Finite Group Databasebeta

← C2×#10595089 #11901301

Subgroups — C2×#10595089 #11901301

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic, complemented
3C2×C3×#929C211yesmaximal, characteristic, complemented
4C2×#63983C211yesmaximal, characteristic, complemented
5C2×#63970C211yesmaximal, characteristic, complemented
6C2×#63959C211yesmaximal, characteristic, complemented
7C2×#63958C211yesmaximal, characteristic, complemented
8#10595089C2116yesmaximal, direct product factor
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×#63921C211yesmaximal, characteristic, complemented
11C2×#63915C211yesmaximal, characteristic, complemented
12C2×#63895C211yesmaximal, characteristic, complemented
13C2×#63884C211yesmaximal, characteristic, complemented
14C2×#63881C211yesmaximal, characteristic, complemented
15C2×#63862C211yesmaximal, characteristic, complemented
16C2×#63858C211yesmaximal, characteristic, complemented
17C2×#5657—31nomaximal
18C2×#5613—31nomaximal
19C23×D32C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic, complemented
21C22×#638C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic
27C22×#627C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#624C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×#3757C2211yescharacteristic, complemented
33C4×#638C2218yescomplemented
34C2×#3752C2211yescharacteristic
35C2×#3750C2211yescharacteristic, complemented
36C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
37C2×C3×#217C2211yescharacteristic, complemented
38C3×#930C2218yescomplemented
39C3×#929C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47#63983C2218yescomplemented
48#63970C2218yescomplemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
58#63959C2218yescomplemented
59#63958C2218yescomplemented
60C2×Dic32C2211yescharacteristic, complemented
61#63922C2218yescomplemented
62#63921C2218yescomplemented
63#63915C2218yescomplemented
64#63895C2218yescomplemented
65#63884C2218yescomplemented
66#63881C2218yescomplemented
67#63862C2218yescomplemented
68#63858C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#121—31no—
71C2×#939—31no—
72C2×#938—31no—
73C2×#938—31no—
74C2×#937—31no—
75C2×#937—31no—
76C2×#937—31no—
77C2×#936—31no—
78C2×#935—31no—
79C2×#930D311yescharacteristic, complemented
80C2×#929D311yescharacteristic, complemented
81C2×C4×#67—31no—
82C2×C4×#67—31no—
83C2×C4×#67—61no—
84#5657—316no—
85#5613—316no—
86C2×#898—31no—
87C2×#898—31no—
88C2×#897—31no—
89C2×#896—31no—
90C2×#894—31no—
91C2×#893—31no—
92C2×#885—31no—
93C2×#885—31no—
94C2×#885—31no—
95C2×#884—31no—
96C2×#882—31no—
97C2×#67⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×#879—31no—
101C2×#879—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×C4—42no—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2314yescomplemented
115C2×#638—24no—
116C2×#638C2314yes—
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2311yescharacteristic
120C2×C4×C3⋊D3—42no—
121C2×C4×C3⋊D3C2314yes—
122C2×C3×#67—42no—
123C2×C3×#67—42no—
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yescomplemented
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C2×C3×D12—42no—
134C2×C3×D12C2314yes—
135C2×#627—42no—
136C2×#627C2314yescomplemented
137C2×#626—24no—
138C2×#626C2314yes—
139C2×#625—42no—
140C2×#625C2314yes—
141C2×#624—42no—
142C2×#624C2314yes—
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yescomplemented
145#3757C2314yescomplemented
146#3752C2314yes—
147#3750C2314yescomplemented
148C4×C3⋊Dic3C2314yescomplemented
149C3×#217C2314yescomplemented
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yescomplemented
