Finite Group Databasebeta

← C2×#10594199 #11901312

Subgroups — C2×#10594199 #11901312

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic, complemented
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#879C211yesmaximal, characteristic, complemented
4C2×#63977C211yesmaximal, characteristic, complemented
5C2×#63977C211yesmaximal, characteristic, complemented
6C2×#63975C211yesmaximal, characteristic, complemented
7C2×#63953C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×#63909C211yesmaximal, characteristic, complemented
10C2×#63904C211yesmaximal, characteristic, complemented
11C2×C4×#626C211yesmaximal, characteristic, complemented
12C2×#63858C211yesmaximal, characteristic, complemented
13C2×#63853C211yesmaximal, characteristic, complemented
14C2×#63852C211yesmaximal, characteristic, complemented
15C2×#63851C211yesmaximal, characteristic, complemented
16#10594199C2116yesmaximal, direct product factor
17C2×#5704—31nomaximal
18C2×#5494—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#627C2211yescharacteristic, complemented
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#624C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3752C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35#64093C2218yescomplemented
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×C4×Dic3C2211yescharacteristic, complemented
45C3×D3×C22⋊C4C2218yescomplemented
46C3×#879C2218yescomplemented
47#63977C2218yescomplemented
48#63977C2218yescomplemented
49#63975C2218yescomplemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×#3722C2211yescharacteristic, complemented
53C2×#3722C2211yescharacteristic, complemented
54C2×#3722C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×Dic32C2211yescharacteristic, complemented
60#63953C2218yescomplemented
61#63910C2218yescomplemented
62#63909C2218yescomplemented
63#63904C2218yescomplemented
64C4×#626C2218yescomplemented
65#63858C2218yescomplemented
66#63853C2218yescomplemented
67#63852C2218yescomplemented
68#63851C2218yescomplemented
69C2×C3×#126—31no—
70C22×C3×C22⋊C4—31no—
71C2×#953—31no—
72C2×#953—31no—
73C2×#930—31no—
74C2×C4×#67—31no—
75C2×C4×#67—31no—
76C2×#924—31no—
77#5704—316no—
78C2×#898—31no—
79C2×#896—31no—
80C2×#895—31no—
81C2×#895—31no—
82C2×#894—31no—
83C2×#893—31no—
84#5494—316no—
85C2×#885—31no—
86C2×#885—31no—
87C2×#885—31no—
88C2×#884—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—61no—
92C2×#883—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×D3×C22⋊C4D311yescharacteristic, complemented
98C2×#879—31no—
99C2×#879D311yescharacteristic, complemented
100C2×#875—31no—
101C2×C4×D12—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3—24no—
106C23×C3×D3—42no—
107C23×C3×D3—42no—
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2314yes—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C2×#638—42no—
114C2×#638—42no—
115C2×#638C2314yes—
116C2×#638C2314yes—
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C2×C4⋊(C3⋊D3)—42no—
120C2×C4⋊(C3⋊D3)C2314yescomplemented
121C2×C4×C3⋊D3—42no—
122C2×C4×C3⋊D3C2314yescomplemented
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×C4×D3—42no—
130C2×C3×C4×D3—42no—
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2314yes—
133C2×#627—42no—
134C2×#627C2314yescomplemented
135C2×#626—24no—
136C2×#626—24no—
137C2×#626—42no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×#624—42no—
144C2×#624C2314yescomplemented
145C32×C22⋊C4C2314yes—
146#3752C2314yescomplemented
147#3750C2314yescomplemented
148C3×#217C2314yes—
149C3×#217C2314yes—
150C3×#217C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×C4⋊Dic3C2314yescomplemented
154C3×Dic3⋊C4C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156C3×C4×Dic3C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yescomplemented
