Finite Group Databasebeta

← C2×#10594366 #11901101

Subgroups — C2×#10594366 #11901101

Order 1152.

3185 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64105C211yesmaximal, characteristic, complemented
4C2×C3×#894C211yesmaximal, characteristic, complemented
5C2×C3×#888C211yesmaximal, characteristic, complemented
6C2×#63907C211yesmaximal, characteristic, complemented
7C2×#63899C211yesmaximal, characteristic, complemented
8C2×#63896C211yesmaximal, characteristic, complemented
9C2×#63890C211yesmaximal, characteristic, complemented
10C2×#63884C211yesmaximal, characteristic, complemented
11C2×#63877C211yesmaximal, characteristic, complemented
12C2×#63865C211yesmaximal, characteristic, complemented
13C2×#63852C211yesmaximal, characteristic, complemented
14C2×#63850C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10594366C2116yesmaximal, direct product factor
17C2×#5724—31nomaximal
18C2×#5648—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C2×#3796—28no—
33C2×#3796C2218yes—
34C2×D3×Dic6—28no—
35C2×D3×Dic6C2218yescomplemented
36C2×C32×C4⋊C4C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3750C2211yescharacteristic
40C2×#3750C2211yescharacteristic
41#64105C2218yescomplemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×C4⋊Dic3C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×C4×Dic3C2211yescharacteristic
50C3×#894C2218yescomplemented
51C3×#888C2218yescomplemented
52C2×#3724C2211yescharacteristic
53C2×#3724C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63907C2218yescomplemented
62#63899C2218yescomplemented
63#63896C2218yescomplemented
64#63890C2218yescomplemented
65#63884C2218yescomplemented
66#63877C2218yescomplemented
67#63865C2218yescomplemented
68#63852C2218yescomplemented
69#63850C2218yescomplemented
70#63839C2218yescomplemented
71C22×#239—31no—
72C22×D3×Q8—31no—
73C22×#237—31no—
74C23×Dic6—31no—
75C2×C3×C4⋊Q8—31no—
76C2×C3×#123—31no—
77C2×#947—31no—
78C2×#944—31no—
79C2×#935—31no—
80C2×#929—31no—
81#5724—316no—
82#5648—316no—
83C2×#896—31no—
84C2×#896—31no—
85C2×#896—31no—
86C2×#896—31no—
87C2×#896—31no—
88C2×#896—31no—
89C2×#896—61no—
90C2×#894—31no—
91C2×#894—31no—
92C2×#894—31no—
93C2×#894D311yescharacteristic, complemented
94C2×#888—31no—
95C2×#888D311yescharacteristic, complemented
96C2×#886—31no—
97C2×#885—31no—
98C2×#885—31no—
99C2×#878—31no—
100C2×#878—31no—
101C2×#877—31no—
102C2×#875—31no—
103C2×#872—31no—
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×C4×C3⋊D3—24no—
114C2×C4×C3⋊D3C2314yes—
115C2×#634—24no—
116C2×#634C2314yes—
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×D12—24no—
124C2×C3×D12C2314yes—
125C2×C3×C4×D3—24no—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6—24no—
128C2×C3×Dic6—24no—
129C2×C3×Dic6C2314yes—
130C2×C3×Dic6C2314yes—
131C2×#627—24no—
132C2×#627—24no—
133C2×#627C2314yes—
134C2×#627C2314yes—
135C2×#626—24no—
136C2×#626—24no—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×D3×Dic3—24no—
140C2×D3×Dic3—24no—
141C2×D3×Dic3D418yes—
142C2×D3×Dic3C2314yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yes—
145#3796—232no—
146D3×Dic6—232no—
147C32×C4⋊C4C2314yes—
148#3752C2314yes—
149#3752C2314yes—
150#3750C2314yes—
151#3750C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×C4⋊Dic3C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×C4×Dic3C2314yes—
160#3724C2314yes—
161#3724C2314yes—
162Dic3⋊Dic3C2314yes—
163#3722C2314yes—