154C3×C4⋊Dic3C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156C3×Dic3⋊C4C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C23×C3×C4—21no—
175C23×C3×C4C2×D311yescharacteristic, complemented
176C23×C3×C4C2×D311yescharacteristic, complemented
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—61no—
183C22×#67C2×D311yescharacteristic
184C22×#67C2×D311yescharacteristic
185C22×#67C2×D311yescharacteristic, complemented
186C23×Dic3—31no—
187C22×D12—31no—
188C22×D12C2×D311yescharacteristic
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—61no—
195C22×Dic6—31no—
196C22×Dic6—31no—
197C3×#123—38no—
198C3×#121—38no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—61no—
216C2×#217C2×D311yescharacteristic, complemented
217#939—38no—
218#938—38no—
219#938—38no—
220#937—38no—
221#937—38no—
222#937—38no—
223#936—38no—
224#935—38no—
225#930C2×D318yescomplemented
226#929C2×D318yescomplemented
227C4×#67—38no—
228C4×#67—38no—
229C4×#67—68no—
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—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—61no—
241C2×(C2×D3)⋊C4C2×D311yescharacteristic
242C2×(C2×D3)⋊C4C2×D311yescharacteristic
243C2×(C2×D3)⋊C4C2×D311yescharacteristic
244C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
245C2×C4⋊Dic3—31no—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3C2×D311yescharacteristic, complemented
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—61no—
253C2×Dic3⋊C4C2×D311yescharacteristic, complemented
254C2×Dic3⋊C4C2×D311yescharacteristic, complemented
255C2×C4×Dic3—31no—
256C2×C4×Dic3—31no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3—31no—
259C2×C4×Dic3—61no—
260#898—38no—
261#898—38no—
262#897—38no—
263#896—38no—
264#894—38no—
265#893—38no—
266#885—38no—
267#885—38no—
268#885—38no—
269#884—38no—
270#882—38no—
271#67⋊C4—38no—
272D3×C22⋊C4—38no—
273D3×C22⋊C4—38no—
274#879—38no—
275#879—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#4114yes—
284C22×C3⋊D3C2412yes—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3C2412yes—
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×C4—44no—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306#638—28no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C4×C3⋊D3—44no—
314C3×#67—44no—
315C3×#67—44no—
316C3×#67—44no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C3×D12—44no—
328#627—44no—
329#626—28no—
330#625—44no—
331#624—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—91no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—31no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—31no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—91no—
345C2×#120—91no—
346C2×C4×D4—91no—
347C2×C4×D4—91no—
348C22×C22⋊C4—91no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3—31no—
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—34no—
358C23×D3—34no—
359C23×D3—61no—
360C23×D3—64no—
361C23×D3—64no—
362C23×D3—122no—
363C23×D3—122no—
364C23×D3—122no—
365C23×D3—122no—
366C23×D3C22×D311yescharacteristic
367C23×D3C22×D311yescharacteristic
368C23×D3C22×D311yescharacteristic
369C2×C3×D4—34no—
370C2×C3×D4—34no—
371C2×C3×D4—34no—
372C2×C3×D4—34no—
373C2×C3×D4—122no—
374C2×C3×D4—122no—
375C2×C3×D4—122no—
376C2×C3×D4—122no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—24no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—42no—
386C22×C3×C4—42no—
387C22×C3×C4—44no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D314yescomplemented
393C22×C3×C4C22×D314yescomplemented
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—34no—
399C2×#67—42no—
400C2×#67—42no—
401C2×#67—42no—
402C2×#67—64no—
403C2×#67—64no—
404C2×#67—64no—
405C2×#67—64no—
406C2×#67—68no—
407C2×#67—122no—
408C2×#67—122no—