160#3722C2314yescomplemented
161#3722C2314yescomplemented
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C25×C3—31no—
169C24×D3C2×D311yescharacteristic
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—61no—
181C22×#67—61no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—61no—
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×C4×D3C2×D311yescharacteristic
196C22×Dic6—31no—
197C22×Dic6—31no—
198C3×#126—38no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C22⋊C4—21no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—38no—
209C2×C3×C22⋊C4C2×D311yescharacteristic
210C2×C3×C22⋊C4C2×D311yescharacteristic
211C2×C3×C42—31no—
212#953—38no—
213#953—38no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—31no—
217C2×#217—31no—
218C2×#217C2×D311yescharacteristic
219C2×#217C2×D311yescharacteristic
220C2×#217C2×D311yescharacteristic
221#930—38no—
222C4×#67—38no—
223C4×#67—38no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
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—61no—
237C2×(C2×D3)⋊C4C2×D311yescharacteristic
238C2×(C2×D3)⋊C4C2×D311yescharacteristic
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3—31no—
241C2×C4⋊Dic3C2×D311yescharacteristic, complemented
242#924—38no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—61no—
248C2×Dic3⋊C4C2×D311yescharacteristic, complemented
249C2×Dic3⋊C4C2×D311yescharacteristic, complemented
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3C2×D311yescharacteristic, complemented
253#898—38no—
254#896—38no—
255#895—38no—
256#895—38no—
257#894—38no—
258#893—38no—
259#885—38no—
260#885—38no—
261#885—38no—
262#884—38no—
263#884—38no—
264#884—38no—
265#884—68no—
266#883—38no—
267#883—38no—
268#883—38no—
269#882—38no—
270#882—38no—
271D3×C22⋊C4C2×D318yescomplemented
272#879—38no—
273#879C2×D318yescomplemented
274#875—38no—
275C4×D12—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32C2412yes—
280C23×C32C2411yescharacteristic
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3C2412yes—
288C22×C3⋊D3C2412yes—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—28no—
295C22×C3×D3—44no—
296C22×C3×D3—44no—
297C22×C3×D3—416no—
298C22×C3×D3#4114yes—
299C22×C3×D3C2412yes—
300C22×C3×D3C2412yes—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4C2412yes—
304C2×C32×C4C2412yes—
305#638—44no—
306#638—44no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3C2412yes—
310C2×C3⋊Dic3C2412yes—
311C4⋊(C3⋊D3)—44no—
312C4×C3⋊D3—44no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C3×C4×D3—44no—
326C3×C4×D3—44no—
327#627—44no—
328#626—28no—
329#626—28no—
330#626—44no—
331#626—44no—
332#624—44no—
333#538—916no—
334C2×#126—31no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—91no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—91no—
345C2×#120—91no—
346C2×C4×D4—91no—
347C2×C4×D4—91no—
348C22×C22⋊C4—31no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3—34no—
353C24×C3—64no—
354C24×C3—122no—
355C24×C3—122no—
356C24×C3C22×D311yescharacteristic
357C24×C3C22×D311yescharacteristic
358C23×D3—24no—
359C23×D3—31no—
360C23×D3—31no—
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—42no—
364C23×D3—42no—
365C23×D3—61no—
366C23×D3—61no—
367C23×D3C22×D311yescharacteristic
368C23×D3C22×D311yescharacteristic
369C23×D3C22×D314yes—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—34no—
379C22×C3×C4—34no—
380C22×C3×C4—122no—
381C22×C3×C4—122no—
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C2×#67—34no—
387C2×#67—34no—
388C2×#67—34no—
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—64no—
395C2×#67—64no—
396C2×#67—64no—
397C2×#67—64no—
398C2×#67—122no—
399C2×#67—122no—