164#3722C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168Dic32C2314yes—
169C2×#536—91noSylow
170C22×C3×Q8—31no—
171C22×C3×Q8—31no—
172C22×C3×D4—31no—
173C23×C3×C4—31no—
174C22×#67—31no—
175C22×#67—31no—
176C23×Dic3—31no—
177C23×Dic3—31no—
178C23×Dic3—31no—
179C2×#239—38no—
180C2×#239—68no—
181C2×D3×Q8—38no—
182C2×D3×Q8—68no—
183C2×#237—38no—
184C2×#237—68no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12C2×D311yescharacteristic
188C22×C4×D3—31no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—61no—
194C22×C4×D3C2×D311yescharacteristic
195C22×Dic6—31no—
196C22×Dic6—31no—
197C22×Dic6—31no—
198C22×Dic6—31no—
199C22×Dic6—31no—
200C22×Dic6—31no—
201C22×Dic6—38no—
202C22×Dic6—61no—
203C22×Dic6—68no—
204C22×Dic6C2×D311yescharacteristic
205C22×Dic6C2×D311yescharacteristic
206C3×C4⋊Q8—38no—
207C3×#123—38no—
208C2×C3×C4⋊C4—21no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4—31no—
212C2×C3×C4⋊C4—31no—
213C2×C3×C4⋊C4C2×D311yescharacteristic
214C2×C3×C4⋊C4C2×D311yescharacteristic
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C22⋊C4—31no—
218C2×C3×C42—31no—
219C2×#217—31no—
220C2×#217—31no—
221C2×#217—31no—
222#947—38no—
223#944—38no—
224#935—38no—
225#929—38no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—61no—
238C2×(C2×D3)⋊C4—61no—
239C2×(C2×D3)⋊C4C2×D311yescharacteristic
240C2×(C2×D3)⋊C4C2×D311yescharacteristic
241C2×(C2×D3)⋊C4C2×D311yescharacteristic
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3C2×D311yescharacteristic
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—61no—
254C2×Dic3⋊C4—61no—
255C2×Dic3⋊C4C2×D311yescharacteristic
256C2×Dic3⋊C4C2×D311yescharacteristic
257C2×Dic3⋊C4C2×D311yescharacteristic
258C2×C4×Dic3—31no—
259C2×C4×Dic3—31no—
260C2×C4×Dic3C2×D311yescharacteristic
261#896—38no—
262#896—38no—
263#896—38no—
264#896—38no—
265#896—38no—
266#896—38no—
267#896—68no—
268#894—38no—
269#894—38no—
270#894—38no—
271#894C2×D318yescomplemented
272#888—38no—
273#888C2×D318yescomplemented
274#886—38no—
275#885—38no—
276#885—38no—
277#878—38no—
278#878—38no—
279#877—38no—
280#875—38no—
281#872—38no—
282C23×C32C2411yescharacteristic
283C22×C3⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3C2412yes—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3C2×D414yes—
293C22×C3×D3C2412yes—
294C22×C3×D3C2412yes—
295C2×C32×C4—22no—
296C2×C32×C4—22no—
297C2×C32×C4—22no—
298C2×C32×C4C2412yes—
299C2×C32×C4C2412yes—
300C2×C32×C4C2412yes—
301C2×C3⋊Dic3—22no—
302C2×C3⋊Dic3—22no—
303C2×C3⋊Dic3C2×D414yes—
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2412yes—
307C4×C3⋊D3—28no—
308#634—28no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3C2×D414yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C3×D12—28no—
322C3×C4×D3—28no—
323C3×Dic6—28no—
324C3×Dic6—28no—
325#627—28no—
326#627—28no—
327#626—28no—
328#626—28no—
329D3×Dic3—28no—
330D3×Dic3—28no—
331D3×Dic3C2×D4116yes—
332C22×#41—91no—
333C23×Q8—91no—
334#536—916no—
335C2×C4⋊Q8—31no—
336C2×C4⋊Q8—91no—
337C2×#124—91no—
338C2×#124—91no—
339C2×#123—31no—
340C2×#123—91no—
341C2×#123—91no—
342C2×#123—91no—
343C2×C22⋊Q8—91no—
344C2×C22⋊Q8—91no—
345C2×C22⋊Q8—91no—
346C2×C22⋊Q8—91no—
347C2×#117—91no—
348C24×C3—31no—
349C24×C3—31no—
350C23×D3—31no—
351C23×D3—31no—
352C23×D3—61no—
353C23×D3C22×D311yescharacteristic
354C23×D3C22×D311yescharacteristic
355C2×C3×Q8—34no—
356C2×C3×Q8—34no—
357C2×C3×Q8—64no—
358C2×C3×Q8—64no—
359C2×C3×D4—34no—