409C2×#67C22×D314yes—
410C2×#67C22×D314yes—
411C2×#67C22×D314yescomplemented
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—31no—
417C22×Dic3—31no—
418C22×Dic3—34no—
419C22×Dic3—61no—
420C22×Dic3—61no—
421C22×Dic3—61no—
422C22×Dic3—122no—
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425C22×Dic3C22×D311yescharacteristic
426C22×Dic3C22×D311yescharacteristic
427C22×Dic3C22×D311yescharacteristic
428C2×D12—34no—
429C2×D12—42no—
430C2×D12—64no—
431C2×D12C22×D314yes—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—64no—
438C2×C4×D3—122no—
439C2×C4×D3—122no—
440C2×C4×D3—122no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—124no—
444C2×Dic6—34no—
445C2×Dic6—34no—
446C2×Dic6—122no—
447C2×Dic6—122no—
448C3×C4⋊C4—34no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456#217—34no—
457#217—34no—
458#217—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—64no—
465#217C22×D314yescomplemented
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—64no—
477(C2×D3)⋊C4C22×D314yes—
478(C2×D3)⋊C4C22×D314yes—
479(C2×D3)⋊C4C22×D314yes—
480(C2×D3)⋊C4C22×D314yescomplemented
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3C22×D314yescomplemented
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—64no—
489Dic3⋊C4C22×D314yescomplemented
490Dic3⋊C4C22×D314yescomplemented
491C4×Dic3—34no—
492C4×Dic3—34no—
493C4×Dic3—34no—
494C4×Dic3—34no—
495C4×Dic3—64no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—44no—
500C22×C32C2×#4112yes—
501C22×C32H(5,𝔽2)12yes—
502C22×C32H(5,𝔽2)12yes—
503C22×C32C2511yescharacteristic
504C2×C3⋊D3—28no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3C2×#4114yes—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—44no—
518C2×C3×D3—44no—
519C2×C3×D3—44no—
520D32—416no—
521C32×C4—22no—
522C32×C4—22no—
523C3⋊Dic3—22no—
524C3⋊Dic3—22no—
525C3⋊Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C25—91no—
532C22×Q8—91no—
533C22×D4—31no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—31no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C23×C4—91no—
541C23×C4—91no—
542C23×C4—91no—
543C23×C4D3211yescharacteristic, complemented
544#126—98no—
545#126—98no—
546#124—98no—
547#124—98no—
548#123—38no—
549#123—98no—
550C22⋊Q8—98no—
551#121—38no—
552#121—98no—
553#121—98no—
554#120—98no—
555#120—98no—
556C4×D4—98no—
557C4×D4—98no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C22⋊C4—31no—
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×C42—91no—
580C2×C42—91no—
581C23×C3—24no—
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—32no—
591C23×C3—32no—
592C23×C3—32no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—62no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3—62no—
602C23×C3—62no—
603C23×C3—62no—
604C23×C3C23×D312yes—
605C23×C3C23×D312yes—
606C23×C3C23×D311yescharacteristic
607C23×C3C23×D311yescharacteristic
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—34no—
618C22×D3—34no—
619C22×D3—32no—
620C22×D3—32no—
621C22×D3—64no—
622C22×D3—62no—
623C22×D3—68no—
624C22×D3—68no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3—124no—
632C22×D3—124no—
633C22×D3—124no—
634C22×D3—124no—
635C22×D3—1216no—
636C22×D3—1216no—
637C22×D3C23×D312yes—
638C22×D3C23×D312yes—
639C22×D3C23×D312yes—
640C3×D4—124no—
641C3×D4—124no—
642C3×D4—124no—
643C3×D4—124no—
644C2×C3×C4—24no—
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—42no—
657C2×C3×C4—44no—
658C2×C3×C4—44no—
659C2×C3×C4—48no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669#67—44no—
670#67—44no—
671#67—44no—
672#67—68no—
673#67—68no—
674#67—68no—
675#67—616no—
676#67—124no—
677#67—124no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—64no—