400C2×#67—122no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67—124no—
405C2×#67—124no—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—61no—
411C22×Dic3—61no—
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D311yescharacteristic
417C22×Dic3C22×D311yescharacteristic
418C2×D12—34no—
419C2×D12—34no—
420C2×D12—34no—
421C2×D12—34no—
422C2×D12—34no—
423C2×D12—34no—
424C2×D12—64no—
425C2×D12—64no—
426C2×D12—64no—
427C2×D12—122no—
428C2×D12—122no—
429C2×D12—124no—
430C2×D12—122no—
431C2×D12—122no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3—42no—
437C2×C4×D3—42no—
438C2×C4×D3—64no—
439C2×C4×D3—122no—
440C2×C4×D3—122no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—124no—
444C2×C4×D3C22×D314yes—
445C2×C4×D3C22×D314yes—
446C2×Dic6—34no—
447C2×Dic6—34no—
448C2×Dic6—122no—
449C2×Dic6—122no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—34no—
453C3×C22⋊C4—24no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4C22×D314yes—
460C3×C22⋊C4C22×D314yes—
461C3×C42—34no—
462#217—34no—
463#217—34no—
464#217—34no—
465#217—34no—
466#217C22×D314yes—
467#217C22×D314yes—
468#217C22×D314yes—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—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—64no—
482(C2×D3)⋊C4C22×D314yes—
483(C2×D3)⋊C4C22×D314yes—
484C4⋊Dic3—34no—
485C4⋊Dic3—34no—
486C4⋊Dic3C22×D314yescomplemented
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—64no—
492Dic3⋊C4C22×D314yescomplemented
493Dic3⋊C4C22×D314yescomplemented
494C4×Dic3—34no—
495C4×Dic3—34no—
496C4×Dic3C22×D314yescomplemented
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—44no—
501C22×C32C2×#4112yes—
502C22×C32H(5,𝔽2)12yes—
503C22×C32H(5,𝔽2)12yes—
504C22×C32C2511yescharacteristic
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—22no—
508C2×C3⋊D3—22no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—44no—
512C2×C3⋊D3—44no—
513C2×C3×D3—28no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—416no—
520C2×C3×D3—44no—
521C2×C3×D3C2×#4114yes—
522C32×C4—22no—
523C32×C4—22no—
524C3⋊Dic3—22no—
525C3⋊Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C25—31no—
533C22×Q8—91no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4—91no—
541C23×C4—31no—
542C23×C4—31no—
543C23×C4—91no—
544C23×C4—91no—
545#126—38no—
546#126—98no—
547#124—98no—
548#124—98no—
549#123—98no—
550#123—98no—
551C22⋊Q8—98no—
552#121—98no—
553#121—98no—
554#121—98no—
555#120—98no—
556#120—98no—
557C4×D4—98no—
558C4×D4—98no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—38no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—91no—
579C2×C22⋊C4D3211yescharacteristic
580C2×C42—31no—
581C2×C42—91no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—21no—
590C23×C3—34no—
591C23×C3—32no—
592C23×C3—32no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—42no—
596C23×C3—68no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3—62no—
602C23×C3—124no—
603C23×C3—124no—
604C23×C3—1216no—
605C23×C3C23×D312yes—
606C23×C3C23×D312yes—
607C23×C3C23×D311yescharacteristic
608C23×C3C23×D311yescharacteristic
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—28no—
615C22×D3—32no—
616C22×D3—32no—
617C22×D3—32no—
618C22×D3—32no—
619C22×D3—44no—
620C22×D3—44no—
621C22×D3—416no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—64no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—62no—
634C22×D3—62no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—122no—
638C22×D3—122no—
639C22×D3—122no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3#23514yes—
643C22×D3C23×D312yes—
644C22×D3C23×D312yes—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—42no—
658C2×C3×C4—42no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4—124no—