360C2×C3×D4—64no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—34no—
371C22×C3×C4—64no—
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—64no—
381C2×#67—64no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—38no—
385C22×Dic3—34no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—34no—
391C22×Dic3—34no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C22×Dic3—64no—
396C22×Dic3—64no—
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403#239—632no—
404D3×Q8—632no—
405#237—632no—
406C2×D12—24no—
407C2×D12—34no—
408C2×D12—34no—
409C2×D12—64no—
410C2×D12—64no—
411C2×D12C22×D314yes—
412C2×C4×D3—24no—
413C2×C4×D3—38no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3—64no—
420C2×C4×D3—64no—
421C2×C4×D3—64no—
422C2×C4×D3—64no—
423C2×C4×D3—64no—
424C2×C4×D3—124no—
425C2×C4×D3C22×D314yes—
426C2×Dic6—24no—
427C2×Dic6—24no—
428C2×Dic6—34no—
429C2×Dic6—34no—
430C2×Dic6—34no—
431C2×Dic6—34no—
432C2×Dic6—34no—
433C2×Dic6—34no—
434C2×Dic6—64no—
435C2×Dic6—632no—
436C2×Dic6—64no—
437C2×Dic6—64no—
438C2×Dic6—64no—
439C2×Dic6—64no—
440C2×Dic6—64no—
441C2×Dic6—64no—
442C2×Dic6—124no—
443C2×Dic6C22×D314yes—
444C2×Dic6C22×D314yes—
445C3×C4⋊C4—24no—
446C3×C4⋊C4—34no—
447C3×C4⋊C4—34no—
448C3×C4⋊C4—34no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4C22×D314yes—
451C3×C4⋊C4C22×D314yes—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C42—34no—
456#217—34no—
457#217—34no—
458#217—34no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—64no—
471(C2×D3)⋊C4—64no—
472(C2×D3)⋊C4C22×D314yes—
473(C2×D3)⋊C4C22×D314yes—
474(C2×D3)⋊C4C22×D314yes—
475C4⋊Dic3—34no—
476C4⋊Dic3C22×D314yes—
477Dic3⋊C4—34no—
478Dic3⋊C4—34no—
479Dic3⋊C4—34no—
480Dic3⋊C4—34no—
481Dic3⋊C4—34no—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—64no—
487Dic3⋊C4—64no—
488Dic3⋊C4C22×D314yes—
489Dic3⋊C4C22×D314yes—
490Dic3⋊C4C22×D314yes—
491C4×Dic3—34no—
492C4×Dic3—34no—
493C4×Dic3C22×D314yes—
494C22×C32C22×D412yes—
495C22×C322−1+412yes—
496C22×C322−1+412yes—
497C22×C32C2511yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—44no—
502C2×C3×D3—28no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—44no—
509C2×C3×D3C22×D414yes—
510C32×C4—22no—
511C32×C4—22no—
512C32×C4—22no—
513C3⋊Dic3—22no—
514C3⋊Dic3—22no—
515C3⋊Dic3C22×D414yes—
516C3×Dic3—22no—
517C3×Dic3—22no—
518C3×Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3—22no—
521C3×Dic3C22×D414yes—
522C2×#41—98no—
523C2×#41—188no—
524C22×Q8—31no—
525C22×Q8—31no—
526C22×Q8—91no—
527C22×Q8—91no—
528C22×Q8—98no—
529C22×Q8—91no—
530C22×Q8—188no—
531C22×D4—31no—
532C22×D4—91no—
533C22×D4—91no—
534C23×C4—31no—
535C23×C4—91no—
536C23×C4—91no—
537C23×C4—91no—
538C23×C4—91no—
539C4⋊Q8—38no—
540C4⋊Q8—98no—
541#124—98no—
542#124—98no—
543#123—38no—
544#123—98no—
545#123—98no—
546#123—98no—
547C22⋊Q8—98no—
548C22⋊Q8—98no—
549C22⋊Q8—98no—
550C22⋊Q8—98no—
551#117—98no—
552C2×C4⋊C4—31no—
553C2×C4⋊C4—31no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4—31no—
556C2×C4⋊C4—91no—
557C2×C4⋊C4—91no—
558C2×C4⋊C4—91no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4D3211yescharacteristic
562C2×C22⋊C4—31no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—91no—
566C2×C22⋊C4—91no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572C2×C42—31no—
573C2×C42—91no—
574C23×C3—21no—
575C23×C3—34no—
576C23×C3—32no—
577C23×C3—32no—
578C23×C3—62no—
579C23×C3—62no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3—62no—
