Finite Group Databasebeta

← C2×#10594650 #11901350

Subgroups — C2×#10594650 #11901350

Order 1152.

2843 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64103C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C3×#894C211yesmaximal, characteristic, complemented
4C2×#63923C211yesmaximal, characteristic, complemented
5C2×#63922C211yesmaximal, characteristic, complemented
6C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63909C211yesmaximal, characteristic, complemented
9C2×#63907C211yesmaximal, characteristic, complemented
10C2×#63907C211yesmaximal, characteristic, complemented
11C2×#63906C211yesmaximal, characteristic, complemented
12C2×#63881C211yesmaximal, characteristic, complemented
13C2×#63879C211yesmaximal, characteristic, complemented
14C2×#63858C211yesmaximal, characteristic, complemented
15C2×#63848C211yesmaximal, characteristic, complemented
16#10594650C2116yesmaximal, direct product factor
17C2×#5657—31nomaximal
18C2×#5644—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×C3×Dic6C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic, complemented
30C22×#625C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic, complemented
36C2×#3750C2211yescharacteristic, complemented
37#64103C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C3×#897C2218yescomplemented
47C3×#894C2218yescomplemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic, complemented
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C2×Dic32C2211yescharacteristic, complemented
56C2×Dic32C2211yescharacteristic, complemented
57#63923C2218yescomplemented
58#63922C2218yescomplemented
59D3×(C2×D3)⋊C4C2218yescomplemented
60#63916C2218yescomplemented
61#63909C2218yescomplemented
62#63907C2218yescomplemented
63#63907C2218yescomplemented
64#63906C2218yescomplemented
65#63881C2218yescomplemented
66#63879C2218yescomplemented
67#63858C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#947—31no—
72C2×#947—31no—
73C2×#938—31no—
74C2×#937—31no—
75C2×#930—31no—
76C2×#930—31no—
77C2×C4×#67—31no—
78C22×(C2×D3)⋊C4—31no—
79#5657—316no—
80#5644—316no—
81C2×#898—31no—
82C2×#898—31no—
83C2×#898—31no—
84C2×#897D311yescharacteristic, complemented
85C2×#895—31no—
86C2×#895—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#894—61no—
90C2×#894D311yescharacteristic, complemented
91C2×#893—31no—
92C2×#885—31no—
93C2×#885—31no—
94C2×#884—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#67⋊C4—31no—
99C2×#67⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×#879—31no—
102C23×C3⋊D3C2311yescharacteristic
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
113C22×C32×C4C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C4⋊(C3⋊D3)—42no—
117C2×C4⋊(C3⋊D3)C2314yes—
118C2×C4×C3⋊D3—42no—
119C2×C4×C3⋊D3C2314yescomplemented
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×D12—42no—
126C2×C3×D12C2314yes—
127C2×C3×C4×D3—42no—
128C2×C3×C4×D3—42no—
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2314yescomplemented
131C2×C3×Dic6—42no—
132C2×C3×Dic6C2314yescomplemented
133C2×#626—24no—
134C2×#626—42no—
135C2×#626—42no—
136C2×#626—42no—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#626C2314yes—
140C2×#626C2314yescomplemented
141C2×#625—24no—
142C2×#625C2314yes—
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yes—
145C32×C4⋊C4C2314yescomplemented
146#3752C2314yes—
147#3752C2314yes—
148#3752C2314yescomplemented
149#3750C2314yescomplemented
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yescomplemented
155C3×C4⋊Dic3C2314yescomplemented
156C3×C4⋊Dic3C2314yescomplemented
157C3×Dic3⋊C4C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yescomplemented
