Finite Group Databasebeta

← C2×#10594516 #11902535

Subgroups — C2×#10594516 #11902535

Order 1152.

3435 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64103C211yesmaximal, characteristic, complemented
4C2×C3×#896C211yesmaximal, characteristic, complemented
5C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×#63910C211yesmaximal, characteristic, complemented
7C2×#63906C211yesmaximal, characteristic, complemented
8C2×#63905C211yesmaximal, characteristic, complemented
9C2×#63904C211yesmaximal, characteristic, complemented
10C2×#63904C211yesmaximal, characteristic, complemented
11C2×#63895C211yesmaximal, characteristic, complemented
12C2×#63883C211yesmaximal, characteristic, complemented
13C2×#63854C211yesmaximal, characteristic, complemented
14C2×#63850C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10594516C2116yesmaximal, direct product factor
17C2×#5631—31nomaximal
18C2×#5507—31nomaximal
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#625C2211yescharacteristic
32C22×#624C2211yescharacteristic
33C22×#624C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C2×#3799—28no—
36C2×#3799C2218yescomplemented
37C2×#3798—28no—
38C2×#3798C2218yescomplemented
39C2×C32×C4⋊C4C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×#3750C2211yescharacteristic
44#64103C2218yescomplemented
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×C4⋊Dic3C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×Dic3⋊C4C2211yescharacteristic
52C3×#896C2218yescomplemented
53C3×D3×C4⋊C4C2218yescomplemented
54C2×#3724C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×Dic3⋊Dic3C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63910C2218yescomplemented
62#63906C2218yescomplemented
63#63905C2218yescomplemented
64#63904C2218yescomplemented
65#63904C2218yescomplemented
66#63895C2218yescomplemented
67#63883C2218yescomplemented
68#63854C2218yescomplemented
69#63850C2218yescomplemented
70#63839C2218yescomplemented
71C22×#239—31no—
72C22×#235—31no—
73C22×#235—31no—
74C22×#235—31no—
75C2×C3×C22⋊Q8—31no—
76C22×C3×C4⋊C4—31no—
77C2×#944—31no—
78C2×#930—31no—
79C2×#929—31no—
80C2×#929—31no—
81C2×C4×#67—31no—
82C2×C4×#67—31no—
83#5631—316no—
84C2×#897—31no—
85C2×#896—31no—
86C2×#896D311yescharacteristic, complemented
87#5507—316no—
88C2×#895—31no—
89C2×#894—31no—
90C2×#894—31no—
91C2×#894—31no—
92C2×#894—31no—
93C2×#894—61no—
94C2×#893—31no—
95C2×#893—31no—
96C2×D3×C4⋊C4—31no—
97C2×D3×C4⋊C4—31no—
98C2×D3×C4⋊C4D311yescharacteristic, complemented
99C2×#888—31no—
100C2×#884—31no—
101C2×#884—31no—
102C2×#883—31no—
103C2×#883—31no—
104C23×C3⋊D3C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×C4⋊(C3⋊D3)—24no—
114C2×C4⋊(C3⋊D3)C2314yes—
115C2×C4×C3⋊D3—24no—
116C2×C4×C3⋊D3C2314yes—
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×C4×D3—24no—
124C2×C3×C4×D3—24no—
125C2×C3×C4×D3—24no—
126C2×C3×C4×D3—24no—
127C2×C3×C4×D3C2314yes—
128C2×C3×C4×D3C2314yes—
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2314yes—
131C2×C3×Dic6—24no—
132C2×C3×Dic6C2314yes—