583C23×C3C23×D311yescharacteristic
584C23×C3C23×D311yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—62no—
593C22×D3—64no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3D3×D414yes—
603C22×D3C23×D312yes—
604C22×D3C23×D312yes—
605C3×Q8—68no—
606C3×Q8—68no—
607C3×D4—68no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—34no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—42no—
625C2×C3×C4—42no—
626C2×C3×C4—42no—
627C2×C3×C4—68no—
628C2×C3×C4—62no—
629C2×C3×C4—62no—
630C2×C3×C4—62no—
631C2×C3×C4—62no—
632C2×C3×C4—62no—
633C2×C3×C4C23×D312yes—
634C2×C3×C4C23×D312yes—
635C2×C3×C4C23×D312yes—
636C2×C3×C4C23×D312yes—
637C2×C3×C4C23×D312yes—
638C2×C3×C4C23×D312yes—
639#67—68no—
640#67—68no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—34no—
647C2×Dic3—34no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—316no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—64no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—68no—
660C2×Dic3—68no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—122no—
666C2×Dic3—122no—
667C2×Dic3D3×D414yes—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674D12—28no—
675D12—68no—
676D12—68no—
677C4×D3—28no—
678C4×D3—316no—
679C4×D3—68no—
680C4×D3—68no—
681C4×D3—68no—
682C4×D3—68no—
683C4×D3—128no—
684Dic6—28no—
685Dic6—28no—
686Dic6—68no—
687Dic6—68no—
688Dic6—68no—
689Dic6—68no—
690Dic6—68no—
691Dic6—68no—
692Dic6—128no—
693C2×C32#53614yescomplemented
694C2×C32C23×D411yescharacteristic
695C2×C32C2×2−1+411yescharacteristic
696C2×C32C2×2−1+411yescharacteristic
697C3⋊D3—42no—
698C3×D3—24no—
699C3×D3—42no—
700C24—31no—
701C24—31no—
702C24—91no—
703#41—1832no—
704C2×Q8—34no—
705C2×Q8—34no—
706C2×Q8—64no—
707C2×Q8—64no—
708C2×Q8—94no—
709C2×Q8—94no—
710C2×Q8—94no—
711C2×Q8—184no—
712C2×Q8—184no—
713C2×Q8—184no—
714C2×Q8—1832no—
715C2×D4—34no—
716C2×D4—64no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—184no—
720C2×D4—184no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—34no—
728C22×C4—64no—
729C22×C4—94no—
730C22×C4—98no—
731C22×C4—94no—
732C22×C4—94no—
733C22×C4—91no—
734C22×C4—91no—
735C22×C4—91no—
736C22×C4—94no—
737C22×C4—184no—
738C22×C4—184no—
739C22×C4—184no—
740C22×C4C2×D3211yescharacteristic
741C22×C4C2×D3211yescharacteristic
742C22×C4C2×D3211yescharacteristic
743C4⋊C4—34no—
744C4⋊C4—34no—
745C4⋊C4—34no—
746C4⋊C4—34no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4C2×D3214yes—
753C22⋊C4—34no—
754C22⋊C4—34no—
755C22⋊C4—34no—
756C22⋊C4—94no—
757C22⋊C4—94no—
758C22⋊C4—94no—
759C22⋊C4—94no—
760C22⋊C4—94no—
761C22⋊C4—94no—
762C22⋊C4—94no—
763C42—34no—
764C42—94no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—21no—
769C22×C3—34no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—68no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—124no—
777C22×C3C2×D3×D412yes—
778C22×C3C2×D3×D412yes—
779C22×C3#100712yes—
780C22×C3#100712yes—
781C22×C3#101012yes—
782C22×C3#101012yes—
783C22×C3C24×D311yescharacteristic
784C22×C3C24×D311yescharacteristic
785C2×D3—28no—
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—44no—
792C2×D3—64no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—122no—
800C2×D3—122no—
801C2×D3—128no—
802C2×D3—124no—
803C2×D3—124no—
804C2×D3C2×D3×D414yes—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—34no—
812C3×C4—42no—
813C3×C4—42no—
814C3×C4—42no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—62no—
819C3×C4—62no—
