Finite Group Databasebeta

← C2×#10594298 #11901297

Subgroups — C2×#10594298 #11901297

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×#885C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×#63983C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63971C211yesmaximal, characteristic, complemented
7C2×#63966C211yesmaximal, characteristic, complemented
8C2×#63923C211yesmaximal, characteristic, complemented
9C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×#63887C211yesmaximal, characteristic, complemented
12C2×#63868C211yesmaximal, characteristic, complemented
13C2×#63864C211yesmaximal, characteristic, complemented
14C2×#63859C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594298C2116yesmaximal, direct product factor
17C2×#5678—31nomaximal
18C2×#5560—31nomaximal
19C23×D32C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic, complemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic
28C22×C3×Dic6C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3750C2211yescharacteristic, complemented
35#64093C2218yescomplemented
36C2×C3×#217C2211yescharacteristic, complemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×C4×Dic3C2211yescharacteristic, complemented
42C2×C3×C4×Dic3C2211yescharacteristic, complemented
43C3×#885C2218yescomplemented
44C3×#67⋊C4C2218yescomplemented
45#63983C2218yescomplemented
46#63978C2218yescomplemented
47#63971C2218yescomplemented
48C2×#3724C2211yescharacteristic, complemented
49#63966C2218yescomplemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61#63923C2218yescomplemented
62D3×(C2×D3)⋊C4C2218yescomplemented
63C4×#626C2218yescomplemented
64#63887C2218yescomplemented
65#63868C2218yescomplemented
66#63864C2218yescomplemented
67#63859C2218yescomplemented
68#63853C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×C4×D4—31no—
71C2×#947—31no—
72C2×#946—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#937—31no—
76C2×#937—31no—
77C2×#930—31no—
78C2×#929—31no—
79C2×C4×#67—31no—
80C22×(C2×D3)⋊C4—31no—
81#5678—316no—
82#5560—316no—
83C2×#898—31no—
84C2×#894—31no—
85C2×#886—31no—
86C2×#885D311yescharacteristic, complemented
87C2×#884—31no—
88C2×#884—31no—
89C2×#884—31no—
90C2×#884—61no—
91C2×#883—31no—
92C2×#882—31no—
93C2×#882—31no—
94C2×#67⋊C4D311yescharacteristic, complemented
95C2×D3×C22⋊C4—31no—
96C2×#879—31no—
97C2×#878—31no—
98C2×#876—31no—
99C2×#876—31no—
100C2×#875—31no—
101C2×C4×D12—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×D32—24no—
108C22×D32—42no—
109C22×D32—42no—
110C22×D32C2314yes—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C2×#638—42no—
114C2×#638—42no—
115C2×#638C2314yes—
116C2×#638C2314yescomplemented
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C2×C4⋊(C3⋊D3)—42no—
120C2×C4⋊(C3⋊D3)C2314yes—
121C2×C4×C3⋊D3—42no—
122C2×C4×C3⋊D3C2314yescomplemented
123C2×C3×#67—24no—
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C22×C3×Dic3—42no—
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2314yescomplemented
135C2×C3×C4×D3—42no—
136C2×C3×C4×D3C2314yes—
137C2×C3×Dic6—42no—
138C2×C3×Dic6C2314yescomplemented
139C2×#626—24no—
140C2×#626—42no—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yes—
145C32×C22⋊C4C2314yescomplemented
146#3752C2314yes—
147#3750C2314yescomplemented
148C3×#217C2314yescomplemented
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×Dic3⋊C4C2314yescomplemented
153C3×C4×Dic3C2314yescomplemented
154C3×C4×Dic3C2314yescomplemented
155#3724C2314yescomplemented
156Dic3⋊Dic3C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162#3722C2314yescomplemented
163#3722C2314yescomplemented
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×Q8—31no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C23×C3×C4—31no—
174C23×C3×C4—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—61no—
182C22×#67—61no—
183C22×#67C2×D311yescharacteristic
184C22×#67C2×D311yescharacteristic