133C2×#627—24no—
134C2×#627C2314yes—
135C2×#626—24no—
136C2×#626—24no—
137C2×#626—24no—
138C2×#626D418yescomplemented
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×#625—24no—
144C2×#625C2314yes—
145C2×#624—24no—
146C2×#624—24no—
147C2×#624—24no—
148C2×#624C2314yes—
149C2×#624C2314yes—
150C2×#624C2314yes—
151#3799—232no—
152#3798—232no—
153C32×C4⋊C4C2314yes—
154#3752C2314yes—
155#3752C2314yes—
156#3752C2314yes—
157#3750C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×C4⋊Dic3C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165#3724C2314yes—
166Dic3⋊Dic3C2314yes—
167Dic3⋊Dic3C2314yes—
168#3722C2314yes—
169(C2×D3)⋊Dic3C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171Dic32C2314yes—
172C2×#547—91noSylow
173C22×C3×Q8—31no—
174C23×C3×C4—31no—
175C23×C3×C4—31no—
176C23×C3×C4—31no—
177C23×C3×C4—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C2×#239—38no—
185C2×#239—68no—
186C2×#235—38no—
187C2×#235—38no—
188C2×#235—38no—
189C2×#235—68no—
190C2×#235—68no—
191C2×#235—68no—
192C22×D12—31no—
193C22×D12—31no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—31no—
198C22×D12—61no—
199C22×C4×D3—31no—
200C22×C4×D3—31no—
201C22×C4×D3—31no—
202C22×C4×D3—31no—
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—31no—
206C22×C4×D3—31no—
207C22×C4×D3—61no—
208C22×C4×D3C2×D311yescharacteristic
209C22×C4×D3C2×D311yescharacteristic
210C22×C4×D3C2×D311yescharacteristic
211C22×C4×D3C2×D311yescharacteristic
212C22×Dic6—31no—
213C22×Dic6—31no—
214C22×Dic6C2×D311yescharacteristic
215C3×C22⋊Q8—38no—
216C2×C3×C4⋊C4—21no—
217C2×C3×C4⋊C4—31no—
218C2×C3×C4⋊C4—31no—
219C2×C3×C4⋊C4—31no—
220C2×C3×C4⋊C4—31no—
221C2×C3×C4⋊C4—31no—
222C2×C3×C4⋊C4—38no—
223C2×C3×C4⋊C4C2×D311yescharacteristic
224C2×C3×C4⋊C4C2×D311yescharacteristic
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×#217—31no—
228C2×#217—31no—
229#944—38no—
230#930—38no—
231#929—38no—
232#929—38no—
233C4×#67—38no—
234C4×#67—38no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—61no—
246C2×(C2×D3)⋊C4—61no—
247C2×(C2×D3)⋊C4—61no—
248C2×(C2×D3)⋊C4C2×D311yescharacteristic
249C2×(C2×D3)⋊C4C2×D311yescharacteristic
250C2×C4⋊Dic3—31no—
251C2×C4⋊Dic3—31no—
252C2×C4⋊Dic3C2×D311yescharacteristic
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—61no—
260C2×Dic3⋊C4C2×D311yescharacteristic
261C2×Dic3⋊C4C2×D311yescharacteristic
262C2×Dic3⋊C4C2×D311yescharacteristic
263C2×Dic3⋊C4C2×D311yescharacteristic
264C2×C4×Dic3—31no—
265C2×C4×Dic3—31no—
266#897—38no—
267#896—38no—
268#896C2×D318yescomplemented
269#895—38no—
270#894—38no—
271#894—38no—
272#894—38no—
273#894—38no—
274#894—68no—
275#893—38no—
276#893—38no—
277D3×C4⋊C4—38no—
278D3×C4⋊C4—38no—
279D3×C4⋊C4C2×D318yescomplemented
280#888—38no—
281#884—38no—
282#884—38no—
283#883—38no—
284#883—38no—
285C23×C32C2411yescharacteristic
286C22×C3⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—22no—
289C22×C3⋊D3—22no—
290C22×C3⋊D3—22no—
291C22×C3⋊D3C2×D414yes—
292C22×C3⋊D3C2412yes—
293C22×C3⋊D3C2412yes—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3C2×D414yes—