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yescomplemented
165Dic32C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×Q8—31no—
171C22×C3×D4—31no—
172C23×C3×C4—31no—
173C23×C3×C4—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C23×Dic3—31no—
181C22×D12—31no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—61no—
188C22×D12C2×D311yescharacteristic
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—61no—
193C22×C4×D3C2×D311yescharacteristic
194C22×C4×D3C2×D311yescharacteristic, complemented
195C22×Dic6C2×D311yescharacteristic, complemented
196C3×#123—38no—
197C3×C22⋊Q8—38no—
198C2×C3×C4⋊C4—21no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
203C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—31no—
212#947—38no—
213#947—38no—
214#938—38no—
215#937—38no—
216#930—38no—
217#930—38no—
218C4×#67—38no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
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—38no—
235C2×(C2×D3)⋊C4—61no—
236C2×(C2×D3)⋊C4—61no—
237C2×(C2×D3)⋊C4—61no—
238C2×(C2×D3)⋊C4C2×D311yescharacteristic
239C2×(C2×D3)⋊C4C2×D311yescharacteristic
240C2×(C2×D3)⋊C4C2×D311yescharacteristic
241C2×(C2×D3)⋊C4C2×D311yescharacteristic
242C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3C2×D311yescharacteristic, complemented
245C2×C4⋊Dic3C2×D311yescharacteristic, complemented
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—61no—
250C2×Dic3⋊C4C2×D311yescharacteristic, complemented
251C2×C4×Dic3—31no—
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3—31no—
255#898—38no—
256#898—38no—
257#898—38no—
258#897C2×D318yescomplemented
259#895—38no—
260#895—38no—
261#894—38no—
262#894—38no—
263#894—68no—
264#894C2×D318yescomplemented
265#893—38no—
266#885—38no—
267#885—38no—
268#884—38no—
269#882—38no—
270#882—38no—
271#882—38no—
272#67⋊C4—38no—
273#67⋊C4—38no—
274D3×C22⋊C4—38no—
275#879—38no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3—22no—
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—22no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3C2412yes—
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#4114yes—
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—22no—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
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×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C3×D12—44no—
324C3×C4×D3—44no—
325C3×C4×D3—44no—
326C3×Dic6—44no—
327#626—28no—
328#626—44no—
329#626—44no—
330#626—44no—
331#625—28no—
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—31no—
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—91no—
349C24×C3—31no—
350C24×C3—31no—
351C24×C3—31no—
352C23×D3—31no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—34no—
357C23×D3—34no—
358C23×D3—61no—
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×Q8—34no—
370C2×C3×Q8—122no—
371C2×C3×D4—34no—
372C2×C3×D4—122no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—34no—
382C22×C3×C4—34no—
383C22×C3×C4—122no—
384C22×C3×C4—122no—
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—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—64no—
398C2×#67—64no—
399C2×#67—64no—
400C2×#67—122no—
401C2×#67—122no—
402C2×#67—122no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—31no—
406C22×Dic3—31no—
407C22×Dic3—34no—
408C22×Dic3—61no—
409C22×Dic3—61no—
410C22×Dic3—122no—
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C2×D12—34no—
417C2×D12—34no—
418C2×D12—34no—
419C2×D12—34no—
420C2×D12—34no—
421C2×D12—34no—
422C2×D12—42no—
423C2×D12—64no—
424C2×D12—64no—
425C2×D12—122no—
426C2×D12—122no—