185C23×Dic3—31no—
186C23×Dic3C2×D311yescharacteristic, complemented
187C22×D12—31no—
188C22×D12—31no—
189C22×D12—31no—
190C22×D12—31no—
191C22×D12—61no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3—61no—
196C22×C4×D3C2×D311yescharacteristic
197C22×Dic6C2×D311yescharacteristic, complemented
198C3×#124—38no—
199C3×C4×D4—38no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C22⋊C4—21no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
207C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
208C2×C3×C42—31no—
209C2×C3×C42—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217C2×D311yescharacteristic, complemented
214#947—38no—
215#946—38no—
216#939—38no—
217#939—38no—
218#937—38no—
219#937—38no—
220#930—38no—
221#929—38no—
222C4×#67—38no—
223C2×(C2×D3)⋊C4—31no—
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—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—38no—
239C2×(C2×D3)⋊C4—61no—
240C2×(C2×D3)⋊C4C2×D311yescharacteristic
241C2×(C2×D3)⋊C4C2×D311yescharacteristic
242C2×(C2×D3)⋊C4C2×D311yescharacteristic
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3—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⋊C4C2×D311yescharacteristic, complemented
255C2×C4×Dic3C2×D311yescharacteristic, complemented
256C2×C4×Dic3C2×D311yescharacteristic, complemented
257#898—38no—
258#894—38no—
259#886—38no—
260#885C2×D318yescomplemented
261#884—38no—
262#884—38no—
263#884—38no—
264#884—68no—
265#883—38no—
266#882—38no—
267#882—38no—
268#67⋊C4C2×D318yescomplemented
269D3×C22⋊C4—38no—
270#879—38no—
271#878—38no—
272#876—38no—
273#876—38no—
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#4114yes—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C2×D32—28no—
298C2×D32—44no—
299C2×D32—44no—
300C2×D32—416no—
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—
313C3×#67—28no—
314C3×#67—44no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—44no—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C3×C4×D3—44no—
329C3×Dic6—44no—
330#626—28no—
331#626—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—91no—
335C2×#126—91no—
336C2×#124—31no—
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—31no—
347C2×C4×D4—91no—
348C22×C22⋊C4—91no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3C22×D311yescharacteristic
353C24×C3C22×D311yescharacteristic
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—34no—
359C23×D3—34no—
360C23×D3—61no—
361C23×D3—61no—
362C23×D3—64no—
363C23×D3—64no—
364C23×D3—122no—
365C23×D3—122no—
366C23×D3—122no—
367C23×D3—122no—
368C23×D3C22×D311yescharacteristic
369C23×D3C22×D311yescharacteristic
370C2×C3×Q8—34no—
371C2×C3×Q8—122no—
372C2×C3×D4—34no—
373C2×C3×D4—34no—
374C2×C3×D4—64no—
375C2×C3×D4—122no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—34no—
385C22×C3×C4—34no—
386C22×C3×C4—122no—
387C22×C3×C4—122no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C2×#67—24no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—34no—
399C2×#67—42no—
400C2×#67—64no—
401C2×#67—64no—
402C2×#67—64no—
403C2×#67—122no—
404C2×#67—122no—
405C2×#67—122no—
406C2×#67—122no—
407C2×#67—122no—
408C2×#67—124no—
409C2×#67—124no—
410C2×#67C22×D314yes—
411C2×#67C22×D314yes—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—34no—
417C22×Dic3—42no—
418C22×Dic3—61no—
419C22×Dic3—61no—
420C22×Dic3—122no—
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425C22×Dic3C22×D311yescharacteristic
426C22×Dic3C22×D311yescharacteristic
427C22×Dic3C22×D314yescomplemented
428C2×D12—34no—
429C2×D12—34no—
430C2×D12—34no—
431C2×D12—34no—
432C2×D12—64no—
433C2×D12—64no—
434C2×D12—122no—
435C2×D12—122no—
436C2×D12—124no—
437C2×D12—122no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—42no—
442C2×C4×D3—64no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—124no—
446C2×C4×D3—122no—
447C2×C4×D3C22×D314yes—
448C2×Dic6—42no—
449C2×Dic6C22×D314yescomplemented