300C22×C3×D3C2412yes—
301C22×C3×D3C2412yes—
302C2×C32×C4—22no—
303C2×C32×C4—22no—
304C2×C32×C4—22no—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307C2×C32×C4C2412yes—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C4⋊(C3⋊D3)—28no—
313C4×C3⋊D3—28no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3C2×D414yes—
319C2×C3×Dic3#4114yescomplemented
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C3×C4×D3—28no—
327C3×C4×D3—28no—
328C3×C4×D3—28no—
329C3×C4×D3—28no—
330C3×Dic6—28no—
331#627—28no—
332#626—28no—
333#626—28no—
334#626—28no—
335#626C2×D4116yescomplemented
336#625—28no—
337#624—28no—
338#624—28no—
339#624—28no—
340C22×#41—91no—
341C22×#41—91no—
342#547—916no—
343C2×C4⋊Q8—91no—
344C2×#123—91no—
345C2×#123—91no—
346C2×#123—91no—
347C2×#123—91no—
348C2×C22⋊Q8—31no—
349C2×C22⋊Q8—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×C4×D4—91no—
353C2×C4×D4—91no—
354C22×C4⋊C4—31no—
355C22×C4⋊C4—91no—
356C24×C3—31no—
357C24×C3—31no—
358C23×D3—31no—
359C23×D3—31no—
360C23×D3—31no—
361C23×D3—31no—
362C23×D3—61no—
363C23×D3—61no—
364C23×D3C22×D311yescharacteristic
365C23×D3C22×D311yescharacteristic
366C2×C3×Q8—34no—
367C2×C3×Q8—64no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—34no—
378C22×C3×C4—34no—
379C22×C3×C4—34no—
380C22×C3×C4—34no—
381C22×C3×C4—64no—
382C22×C3×C4—64no—
383C22×C3×C4—64no—
384C22×C3×C4—64no—
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—38no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—64no—
399C2×#67—64no—
400C2×#67—64no—
401C2×#67—64no—
402C2×#67—64no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—31no—
406C22×Dic3—31no—
407C22×Dic3—61no—
408C22×Dic3—61no—
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415#239—632no—
416#235—632no—
417#235—632no—
418#235—632no—
419C2×D12—38no—
420C2×D12—34no—
421C2×D12—34no—
422C2×D12—34no—
423C2×D12—34no—
424C2×D12—34no—
425C2×D12—34no—
426C2×D12—64no—
427C2×D12—64no—
428C2×D12—64no—
429C2×D12—64no—
430C2×D12—64no—
431C2×D12—64no—
432C2×D12—124no—
433C2×C4×D3—24no—
434C2×C4×D3—24no—
435C2×C4×D3—24no—
436C2×C4×D3—24no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—34no—
443C2×C4×D3—34no—
444C2×C4×D3—34no—
445C2×C4×D3—64no—
446C2×C4×D3—64no—
447C2×C4×D3—64no—
448C2×C4×D3—64no—
449C2×C4×D3—64no—
450C2×C4×D3—64no—
451C2×C4×D3—64no—
452C2×C4×D3—64no—
453C2×C4×D3—64no—
454C2×C4×D3—124no—
455C2×C4×D3C22×D314yes—
456C2×C4×D3C22×D314yes—
457C2×C4×D3C22×D314yes—
458C2×C4×D3C22×D314yes—
459C2×Dic6—24no—
460C2×Dic6—34no—
461C2×Dic6—34no—
462C2×Dic6—64no—
463C2×Dic6—64no—
464C2×Dic6C22×D314yes—
465C3×C4⋊C4—24no—
466C3×C4⋊C4—34no—
467C3×C4⋊C4—34no—
468C3×C4⋊C4—34no—
469C3×C4⋊C4—34no—
470C3×C4⋊C4—34no—
471C3×C4⋊C4C22×D314yes—
472C3×C4⋊C4C22×D314yes—
473C3×C22⋊C4—34no—
474C3×C22⋊C4—34no—
475#217—34no—
476#217—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—64no—
488(C2×D3)⋊C4—64no—
489(C2×D3)⋊C4—64no—
490(C2×D3)⋊C4C22×D314yes—
491(C2×D3)⋊C4C22×D314yes—
492C4⋊Dic3—34no—
493C4⋊Dic3—34no—
494C4⋊Dic3C22×D314yes—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—64no—
