366C22×Dic3—64no—
367C22×Dic3—61no—
368C22×Dic3—64no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—64no—
372C22×Dic3—64no—
373C22×Dic3—64no—
374C22×Dic3—68no—
375C22×Dic3—64no—
376C22×Dic3—64no—
377C22×Dic3—124no—
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C2×C4×D3—34no—
386C2×C4×D3—64no—
387C2×Dic6—34no—
388C2×Dic6—34no—
389C2×Dic6—64no—
390C2×Dic6—64no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4—34no—
398C3×C22⋊C4—34no—
399C3×C22⋊C4—34no—
400C3×C42—34no—
401C3×C42—34no—
402#217—34no—
403#217—34no—
404#217—34no—
405#217C22×D314yes—
406#217C22×D314yes—
407#217C22×D314yes—
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—
413C4⋊Dic3—34no—
414C4⋊Dic3—34no—
415C4⋊Dic3—34no—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3C22×D314yes—
419C4⋊Dic3C22×D314yes—
420Dic3⋊C4—34no—
421Dic3⋊C4—34no—
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—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—64no—
440Dic3⋊C4—64no—
441Dic3⋊C4—64no—
442Dic3⋊C4—64no—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D314yes—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3—34no—
451C4×Dic3C22×D314yes—
452C4×Dic3C22×D314yes—
453C22×C32—28no—
454C22×C32—22no—
455C22×C32—22no—
456C22×C32C2×#4114yes—
457C22×C32C2×#4112yes—
458C22×C32C2×#4112yes—
459C22×C322−1+412yes—
460C22×C32C2511yescharacteristic
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—44no—
465C32×C4—22no—
466C32×C4—22no—
467C3⋊Dic3—22no—
468C3⋊Dic3—22no—
469C3⋊Dic3—22no—
470C3⋊Dic3C2×#4114yes—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C22×Q8—91no—
479C22×D4—31no—
480C23×C4—91no—
481C23×C4—91no—
482C23×C4—91no—
483C23×C4D3211yescharacteristic
484#126—98no—
485#126—98no—
486#125—98no—
487#125—98no—
488#125—98no—
489#123—38no—
490#123—98no—
491C22⋊Q8—98no—
492C22⋊Q8—98no—
493C4×Q8—98no—
494C4×D4—98no—
495#117—38no—
496#117—98no—
497#117—98no—
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×C4⋊C4—91no—
510C2×C4⋊C4—91no—
511C2×C4⋊C4—91no—
512C2×C4⋊C4—91no—
513C2×C4⋊C4—91no—
514C2×C4⋊C4—98no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—31no—
517C2×C22⋊C4—31no—
518C2×C22⋊C4—31no—
519C2×C22⋊C4—31no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522C2×C22⋊C4—91no—
523C2×C42—31no—
524C2×C42—31no—
525C2×C42—91no—
526C2×C42—91no—
527C2×C42—91no—
528C23×C3—24no—
529C23×C3—24no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—21no—
536C23×C3—24no—
537C23×C3—32no—
538C23×C3—62no—
539C23×C3—62no—
540C23×C3—62no—
541C23×C3#23514yes—
542C23×C3#23714yes—
543C23×C3C23×D312yes—
544C23×C3C23×D312yes—
545C23×C3C23×D311yescharacteristic
546C23×C3C23×D311yescharacteristic
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3C23×D312yes—
551C3×D4—68no—
552C2×C3×C4—28no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—28no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—32no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—48no—
568C2×C3×C4—42no—
569C2×C3×C4—42no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—62no—
576C2×C3×C4—62no—
577C2×C3×C4C23×D312yes—
578C2×C3×C4C23×D312yes—
579C2×C3×C4C23×D312yes—
580C2×C3×C4C23×D312yes—
581#67—28no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—34no—
590C2×Dic3—34no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—64no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—68no—
605C2×Dic3—68no—
606C2×Dic3—68no—
607C2×Dic3—616no—
608C2×Dic3—64no—
609C2×Dic3—68no—
610C2×Dic3—62no—
611C2×Dic3—62no—
612C2×Dic3—68no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3—62no—
616C2×Dic3—62no—
617C2×Dic3—128no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3C23×D312yes—
621C2×Dic3C23×D312yes—
622C2×Dic3C23×D312yes—
623C2×Dic3C23×D312yes—
624C2×Dic3C23×D312yes—
625C2×Dic3C23×D312yes—
626C2×Dic3C23×D312yes—
627C4×D3—68no—
628Dic6—68no—
629Dic6—68no—
630C2×C32—24no—
631C2×C32#55214yescomplemented
632C2×C32C22×#4111yescharacteristic
633C2×C32C22×#4111yescharacteristic
634C2×C32C2×2−1+411yescharacteristic
635C3×D3—42no—
636C24—31no—
637C24C2×D3211yescharacteristic
638C2×Q8—94no—
639C2×Q8—184no—
640C2×D4—34no—
641C2×D4—64no—