450C3×C4⋊C4—34no—
451C3×C22⋊C4—24no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4C22×D314yescomplemented
457C3×C22⋊C4C22×D314yescomplemented
458C3×C42—34no—
459C3×C42—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217C22×D314yescomplemented
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—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—64no—
480(C2×D3)⋊C4C22×D314yes—
481(C2×D3)⋊C4C22×D314yes—
482(C2×D3)⋊C4C22×D314yes—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—64no—
494Dic3⋊C4C22×D314yescomplemented
495C4×Dic3C22×D314yescomplemented
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—44no—
520C2×C3×D3C2×#4114yes—
521D32—416no—
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—91no—
533C22×Q8—31no—
534C22×D4—31no—
535C22×D4—31no—
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—98no—
546#126—98no—
547#124—38no—
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—38no—
558C4×D4—98no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—91no—
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—98no—
570C2×C22⋊C4—91no—
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, complemented
580C2×C42—31no—
581C2×C42—31no—
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—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3C23×D312yes—
602C23×C3C23×D312yes—
603C23×C3C23×D311yescharacteristic
604C23×C3C23×D311yescharacteristic
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—32no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—68no—
617C22×D3—64no—
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—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—68no—
631C22×D3—122no—
632C22×D3—122no—
633C22×D3—122no—
634C22×D3—122no—
635C22×D3—122no—
636C22×D3—124no—
637C22×D3—124no—
638C22×D3—124no—
639C22×D3—124no—
640C22×D3—1216no—
641C22×D3—1216no—
642C22×D3#23514yes—
643C22×D3C23×D312yes—
644C22×D3C23×D312yes—
645C3×Q8—124no—
646C3×D4—68no—
647C3×D4—124no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—42no—
661C2×C3×C4—42no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4—62no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—124no—
669C2×C3×C4—124no—
670C2×C3×C4C23×D312yes—
671C2×C3×C4C23×D312yes—
672C2×C3×C4C23×D312yes—
673C2×C3×C4C23×D312yes—
674#67—28no—
675#67—44no—
676#67—68no—
677#67—124no—
678#67—124no—
679#67—124no—
680#67—124no—
681#67—124no—
682#67—128no—
683#67—128no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—32no—
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—44no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—64no—
698C2×Dic3—62no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—62no—
702C2×Dic3—122no—
703C2×Dic3—124no—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710D12—68no—
711D12—124no—
712D12—124no—
713D12—128no—
714D12—124no—
715C4×D3—44no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—128no—
719C4×D3—124no—
720Dic6—44no—
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—94no—
733C24—91no—
734C24—91no—
735C24—184no—
736C24—362no—
737C24—362no—
738C24C2×D3211yescharacteristic
739C2×Q8—34no—
740C2×Q8—122no—
741C2×D4—34no—
742C2×D4—34no—
743C2×D4—64no—
744C2×D4—94no—
745C2×D4—94no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—94no—
749C2×D4—122no—
750C2×D4—184no—
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—94no—
775C4⋊C4—94no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—34no—
783C22⋊C4—94no—
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×D3214yescomplemented
793C42—34no—
794C42—34no—
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—124no—
819C22×C3C2×#23512yes—
820C22×C3#100412yes—
821C22×C3#100412yes—
822C22×C3D3×#4112yes—
823C22×C3#100912yes—
824C22×C3#100912yes—
825C22×C3C24×D311yescharacteristic
826C22×C3C24×D311yescharacteristic
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—28no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—44no—