502Dic3⋊C4C22×D314yes—
503Dic3⋊C4C22×D314yes—
504Dic3⋊C4C22×D314yes—
505Dic3⋊C4C22×D314yes—
506C4×Dic3—34no—
507C4×Dic3—34no—
508C22×C32C22×D412yes—
509C22×C32C2×#4112yes—
510C22×C322−1+412yes—
511C22×C32C2511yescharacteristic
512C2×C3⋊D3—28no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—22no—
515C2×C3⋊D3—22no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—22no—
518C2×C3⋊D3—44no—
519C2×C3⋊D3C22×D414yes—
520C2×C3×D3—28no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—44no—
527C2×C3×D3C22×D414yes—
528C32×C4—22no—
529C32×C4—22no—
530C32×C4—22no—
531C3⋊Dic3—22no—
532C3⋊Dic3—22no—
533C3×Dic3—22no—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3C22×D414yes—
538C3×Dic3C2×#4114yescomplemented
539C2×#41—98no—
540C2×#41—98no—
541C2×#41—188no—
542C2×#41—188no—
543C22×Q8—31no—
544C22×Q8—91no—
545C22×D4—91no—
546C22×D4—91no—
547C22×D4—91no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C23×C4—31no—
552C23×C4—31no—
553C23×C4—31no—
554C23×C4—31no—
555C23×C4—91no—
556C23×C4—91no—
557C23×C4—91no—
558C23×C4—91no—
559C4⋊Q8—98no—
560#123—98no—
561#123—98no—
562#123—98no—
563#123—98no—
564C22⋊Q8—38no—
565C22⋊Q8—98no—
566#121—98no—
567#121—98no—
568C4×D4—98no—
569C4×D4—98no—
570C2×C4⋊C4—31no—
571C2×C4⋊C4—31no—
572C2×C4⋊C4—31no—
573C2×C4⋊C4—31no—
574C2×C4⋊C4—31no—
575C2×C4⋊C4—38no—
576C2×C4⋊C4—98no—
577C2×C4⋊C4—91no—
578C2×C4⋊C4—91no—
579C2×C4⋊C4—91no—
580C2×C4⋊C4—91no—
581C2×C4⋊C4D3211yescharacteristic
582C2×C22⋊C4—31no—
583C2×C22⋊C4—31no—
584C2×C22⋊C4—91no—
585C2×C22⋊C4—91no—
586C2×C22⋊C4—91no—
587C2×C22⋊C4—91no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4—91no—
590C2×C42—91no—
591C23×C3—21no—
592C23×C3—34no—
593C23×C3—32no—
594C23×C3—32no—
595C23×C3—62no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3C23×D311yescharacteristic
601C23×C3C23×D311yescharacteristic
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—34no—
608C22×D3—34no—
609C22×D3—32no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—64no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3D3×D414yes—
632C22×D3C23×D312yes—
633C22×D3C23×D312yes—
634C3×Q8—68no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—34no—
645C2×C3×C4—34no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—42no—
653C2×C3×C4—42no—
654C2×C3×C4—42no—
655C2×C3×C4—68no—
656C2×C3×C4—68no—
657C2×C3×C4—68no—
658C2×C3×C4—68no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669#67—316no—
670#67—68no—
671#67—68no—
672#67—68no—
673#67—68no—
674#67—68no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—122no—
690C2×Dic3—122no—
691C2×Dic3#23514yescomplemented
692C2×Dic3D3×D414yes—
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699D12—316no—
700D12—68no—
701D12—68no—
702D12—68no—
703D12—68no—
704D12—68no—
705D12—128no—
706C4×D3—28no—
707C4×D3—28no—
708C4×D3—28no—
709C4×D3—28no—
710C4×D3—68no—
711C4×D3—68no—
712C4×D3—68no—
713C4×D3—68no—
714C4×D3—68no—
715C4×D3—68no—
716C4×D3—68no—
717C4×D3—68no—
718C4×D3—128no—
719Dic6—28no—
720Dic6—68no—
721Dic6—68no—