427C2×D12—124no—
428C2×D12—122no—
429C2×D12—122no—
430C2×D12—122no—
431C2×D12C22×D314yes—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—42no—
436C2×C4×D3—42no—
437C2×C4×D3—64no—
438C2×C4×D3—122no—
439C2×C4×D3—122no—
440C2×C4×D3—122no—
441C2×C4×D3—124no—
442C2×C4×D3C22×D314yes—
443C2×C4×D3C22×D314yescomplemented
444C2×Dic6—42no—
445C2×Dic6C22×D314yescomplemented
446C3×C4⋊C4—24no—
447C3×C4⋊C4—34no—
448C3×C4⋊C4—34no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4C22×D314yescomplemented
451C3×C4⋊C4C22×D314yescomplemented
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457#217—34no—
458#217—34no—
459#217—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—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—64no—
476(C2×D3)⋊C4—64no—
477(C2×D3)⋊C4—64no—
478(C2×D3)⋊C4C22×D314yes—
479(C2×D3)⋊C4C22×D314yes—
480(C2×D3)⋊C4C22×D314yes—
481(C2×D3)⋊C4C22×D314yes—
482(C2×D3)⋊C4C22×D314yescomplemented
483C4⋊Dic3—34no—
484C4⋊Dic3C22×D314yescomplemented
485C4⋊Dic3C22×D314yescomplemented
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—64no—
490Dic3⋊C4C22×D314yescomplemented
491C4×Dic3—34no—
492C4×Dic3—34no—
493C4×Dic3—34no—
494C4×Dic3—34no—
495C22×C32C2×#4112yes—
496C22×C32H(5,𝔽2)12yes—
497C22×C32H(5,𝔽2)12yes—
498C22×C32C2511yescharacteristic
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—22no—
505C2×C3⋊D3—44no—
506C2×C3⋊D3—44no—
507C2×C3×D3—28no—
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—44no—
517C2×C3×D3—44no—
518C2×C3×D3C2×#4114yes—
519D32—416no—
520C32×C4—22no—
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—
530C25—91no—
531C22×Q8—31no—
532C22×D4—31no—
533C22×D4—91no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C23×C4—31no—
540C23×C4—31no—
541C23×C4—91no—
542C23×C4—91no—
543#126—98no—
544#126—98no—
545#124—98no—
546#124—98no—
547#123—38no—
548#123—98no—
549C22⋊Q8—38no—
550#121—98no—
551#121—98no—
552#121—98no—
553#120—98no—
554#120—98no—
555C4×D4—98no—
556C4×D4—98no—
557C2×C4⋊C4—31no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4D3211yescharacteristic, complemented
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—98no—
569C2×C22⋊C4—91no—
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×C42—91no—
579C2×C42—91no—
580C23×C3—21no—
581C23×C3—34no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—32no—
585C23×C3—62no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3—62no—
592C23×C3—62no—
593C23×C3C23×D311yescharacteristic
594C23×C3C23×D311yescharacteristic
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—32no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—32no—
607C22×D3—62no—
608C22×D3—62no—
609C22×D3—68no—
610C22×D3—64no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—62no—
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—68no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—124no—
630C22×D3—124no—
631C22×D3—124no—
632C22×D3—124no—
633C22×D3—1216no—
634C22×D3—1216no—
635C22×D3#23914yes—
636C22×D3C23×D312yes—
637C22×D3C23×D312yes—
638C22×D3C23×D312yes—
639C3×Q8—124no—
640C3×D4—124no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—42no—
656C2×C3×C4—42no—
657C2×C3×C4—42no—
658C2×C3×C4—62no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—124no—
664C2×C3×C4—124no—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669C2×C3×C4C23×D312yes—
670C2×C3×C4C23×D312yes—
671#67—68no—
672#67—68no—
673#67—68no—
674#67—124no—
675#67—124no—
676#67—124no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—122no—
693C2×Dic3—122no—
694C2×Dic3—124no—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700D12—44no—
701D12—68no—