693C2×Dic3—62no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—122no—
700C2×Dic3—122no—
701C2×Dic3—124no—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707D12—44no—
708D12—68no—
709C4×D3—124no—
710C4×D3—124no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—128no—
715Dic6—124no—
716Dic6—124no—
717C2×C32—42no—
718C2×C32#53814yescomplemented
719C2×C32C22×#4111yescharacteristic
720C2×C32C2×H(5,𝔽2)11yescharacteristic
721C2×C32C2×H(5,𝔽2)11yescharacteristic
722C3⋊D3—24no—
723C3×D3—42no—
724C3×D3—42no—
725C3×D3—42no—
726C24—31no—
727C24—31no—
728C24—31no—
729C24—94no—
730C24—91no—
731C24—184no—
732C24—362no—
733C24—362no—
734C24C2×D3211yescharacteristic
735C2×Q8—94no—
736C2×Q8—362no—
737C2×D4—34no—
738C2×D4—34no—
739C2×D4—34no—
740C2×D4—34no—
741C2×D4—94no—
742C2×D4—94no—
743C2×D4—94no—
744C2×D4—122no—
745C2×D4—122no—
746C2×D4—122no—
747C2×D4—122no—
748C2×D4—184no—
749C2×D4—184no—
750C2×D4—362no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—42no—
757C22×C4—94no—
758C22×C4—94no—
759C22×C4—91no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—94no—
763C22×C4—362no—
764C22×C4—362no—
765C22×C4—362no—
766C22×C4C2×D3211yescharacteristic
767C22×C4C2×D3211yescharacteristic
768C22×C4C2×D3214yescomplemented
769C4⋊C4—34no—
770C4⋊C4—34no—
771C4⋊C4—34no—
772C4⋊C4—94no—
773C4⋊C4—94no—
774C4⋊C4—94no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—34no—
779C22⋊C4—34no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C42—94no—
790C42—94no—
791C22×C3—24no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—21no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—48no—
805C22×C3—44no—
806C22×C3—44no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—124no—
817C22×C3—124no—
818C22×C3—124no—
819C22×C3#100412yes—
820C22×C3#100412yes—
821C22×C3#100412yes—
822C22×C3D3×#4112yes—
823C22×C3D3×#4112yes—
824C22×C3#100912yes—
825C22×C3C24×D311yescharacteristic
826C22×C3C24×D311yescharacteristic
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—34no—
837C2×D3—34no—
838C2×D3—44no—
839C2×D3—44no—
840C2×D3—44no—
841C2×D3—64no—
842C2×D3—68no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—68no—
848C2×D3—122no—
849C2×D3—128no—
850C2×D3—122no—
851C2×D3—1216no—
852C2×D3—1216no—
853C3×C4—24no—
854C3×C4—22no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—42no—
859C3×C4—62no—
860C3×C4—62no—
861C3×C4—62no—
862C3×C4—62no—
863C3×C4—62no—
864Dic3—22no—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—22no—
869Dic3—64no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—62no—
874Dic3—62no—
875Dic3—62no—
876Dic3—122no—
877Dic3—122no—
878C32C2×#53811yescharacteristic, complemented, Sylow
879C23—22no—
880C23—22no—
881C23—22no—
882C23—32no—
883C23—32no—
884C23—32no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—94no—
895C23—92no—
896C23—188no—
897C23—182no—
898C23—182no—
899C23—364no—
900C23—364no—
901C23—3616no—
902C23C22×D3212yes—
903C23C22×D3211yescharacteristic
904Q8—364no—
905D4—124no—
906D4—124no—
907D4—124no—
908D4—124no—
909D4—188no—
910D4—188no—
911D4—364no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—32no—
919C2×C4—44no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—92no—
926C2×C4—92no—
927C2×C4—92no—
928C2×C4—182no—
929C2×C4—182no—
930C2×C4—182no—
931C2×C4—364no—
932C2×C4—364no—
933C2×C4—364no—
934C2×C4C22×D3212yes—
935C2×C4C22×D3212yes—
936C2×C3—24no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—44no—
941C2×C3—42no—
942C2×C3—42no—
943C2×C3—122no—
944C2×C3—122no—
945C2×C3—122no—
946C2×C3#561314yescomplemented
947C2×C3#565714yescomplemented
948C2×C3C2×#100411yescharacteristic
949C2×C3C2×#100411yescharacteristic