666C2×C3×C4—124no—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669C2×C3×C4C23×D312yes—
670C2×C3×C4C23×D312yes—
671#67—68no—
672#67—68no—
673#67—124no—
674#67—124no—
675#67—124no—
676#67—124no—
677#67—124no—
678#67—124no—
679#67—128no—
680#67—128no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—32no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—64no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—122no—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701C2×Dic3C23×D312yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705D12—68no—
706D12—68no—
707D12—124no—
708D12—124no—
709D12—128no—
710D12—124no—
711D12—124no—
712C4×D3—44no—
713C4×D3—44no—
714C4×D3—124no—
715C4×D3—124no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—128no—
719Dic6—124no—
720Dic6—124no—
721C2×C32—42no—
722C2×C32#53814yescomplemented
723C2×C32C22×#4111yescharacteristic
724C2×C32C2×H(5,𝔽2)11yescharacteristic
725C2×C32C2×H(5,𝔽2)11yescharacteristic
726C3⋊D3—42no—
727C3⋊D3—42no—
728C3×D3—24no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24—34no—
733C24—64no—
734C24—91no—
735C24—91no—
736C24—122no—
737C24—122no—
738C24C2×D3211yescharacteristic
739C2×Q8—94no—
740C2×Q8—362no—
741C2×D4—94no—
742C2×D4—94no—
743C2×D4—94no—
744C2×D4—94no—
745C2×D4—94no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—184no—
749C2×D4—184no—
750C2×D4—362no—
751C2×D4—362no—
752C2×D4—362no—
753C2×D4—362no—
754C2×D4—362no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—34no—
762C22×C4—34no—
763C22×C4—94no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—94no—
767C22×C4—122no—
768C22×C4—122no—
769C22×C4—362no—
770C22×C4—362no—
771C22×C4C2×D3211yescharacteristic
772C22×C4C2×D3211yescharacteristic
773C4⋊C4—34no—
774C4⋊C4—34no—
775C4⋊C4—34no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4C2×D3214yes—
793C42—34no—
794C42—94no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—21no—
805C22×C3—34no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—44no—
810C22×C3—44no—
811C22×C3—68no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—84no—
818C22×C3—1216no—
819C22×C3—124no—
820C22×C3C2×#23512yes—
821C22×C3#100412yes—
822C22×C3#100412yes—
823C22×C3D3×#4112yes—
824C22×C3#100912yes—
825C22×C3#100912yes—
826C22×C3C24×D311yescharacteristic
827C22×C3C24×D311yescharacteristic
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—28no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—416no—
835C2×D3—44no—
836C2×D3—64no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—122no—
852C2×D3—122no—
853C2×D3—122no—
854C2×D3—128no—
855C2×D3—124no—
856C2×D3—124no—
857C2×D3—124no—
858C2×D3—124no—
859C2×D3—244no—
860C2×D3C2×#23514yes—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—62no—
873Dic3—22no—
874Dic3—22no—
875Dic3—22no—
876Dic3—22no—
877Dic3—22no—
878Dic3—22no—
879Dic3—64no—
880Dic3—62no—
881Dic3—62no—
882Dic3—62no—
883Dic3—62no—
884Dic3—122no—
885C32C2×#53811yescharacteristic, complemented, Sylow
886C23—22no—
887C23—22no—
888C23—22no—
889C23—34no—
890C23—32no—
891C23—32no—
892C23—68no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—92no—
899C23—92no—
900C23—124no—
901C23—124no—
902C23—1216no—
903C23—182no—
904C23—182no—
905C23—182no—
906C23—182no—
907C23—182no—
908C23—182no—
909C23C22×D3212yes—
910C23C22×D3211yescharacteristic
911Q8—364no—
912D4—188no—
913D4—188no—
914D4—364no—
915D4—364no—
916D4—364no—
917D4—364no—
918D4—364no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—62no—
930C2×C4—62no—
931C2×C4—62no—
932C2×C4—62no—
933C2×C4—92no—
934C2×C4—92no—
935C2×C4—124no—
936C2×C4—124no—
937C2×C4—182no—
938C2×C4—182no—
939C2×C4—364no—
940C2×C4—364no—
941C2×C4C22×D3212yes—
942C2×C4C22×D3212yes—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—24no—