642C22×C4—24no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—94no—
651C22×C4—91no—
652C22×C4—94no—
653C22×C4—94no—
654C22×C4—91no—
655C22×C4—91no—
656C22×C4—91no—
657C22×C4—184no—
658C22×C4—184no—
659C22×C4—184no—
660C22×C4C2×D3214yes—
661C22×C4C2×D3211yescharacteristic
662C22×C4C2×D3211yescharacteristic
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⋊C4—94no—
679C22⋊C4—34no—
680C22⋊C4—34no—
681C22⋊C4—34no—
682C22⋊C4—34no—
683C22⋊C4—34no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C22⋊C4—94no—
687C42—34no—
688C42—34no—
689C42—94no—
690C42—94no—
691C42—94no—
692C22×C3—24no—
693C22×C3—24no—
694C22×C3—216no—
695C22×C3—28no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—28no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—24no—
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—124no—
710C22×C3C2×#23514yes—
711C22×C3C2×#23512yes—
712C22×C3C2×#23714yes—
713C22×C3C2×#23712yes—
714C22×C3D3×#4112yes—
715C22×C3D3×#4112yes—
716C22×C3#101012yes—
717C22×C3#101012yes—
718C22×C3C24×D311yescharacteristic
719C22×C3C24×D311yescharacteristic
720C2×D3—22no—
721C2×D3—22no—
722C2×D3—22no—
723C2×D3—44no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737Dic3—22no—
738Dic3—22no—
739Dic3—22no—
740Dic3—22no—
741Dic3—22no—
742Dic3—22no—
743Dic3—22no—
744Dic3—34no—
745Dic3—34no—
746Dic3—64no—
747Dic3—64no—
748Dic3—62no—
749Dic3—62no—
750Dic3—62no—
751Dic3—62no—
752Dic3—62no—
753Dic3—62no—
754Dic3—122no—
755Dic3—122no—
756C32C2×#55211yescharacteristic, complemented, Sylow
757C23—22no—
758C23—22no—
759C23—32no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23#380414yes—
764C23C22×D3212yes—
765C23C22×D3211yescharacteristic
766Q8—188no—
767D4—68no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—94no—
786C2×C4—92no—
787C2×C4—92no—
788C2×C4—92no—
789C2×C4—92no—
790C2×C4—188no—
791C2×C4—188no—
792C2×C4—182no—
793C2×C4—188no—
794C2×C4—182no—
795C2×C4—182no—
796C2×C4C22×D3212yes—
797C2×C4C22×D3212yes—
798C2×C3—28no—
799C2×C3—24no—
800C2×C3—24no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—24no—
805C2×C3—122no—
806C2×C3#553114yescomplemented
807C2×C3#565014yescomplemented
808C2×C3C22×#23511yescharacteristic
809C2×C3C22×#23711yescharacteristic
810C2×C3C2×D3×#4111yescharacteristic
811C2×C3C2×D3×#4111yescharacteristic
812C2×C3C2×#101011yescharacteristic
813C2×C3C2×#101011yescharacteristic
814D3—42no—
815C22—22no—
816C22—22no—
817C22—28no—
818C22—62no—
819C22—62no—
820C22—62no—
821C22—124no—
822C22#6429812yes—
823C22#6430612yes—
824C22C2×#380414yes—
825C22C2×#380412yes—
826C22C23×D3211yescharacteristic
827C4—22no—
828C4—22no—
829C4—62no—
830C4—62no—
831C4—62no—
832C4—62no—
833C4—62no—
834C4—62no—
835C4—62no—
836C4—94no—
837C4—182no—
838C4—182no—
839C4—182no—
840C3—21no—
841C3C2×#553111yescharacteristic, complemented
842C3C2×#565011yescharacteristic, complemented
843C2—24no—
844C2—122no—
845C2#1059496014yesdirect product factor
846C2C2×#6429811yescharacteristic
847C2C2×#6430611yescharacteristic
848C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3750C2semidirect
3. C2×C3×#926C2semidirect
4. C2×#63982C2semidirect
7. C2×#63957C2semidirect
8. #10594960C2direct (N × H)
9. C2×#63899C2semidirect
10. C2×#63877C2semidirect
11. C2×#63867C2semidirect
12. C2×#63859C2semidirect
13. C2×#63858C2semidirect
14. C2×#63847C2semidirect
15. C2×#63846C2semidirect
16. C2×#63837C2semidirect
29. C2×#3750C22semidirect
36. C3×#926C22semidirect
43. #63982C22semidirect
57. #63957C22semidirect
61. #63899C22semidirect
62. #63877C22semidirect
63. #63867C22semidirect
64. #63859C22semidirect
65. #63858C22semidirect
66. #63847C22semidirect
67. #63846C22semidirect
68. #63837C22semidirect
74. C2×#926D3semidirect
201. #926C2×D3semidirect
631. C2×C32#552semidirect
756. C32C2×#552semidirect
806. C2×C3#5531semidirect
807. C2×C3#5650semidirect
841. C3C2×#5531semidirect
842. C3C2×#5650semidirect
845. C2#10594960direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C3×#9292
C2×C3×#9262
C2×#639822
C2×#67⋊Dic32
C2×#639622
C2×#639572
#105949602
C2×#638992
C2×#638772
C2×#638672
C2×#638592
C2×#638582
C2×#638472
C2×#638462
C2×#638372
C2×#56503
C2×#55313