820Dic3—22no—
821Dic3—22no—
822Dic3—22no—
823Dic3—22no—
824Dic3—22no—
825Dic3—34no—
826Dic3—34no—
827Dic3—64no—
828Dic3—62no—
829Dic3—62no—
830Dic3—62no—
831Dic3—62no—
832Dic3—122no—
833Dic3—122no—
834Dic3C2×D3×D414yes—
835C32C2×#53611yescharacteristic, complemented, Sylow
836C23—34no—
837C23—32no—
838C23—32no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—92no—
845C23—182no—
846C23—182no—
847C23—182no—
848C23C22×D3211yescharacteristic
849Q8—68no—
850Q8—68no—
851Q8—188no—
852Q8—188no—
853Q8—188no—
854D4—68no—
855D4—188no—
856D4—188no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—34no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—68no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—916no—
874C2×C4—94no—
875C2×C4—92no—
876C2×C4—92no—
877C2×C4—92no—
878C2×C4—188no—
879C2×C4—188no—
880C2×C4—188no—
881C2×C4—182no—
882C2×C4—182no—
883C2×C4C22×D3212yes—
884C2×C4C22×D3212yes—
885C2×C4C22×D3212yes—
886C2×C3—21no—
887C2×C3—24no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—64no—
891C2×C3—122no—
892C2×C3#564814yescomplemented
893C2×C3#572414yescomplemented
894C2×C3C22×D3×D411yescharacteristic
895C2×C3C22×D3×D411yescharacteristic
896C2×C3C2×#100711yescharacteristic
897C2×C3C2×#100711yescharacteristic
898C2×C3C2×#101011yescharacteristic
899C2×C3C2×#101011yescharacteristic
900D3—24no—
901D3—42no—
902D3—124no—
903D3—122no—
904D3—122no—
905C22—34no—
906C22—62no—
907C22—68no—
908C22—62no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—124no—
913C22—182no—
914C22—182no—
915C22—182no—
916C22—364no—
917C22#6429712yes—
918C22D32×D412yes—
919C22#6431512yes—
920C22C23×D3211yescharacteristic
921C4—22no—
922C4—22no—
923C4—22no—
924C4—34no—
925C4—62no—
926C4—62no—
927C4—62no—
928C4—62no—
929C4—62no—
930C4—94no—
931C4—182no—
932C4—182no—
933C3—21no—
934C3C2×#564811yescharacteristic, complemented
935C3C2×#572411yescharacteristic, complemented
936C2—64no—
937C2—122no—
938C2—362no—
939C2#1059436614yesdirect product factor
940C2C2×#6429711yescharacteristic
941C2C2×D32×D411yescharacteristic
942C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#3796C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×D3×Dic6C2semidirect
3. C2×#64105C2semidirect
4. C2×C3×#894C2semidirect
5. C2×C3×#888C2semidirect
6. C2×#63907C2semidirect
7. C2×#63899C2semidirect
8. C2×#63896C2semidirect
9. C2×#63890C2semidirect
10. C2×#63884C2semidirect
11. C2×#63877C2semidirect
12. C2×#63865C2semidirect
13. C2×#63852C2semidirect
14. C2×#63850C2semidirect
15. C2×#63839C2semidirect
16. #10594366C2direct (N × H)
35. C2×D3×Dic6C22semidirect
41. #64105C22semidirect
50. C3×#894C22semidirect
51. C3×#888C22semidirect
61. #63907C22semidirect
62. #63899C22semidirect
63. #63896C22semidirect
64. #63890C22semidirect
65. #63884C22semidirect
66. #63877C22semidirect
67. #63865C22semidirect
68. #63852C22semidirect
69. #63850C22semidirect
70. #63839C22semidirect
93. C2×#894D3semidirect
95. C2×#888D3semidirect
271. #894C2×D3semidirect
273. #888C2×D3semidirect
693. C2×C32#536semidirect
835. C32C2×#536semidirect
892. C2×C3#5648semidirect
893. C2×C3#5724semidirect
934. C3C2×#5648semidirect
935. C3C2×#5724semidirect
939. C2#10594366direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C22×D3×Dic62
C2×#641052
C2×C3×#8942
C2×C3×#8882
C2×#639072
C2×#638992
C2×#638962
C2×#638902
C2×#638842
C2×#638772
C2×#638652
C2×#638522
C2×#638502
C2×#638392
#105943662
C2×#57243
C2×#56483