947C2×C3—42no—
948C2×C3—42no—
949C2×C3—64no—
950C2×C3—82no—
951C2×C3—122no—
952C2×C3#549414yescomplemented
953C2×C3#570414yescomplemented
954C2×C3C22×#23511yescharacteristic
955C2×C3C2×#100411yescharacteristic
956C2×C3C2×#100411yescharacteristic
957C2×C3C2×D3×#4111yescharacteristic
958C2×C3C2×#100911yescharacteristic
959C2×C3C2×#100911yescharacteristic
960D3—24no—
961D3—42no—
962D3—124no—
963D3—122no—
964D3—122no—
965D3—122no—
966D3—122no—
967D3—242no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—34no—
972C22—44no—
973C22—62no—
974C22—62no—
975C22—68no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—1216no—
980C22—124no—
981C22—182no—
982C22—182no—
983C22—182no—
984C22—182no—
985C22—182no—
986C22—182no—
987C22—364no—
988C22—364no—
989C22D3×#23512yes—
990C22#6431412yes—
991C22#6431412yes—
992C22C23×D3211yescharacteristic
993C4—22no—
994C4—22no—
995C4—62no—
996C4—62no—
997C4—62no—
998C4—62no—
999C4—62no—
1000C4—62no—
1001C4—182no—
1002C4—182no—
1003C3—21no—
1004C3C2×#549411yescharacteristic, complemented
1005C3C2×#570411yescharacteristic, complemented
1006C2—42no—
1007C2—64no—
1008C2—122no—
1009C2—362no—
1010C2—362no—
1011C2#1059419914yesdirect product factor
1012C2C2×D3×#23511yescharacteristic
1013C2C2×#6431411yescharacteristic
1014C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64093C2semidirect
2. C2×C3×D3×C22⋊C4C2semidirect
3. C2×C3×#879C2semidirect
4. C2×#63977C2semidirect
5. C2×#63977C2semidirect
6. C2×#63975C2semidirect
7. C2×#63953C2semidirect
8. C2×#63910C2semidirect
9. C2×#63909C2semidirect
10. C2×#63904C2semidirect
11. C2×C4×#626C2semidirect
12. C2×#63858C2semidirect
13. C2×#63853C2semidirect
14. C2×#63852C2semidirect
15. C2×#63851C2semidirect
16. #10594199C2direct (N × H)
22. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C4×C3⋊D3C22semidirect
26. C22×#627C22semidirect
31. C22×#624C22semidirect
33. C2×#3752C22semidirect
34. C2×#3750C22semidirect
35. #64093C22semidirect
41. C2×C3×C4⋊Dic3C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×C4×Dic3C22semidirect
45. C3×D3×C22⋊C4C22semidirect
46. C3×#879C22semidirect
47. #63977C22semidirect
48. #63977C22semidirect
49. #63975C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×#3722C22semidirect
53. C2×#3722C22semidirect
54. C2×#3722C22semidirect
59. C2×Dic32C22semidirect
60. #63953C22semidirect
61. #63910C22semidirect
62. #63909C22semidirect
63. #63904C22semidirect
64. C4×#626C22semidirect
65. #63858C22semidirect
66. #63853C22semidirect
67. #63852C22semidirect
68. #63851C22semidirect
97. C2×D3×C22⋊C4D3semidirect
99. C2×#879D3semidirect
120. C2×C4⋊(C3⋊D3)C23semidirect
122. C2×C4×C3⋊D3C23semidirect
134. C2×#627C23semidirect
144. C2×#624C23semidirect
146. #3752C23semidirect
147. #3750C23semidirect
153. C3×C4⋊Dic3C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. C3×C4×Dic3C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
159. #3722C23semidirect
160. #3722C23semidirect
161. #3722C23semidirect
166. Dic32C23semidirect
241. C2×C4⋊Dic3C2×D3semidirect
248. C2×Dic3⋊C4C2×D3semidirect
249. C2×Dic3⋊C4C2×D3semidirect
252. C2×C4×Dic3C2×D3semidirect
271. D3×C22⋊C4C2×D3semidirect
273. #879C2×D3semidirect
486. C4⋊Dic3C22×D3semidirect
492. Dic3⋊C4C22×D3semidirect
493. Dic3⋊C4C22×D3semidirect
496. C4×Dic3C22×D3semidirect
722. C2×C32#538semidirect
885. C32C2×#538semidirect
952. C2×C3#5494semidirect
953. C2×C3#5704semidirect
1004. C3C2×#5494semidirect
1005. C3C2×#5704semidirect
1011. C2#10594199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640932
C2×C3×D3×C22⋊C42
C2×C3×#8792
C2×#639772
C2×#639752
C2×#639532
C2×#639102
C2×#639092
C2×#639042
C2×C4×#6262
C2×#638582
C2×#638532
C2×#638522
C2×#638512
#105941992
C2×#57043
C2×#54943