702D12—124no—
703D12—124no—
704D12—128no—
705D12—124no—
706D12—124no—
707D12—124no—
708C4×D3—44no—
709C4×D3—44no—
710C4×D3—124no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—128no—
714Dic6—44no—
715C2×C32#53814yescomplemented
716C2×C32C22×#4111yescharacteristic
717C2×C32C2×H(5,𝔽2)11yescharacteristic
718C2×C32C2×H(5,𝔽2)11yescharacteristic
719C3⋊D3—42no—
720C3⋊D3—42no—
721C3×D3—24no—
722C3×D3—42no—
723C3×D3—42no—
724C24—31no—
725C24—31no—
726C24—31no—
727C24—94no—
728C24—91no—
729C24—91no—
730C24—184no—
731C24—362no—
732C24—362no—
733C2×Q8—34no—
734C2×Q8—122no—
735C2×D4—34no—
736C2×D4—94no—
737C2×D4—94no—
738C2×D4—94no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—94no—
742C2×D4—122no—
743C2×D4—184no—
744C2×D4—184no—
745C2×D4—362no—
746C2×D4—362no—
747C2×D4—362no—
748C2×D4—362no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—34no—
755C22×C4—34no—
756C22×C4—94no—
757C22×C4—91no—
758C22×C4—91no—
759C22×C4—94no—
760C22×C4—122no—
761C22×C4—122no—
762C22×C4—362no—
763C22×C4—362no—
764C22×C4C2×D3211yescharacteristic
765C22×C4C2×D3211yescharacteristic
766C22×C4C2×D3211yescharacteristic
767C4⋊C4—34no—
768C4⋊C4—34no—
769C4⋊C4—34no—
770C4⋊C4—94no—
771C4⋊C4—94no—
772C4⋊C4C2×D3214yescomplemented
773C22⋊C4—34no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C42—94no—
788C42—94no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—21no—
793C22×C3—34no—
794C22×C3—68no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—124no—
804C22×C3—124no—
805C22×C3#100412yes—
806C22×C3#100412yes—
807C22×C3C2×#23912yes—
808C22×C3D3×#4112yes—
809C22×C3#100912yes—
810C22×C3#100912yes—
811C22×C3C24×D311yescharacteristic
812C22×C3C24×D311yescharacteristic
813C2×D3—28no—
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—44no—
823C2×D3—44no—
824C2×D3—64no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—1216no—
843C2×D3—1216no—
844C2×D3—128no—
845C2×D3—124no—
846C2×D3—124no—
847C2×D3—124no—
848C2×D3—124no—
849C2×D3—244no—
850C2×D3C2×#23914yes—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—22no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—42no—
858C3×C4—42no—
859C3×C4—42no—
860C3×C4—62no—
861C3×C4—62no—
862C3×C4—62no—
863C3×C4—62no—
864C3×C4—62no—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—22no—
869Dic3—22no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—62no—
874Dic3—122no—
875Dic3—122no—
876C32C2×#53811yescharacteristic, complemented, Sylow
877C23—34no—
878C23—32no—
879C23—32no—
880C23—32no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—92no—
890C23—92no—
891C23—188no—
892C23—182no—
893C23—182no—
894C23—182no—
895C23—182no—
896C23—182no—
897C23—182no—
898C23—364no—
899C23—364no—
900C23—3616no—
901C23C22×D3211yescharacteristic
902Q8—124no—
903D4—124no—
904D4—188no—
905D4—188no—
906D4—364no—
907D4—364no—
908D4—364no—
909D4—364no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—32no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—92no—
924C2×C4—92no—
925C2×C4—124no—
926C2×C4—124no—
927C2×C4—182no—
928C2×C4—182no—
929C2×C4—364no—
930C2×C4—364no—
931C2×C4C22×D3212yes—
932C2×C4C22×D3212yes—
933C2×C4C22×D3212yes—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—24no—
938C2×C3—64no—
939C2×C3—122no—
940C2×C3—122no—
941C2×C3#564414yescomplemented
942C2×C3#565714yescomplemented
943C2×C3C2×#100411yescharacteristic
944C2×C3C2×#100411yescharacteristic
945C2×C3C22×#23911yescharacteristic
946C2×C3C2×D3×#4111yescharacteristic
947C2×C3C2×#100911yescharacteristic
948C2×C3C2×#100911yescharacteristic
949D3—24no—
950D3—42no—
951D3—42no—
952D3—124no—
953D3—122no—
954D3—122no—
955D3—122no—