722C2×C32#54714yescomplemented
723C2×C32C23×D411yescharacteristic
724C2×C32C22×#4111yescharacteristic
725C2×C32C2×2−1+411yescharacteristic
726C3⋊D3—24no—
727C3⋊D3—42no—
728C3×D3—24no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24—91no—
733C24—91no—
734#41—1832no—
735#41—1832no—
736C2×Q8—34no—
737C2×Q8—64no—
738C2×Q8—94no—
739C2×Q8—184no—
740C2×D4—94no—
741C2×D4—98no—
742C2×D4—94no—
743C2×D4—94no—
744C2×D4—94no—
745C2×D4—94no—
746C2×D4—94no—
747C2×D4—184no—
748C2×D4—184no—
749C2×D4—184no—
750C2×D4—184no—
751C2×D4—184no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—34no—
759C22×C4—34no—
760C22×C4—34no—
761C22×C4—34no—
762C22×C4—64no—
763C22×C4—64no—
764C22×C4—64no—
765C22×C4—64no—
766C22×C4—94no—
767C22×C4—94no—
768C22×C4—94no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—94no—
772C22×C4—184no—
773C22×C4—184no—
774C22×C4—184no—
775C22×C4—184no—
776C22×C4C2×D3211yescharacteristic
777C22×C4C2×D3211yescharacteristic
778C22×C4C2×D3211yescharacteristic
779C4⋊C4—34no—
780C4⋊C4—34no—
781C4⋊C4—34no—
782C4⋊C4—34no—
783C4⋊C4—34no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C4⋊C4—94no—
787C4⋊C4—94no—
788C4⋊C4C2×D3214yes—
789C22⋊C4—34no—
790C22⋊C4—34no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C42—94no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—21no—
802C22×C3—34no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—68no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—124no—
810C22×C3C2×#23512yes—
811C22×C3C2×D3×D412yes—
812C22×C3C2×D3×D412yes—
813C22×C3#100712yes—
814C22×C3#100712yes—
815C22×C3D3×#4112yes—
816C22×C3C24×D311yescharacteristic
817C22×C3C24×D311yescharacteristic
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—28no—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—34no—
825C2×D3—34no—
826C2×D3—44no—
827C2×D3—64no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—68no—
833C2×D3—68no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—128no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—124no—
847C2×D3—124no—
848C2×D3—244no—
849C2×D3C2×D3×D414yes—
850C3×C4—22no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—22no—
855C3×C4—22no—
856C3×C4—34no—
857C3×C4—34no—
858C3×C4—42no—
859C3×C4—42no—
860C3×C4—42no—
861C3×C4—62no—
862C3×C4—62no—
863C3×C4—62no—
864C3×C4—62no—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—22no—
869Dic3—62no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—122no—
874Dic3—122no—
875Dic3C2×#23514yescomplemented
876Dic3C2×D3×D414yes—
877C32C2×#54711yescharacteristic, complemented, Sylow
878C23—34no—
879C23—32no—
880C23—32no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—94no—
887C23—92no—
888C23—92no—
889C23—182no—
890C23—182no—
891C23—182no—
892C23—182no—
893C23—182no—
894C23C22×D3211yescharacteristic
895Q8—68no—
896Q8—188no—
897D4—916no—
898D4—188no—
899D4—188no—
900D4—188no—
901D4—188no—
902D4—188no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—34no—
907C2×C4—34no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—32no—
911C2×C4—32no—