950C2×C3C2×#100411yescharacteristic
951C2×C3C2×D3×#4111yescharacteristic
952C2×C3C2×D3×#4111yescharacteristic
953C2×C3C2×#100911yescharacteristic
954D3—42no—
955D3—42no—
956D3—42no—
957D3—64no—
958D3—64no—
959D3—124no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—44no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—62no—
970C22—62no—
971C22—62no—
972C22—62no—
973C22—94no—
974C22—124no—
975C22—124no—
976C22—124no—
977C22—188no—
978C22—182no—
979C22—182no—
980C22—3616no—
981C22#6430612yes—
982C22#6430712yes—
983C22#6433012yes—
984C22C23×D3211yescharacteristic
985C4—22no—
986C4—22no—
987C4—62no—
988C4—62no—
989C4—62no—
990C4—62no—
991C4—62no—
992C4—182no—
993C4—182no—
994C4—182no—
995C3—21no—
996C3C2×#561311yescharacteristic, complemented
997C3C2×#565711yescharacteristic, complemented
998C2—42no—
999C2—122no—
1000C2—122no—
1001C2—122no—
1002C2—184no—
1003C2#1059508914yesdirect product factor
1004C2C2×#6430611yescharacteristic
1005C2C2×#6430711yescharacteristic
1006C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C2×C3×#930C2semidirect
3. C2×C3×#929C2semidirect
4. C2×#63983C2semidirect
5. C2×#63970C2semidirect
6. C2×#63959C2semidirect
7. C2×#63958C2semidirect
8. #10595089C2direct (N × H)
9. C2×#63922C2semidirect
10. C2×#63921C2semidirect
11. C2×#63915C2semidirect
12. C2×#63895C2semidirect
13. C2×#63884C2semidirect
14. C2×#63881C2semidirect
15. C2×#63862C2semidirect
16. C2×#63858C2semidirect
20. C23×C32×C4C22semidirect
25. C22×C3×#67C22semidirect
27. C22×#627C22semidirect
31. C22×D3×Dic3C22semidirect
32. C2×#3757C22semidirect
33. C4×#638C22semidirect
35. C2×#3750C22semidirect
36. C2×C4×C3⋊Dic3C22semidirect
37. C2×C3×#217C22semidirect
38. C3×#930C22semidirect
39. C3×#929C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×C4⋊Dic3C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. #63983C22semidirect
48. #63970C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
57. C2×(C2×D3)⋊Dic3C22semidirect
58. #63959C22semidirect
59. #63958C22semidirect
60. C2×Dic32C22semidirect
61. #63922C22semidirect
62. #63921C22semidirect
63. #63915C22semidirect
64. #63895C22semidirect
65. #63884C22semidirect
66. #63881C22semidirect
67. #63862C22semidirect
68. #63858C22semidirect
79. C2×#930D3semidirect
80. C2×#929D3semidirect
114. C22×C32×C4C23semidirect
127. C2×C3×#67C23semidirect
136. C2×#627C23semidirect
144. C2×D3×Dic3C23semidirect
145. #3757C23semidirect
147. #3750C23semidirect
148. C4×C3⋊Dic3C23semidirect
149. C3×#217C23semidirect
153. C3×(C2×D3)⋊C4C23semidirect
154. C3×C4⋊Dic3C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. C3×Dic3⋊C4C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
175. C23×C3×C4C2×D3semidirect
176. C23×C3×C4C2×D3semidirect
185. C22×#67C2×D3semidirect
216. C2×#217C2×D3semidirect
225. #930C2×D3semidirect
226. #929C2×D3semidirect
244. C2×(C2×D3)⋊C4C2×D3semidirect
247. C2×C4⋊Dic3C2×D3semidirect
253. C2×Dic3⋊C4C2×D3semidirect
254. C2×Dic3⋊C4C2×D3semidirect
392. C22×C3×C4C22×D3semidirect
393. C22×C3×C4C22×D3semidirect
411. C2×#67C22×D3semidirect
465. #217C22×D3semidirect
480. (C2×D3)⋊C4C22×D3semidirect
483. C4⋊Dic3C22×D3semidirect
489. Dic3⋊C4C22×D3semidirect
490. Dic3⋊C4C22×D3semidirect
543. C23×C4D32semidirect
718. C2×C32#538semidirect
768. C22×C4C2×D32semidirect
878. C32C2×#538semidirect
946. C2×C3#5613semidirect
947. C2×C3#5657semidirect
996. C3C2×#5613semidirect
997. C3C2×#5657semidirect
1003. C2#10595089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×#9302
C2×C3×#9292
C2×#639832
C2×#639702
C2×#639592
C2×#639582
#105950892
C2×#639222
C2×#639212
C2×#639152
C2×#638952
C2×#638842
C2×#638812
C2×#638622
C2×#638582
C2×#56573
C2×#56133