956D3—122no—
957D3—242no—
958C22—34no—
959C22—62no—
960C22—62no—
961C22—68no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—124no—
969C22—124no—
970C22—182no—
971C22—182no—
972C22—182no—
973C22—182no—
974C22—182no—
975C22—182no—
976C22—3616no—
977C22—364no—
978C22—364no—
979C22#6430712yes—
980C22#6431412yes—
981C22D3×#23912yes—
982C22C23×D3211yescharacteristic
983C4—22no—
984C4—22no—
985C4—22no—
986C4—62no—
987C4—62no—
988C4—62no—
989C4—62no—
990C4—62no—
991C4—182no—
992C4—182no—
993C3—21no—
994C3C2×#564411yescharacteristic, complemented
995C3C2×#565711yescharacteristic, complemented
996C2—64no—
997C2—122no—
998C2—122no—
999C2—362no—
1000C2—362no—
1001C2#1059465014yesdirect product factor
1002C2C2×#6430711yescharacteristic
1003C2C2×#6431411yescharacteristic
1004C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64103C2semidirect
2. C2×C3×#897C2semidirect
3. C2×C3×#894C2semidirect
4. C2×#63923C2semidirect
5. C2×#63922C2semidirect
6. C2×D3×(C2×D3)⋊C4C2semidirect
7. C2×#63916C2semidirect
8. C2×#63909C2semidirect
9. C2×#63907C2semidirect
10. C2×#63907C2semidirect
11. C2×#63906C2semidirect
12. C2×#63881C2semidirect
13. C2×#63879C2semidirect
14. C2×#63858C2semidirect
15. C2×#63848C2semidirect
16. #10594650C2direct (N × H)
21. C22×C4×C3⋊D3C22semidirect
24. C22×C3×C4×D3C22semidirect
25. C22×C3×Dic6C22semidirect
29. C22×#626C22semidirect
32. C2×C32×C4⋊C4C22semidirect
35. C2×#3752C22semidirect
36. C2×#3750C22semidirect
37. #64103C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×C4⋊Dic3C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C3×#897C22semidirect
47. C3×#894C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
51. C2×#3722C22semidirect
54. C2×(C2×D3)⋊Dic3C22semidirect
55. C2×Dic32C22semidirect
56. C2×Dic32C22semidirect
57. #63923C22semidirect
58. #63922C22semidirect
59. D3×(C2×D3)⋊C4C22semidirect
60. #63916C22semidirect
61. #63909C22semidirect
62. #63907C22semidirect
63. #63907C22semidirect
64. #63906C22semidirect
65. #63881C22semidirect
66. #63879C22semidirect
67. #63858C22semidirect
68. #63848C22semidirect
84. C2×#897D3semidirect
90. C2×#894D3semidirect
119. C2×C4×C3⋊D3C23semidirect
130. C2×C3×C4×D3C23semidirect
132. C2×C3×Dic6C23semidirect
140. C2×#626C23semidirect
145. C32×C4⋊C4C23semidirect
148. #3752C23semidirect
149. #3750C23semidirect
154. C3×(C2×D3)⋊C4C23semidirect
155. C3×C4⋊Dic3C23semidirect
156. C3×C4⋊Dic3C23semidirect
157. C3×Dic3⋊C4C23semidirect
158. Dic3⋊Dic3C23semidirect
161. #3722C23semidirect
164. (C2×D3)⋊Dic3C23semidirect
165. Dic32C23semidirect
166. Dic32C23semidirect
194. C22×C4×D3C2×D3semidirect
195. C22×Dic6C2×D3semidirect
202. C2×C3×C4⋊C4C2×D3semidirect
203. C2×C3×C4⋊C4C2×D3semidirect
242. C2×(C2×D3)⋊C4C2×D3semidirect
244. C2×C4⋊Dic3C2×D3semidirect
245. C2×C4⋊Dic3C2×D3semidirect
250. C2×Dic3⋊C4C2×D3semidirect
258. #897C2×D3semidirect
264. #894C2×D3semidirect
443. C2×C4×D3C22×D3semidirect
445. C2×Dic6C22×D3semidirect
450. C3×C4⋊C4C22×D3semidirect
451. C3×C4⋊C4C22×D3semidirect
482. (C2×D3)⋊C4C22×D3semidirect
484. C4⋊Dic3C22×D3semidirect
485. C4⋊Dic3C22×D3semidirect
490. Dic3⋊C4C22×D3semidirect
562. C2×C4⋊C4D32semidirect
715. C2×C32#538semidirect
772. C4⋊C4C2×D32semidirect
876. C32C2×#538semidirect
941. C2×C3#5644semidirect
942. C2×C3#5657semidirect
994. C3C2×#5644semidirect
995. C3C2×#5657semidirect
1001. C2#10594650direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641032
C2×C3×#8972
C2×C3×#8942
C2×#639232
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639162
C2×#639092
C2×#639072
C2×#639062
C2×#638812
C2×#638792
C2×#638582
C2×#638482
#105946502
C2×#56573
C2×#56443