912C2×C4—32no—
913C2×C4—32no—
914C2×C4—68no—
915C2×C4—68no—
916C2×C4—68no—
917C2×C4—68no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—92no—
923C2×C4—92no—
924C2×C4—188no—
925C2×C4—188no—
926C2×C4—188no—
927C2×C4—188no—
928C2×C4—182no—
929C2×C4—182no—
930C2×C4C22×D3212yes—
931C2×C4C22×D3212yes—
932C2×C4C22×D3212yes—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—24no—
937C2×C3—64no—
938C2×C3—122no—
939C2×C3#550714yescomplemented
940C2×C3#563114yescomplemented
941C2×C3C22×#23511yescharacteristic
942C2×C3C22×D3×D411yescharacteristic
943C2×C3C22×D3×D411yescharacteristic
944C2×C3C2×#100711yescharacteristic
945C2×C3C2×#100711yescharacteristic
946C2×C3C2×D3×#4111yescharacteristic
947D3—24no—
948D3—42no—
949D3—64no—
950D3—64no—
951D3—124no—
952D3—122no—
953D3—122no—
954D3—242no—
955C22—34no—
956C22—62no—
957C22—62no—
958C22—68no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—94no—
963C22—124no—
964C22—182no—
965C22—182no—
966C22—188no—
967C22—182no—
968C22—182no—
969C22—182no—
970C22—364no—
971C22D3×#23512yes—
972C22D32×D412yes—
973C22#6431612yes—
974C22C23×D3211yescharacteristic
975C4—22no—
976C4—22no—
977C4—22no—
978C4—34no—
979C4—34no—
980C4—62no—
981C4—62no—
982C4—62no—
983C4—62no—
984C4—182no—
985C4—182no—
986C3—21no—
987C3C2×#550711yescharacteristic, complemented
988C3C2×#563111yescharacteristic, complemented
989C2—64no—
990C2—122no—
991C2—184no—
992C2—362no—
993C2#1059451614yesdirect product factor
994C2C2×D3×#23511yescharacteristic
995C2C2×D32×D411yescharacteristic
996C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C22×#3798C2semidirect
3. C2×#64103C2semidirect
4. C2×C3×#896C2semidirect
5. C2×C3×D3×C4⋊C4C2semidirect
6. C2×#63910C2semidirect
7. C2×#63906C2semidirect
8. C2×#63905C2semidirect
9. C2×#63904C2semidirect
10. C2×#63904C2semidirect
11. C2×#63895C2semidirect
12. C2×#63883C2semidirect
13. C2×#63854C2semidirect
14. C2×#63850C2semidirect
15. C2×#63839C2semidirect
16. #10594516C2direct (N × H)
36. C2×#3799C22semidirect
38. C2×#3798C22semidirect
44. #64103C22semidirect
52. C3×#896C22semidirect
53. C3×D3×C4⋊C4C22semidirect
61. #63910C22semidirect
62. #63906C22semidirect
63. #63905C22semidirect
64. #63904C22semidirect
65. #63904C22semidirect
66. #63895C22semidirect
67. #63883C22semidirect
68. #63854C22semidirect
69. #63850C22semidirect
70. #63839C22semidirect
86. C2×#896D3semidirect
98. C2×D3×C4⋊C4D3semidirect
138. C2×#626D4semidirect
268. #896C2×D3semidirect
279. D3×C4⋊C4C2×D3semidirect
319. C2×C3×Dic3#41semidirect
335. #626C2×D4semidirect
538. C3×Dic3C2×#41semidirect
691. C2×Dic3#235semidirect
722. C2×C32#547semidirect
875. Dic3C2×#235semidirect
877. C32C2×#547semidirect
939. C2×C3#5507semidirect
940. C2×C3#5631semidirect
987. C3C2×#5507semidirect
988. C3C2×#5631semidirect
993. C2#10594516direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×#37982
C2×#641032
C2×C3×#8962
C2×C3×D3×C4⋊C42
C2×#639102
C2×#639062
C2×#639052
C2×#639042
C2×#638952
C2×#638832
C2×#638542
C2×#638502
C2×#638392
#105945162
C2×#56313
C2×#55073