834C2×D3—64no—
835C2×D3—62no—
836C2×D3—62no—
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—122no—
848C2×D3—122no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—122no—
852C2×D3—1216no—
853C2×D3—1216no—
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—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—92no—
898C23—92no—
899C23—188no—
900C23—182no—
901C23—182no—
902C23—182no—
903C23—182no—
904C23—182no—
905C23—182no—
906C23—364no—
907C23—364no—
908C23—3616no—
909C23C22×D3212yes—
910C23C22×D3211yescharacteristic
911Q8—124no—
912D4—68no—
913D4—124no—
914D4—188no—
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#556014yescomplemented
953C2×C3#567814yescomplemented
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—124no—
980C22—182no—
981C22—182no—
982C22—182no—
983C22—182no—
984C22—182no—
985C22—182no—
986C22—3616no—
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×#556011yescharacteristic, complemented
1005C3C2×#567811yescharacteristic, complemented
1006C2—42no—
1007C2—64no—
1008C2—122no—
1009C2—362no—
1010C2—362no—
1011C2#1059429814yesdirect 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×#885C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C2×#63983C2semidirect
5. C2×#63978C2semidirect
6. C2×#63971C2semidirect
7. C2×#63966C2semidirect
8. C2×#63923C2semidirect
9. C2×D3×(C2×D3)⋊C4C2semidirect
10. C2×C4×#626C2semidirect
11. C2×#63887C2semidirect
12. C2×#63868C2semidirect
13. C2×#63864C2semidirect
14. C2×#63859C2semidirect
15. C2×#63853C2semidirect
16. #10594298C2direct (N × H)
21. C22×#638C22semidirect
23. C22×C4×C3⋊D3C22semidirect
26. C23×C3×Dic3C22semidirect
28. C22×C3×Dic6C22semidirect
32. C2×C32×C22⋊C4C22semidirect
34. C2×#3750C22semidirect
35. #64093C22semidirect
36. C2×C3×#217C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×C4×Dic3C22semidirect
42. C2×C3×C4×Dic3C22semidirect
43. C3×#885C22semidirect
44. C3×#67⋊C4C22semidirect
45. #63983C22semidirect
46. #63978C22semidirect
47. #63971C22semidirect
48. C2×#3724C22semidirect
49. #63966C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
56. C2×#3722C22semidirect
57. C2×#3722C22semidirect
61. #63923C22semidirect
62. D3×(C2×D3)⋊C4C22semidirect
63. C4×#626C22semidirect
64. #63887C22semidirect
65. #63868C22semidirect
66. #63864C22semidirect
67. #63859C22semidirect
68. #63853C22semidirect
86. C2×#885D3semidirect
94. C2×#67⋊C4D3semidirect
116. C2×#638C23semidirect
122. C2×C4×C3⋊D3C23semidirect
134. C22×C3×Dic3C23semidirect
138. C2×C3×Dic6C23semidirect
145. C32×C22⋊C4C23semidirect
147. #3750C23semidirect
148. C3×#217C23semidirect
152. C3×Dic3⋊C4C23semidirect
153. C3×C4×Dic3C23semidirect
154. C3×C4×Dic3C23semidirect
155. #3724C23semidirect
156. Dic3⋊Dic3C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
162. #3722C23semidirect
163. #3722C23semidirect
186. C23×Dic3C2×D3semidirect
197. C22×Dic6C2×D3semidirect
206. C2×C3×C22⋊C4C2×D3semidirect
207. C2×C3×C22⋊C4C2×D3semidirect
213. C2×#217C2×D3semidirect
254. C2×Dic3⋊C4C2×D3semidirect
255. C2×C4×Dic3C2×D3semidirect
256. C2×C4×Dic3C2×D3semidirect
260. #885C2×D3semidirect
268. #67⋊C4C2×D3semidirect
427. C22×Dic3C22×D3semidirect
449. C2×Dic6C22×D3semidirect
456. C3×C22⋊C4C22×D3semidirect
457. C3×C22⋊C4C22×D3semidirect
463. #217C22×D3semidirect
494. Dic3⋊C4C22×D3semidirect
495. C4×Dic3C22×D3semidirect
496. C4×Dic3C22×D3semidirect
579. C2×C22⋊C4D32semidirect
722. C2×C32#538semidirect
792. C22⋊C4C2×D32semidirect
885. C32C2×#538semidirect
952. C2×C3#5560semidirect
953. C2×C3#5678semidirect
1004. C3C2×#5560semidirect
1005. C3C2×#5678semidirect
1011. C2#10594298direct (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×#8852
C2×C3×#67⋊C42
C2×#639832
C2×#639782
C2×#639712
C2×#639662
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×C4×#6262
C2×#638872
C2×#638682
C2×#638642
C2×#638592
C2×#638532
#105942982
C2×#56783
C2×#55603