Finite Group Databasebeta

← C2×#10594232 #11901325

Subgroups — C2×#10594232 #11901325

Order 1152.

3003 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic, complemented
2C2×C3×#883C211yesmaximal, characteristic, complemented
3C2×C3×#879C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic, complemented
5C2×#63974C211yesmaximal, characteristic, complemented
6C2×#63958C211yesmaximal, characteristic, complemented
7C2×#63953C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×#63909C211yesmaximal, characteristic, complemented
10C2×#63904C211yesmaximal, characteristic, complemented
11C2×#63897C211yesmaximal, characteristic, complemented
12C2×#63895C211yesmaximal, characteristic, complemented
13C2×#63894C211yesmaximal, characteristic, complemented
14C2×#63852C211yesmaximal, characteristic, complemented
15C2×#63848C211yesmaximal, characteristic, complemented
16#10594232C2116yesmaximal, direct product factor
17C2×#5704—31nomaximal
18C2×#5657—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×#627C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic, complemented
29C22×#624C2211yescharacteristic
30C22×#624C2211yescharacteristic
31C22×#624C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35#64091C2218yescomplemented
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×C4×Dic3C2211yescharacteristic, complemented
46C3×#883C2218yescomplemented
47C3×#879C2218yescomplemented
48#63981C2218yescomplemented
49#63974C2218yescomplemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic, complemented
56C2×#3722C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
58#63958C2218yescomplemented
59C2×Dic32C2211yescharacteristic, complemented
60#63953C2218yescomplemented
61#63910C2218yescomplemented
62#63909C2218yescomplemented
63#63904C2218yescomplemented
64#63897C2218yescomplemented
65#63895C2218yescomplemented
66#63894C2218yescomplemented
67#63852C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#123—31no—
71C2×#938—31no—
72C2×#937—31no—
73C2×#930—31no—
74C2×C4×#67—31no—
75#5704—316no—
76#5657—316no—
77C2×#898—31no—
78C2×#898—31no—
79C2×#897—31no—
80C2×#896—31no—
81C2×#895—31no—
82C2×#895—31no—
83C2×#894—31no—
84C2×#894—31no—
85C2×#893—31no—
86C2×#893—31no—
87C2×#885—31no—
88C2×#885—31no—
89C2×#885—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#883D311yescharacteristic, complemented
93C2×#882—31no—
94C2×#882—31no—
95C2×#882—31no—
96C2×#882—61no—
97C2×D3×C22⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×#879D311yescharacteristic, complemented
100C2×#875—31no—
101C2×C4×D12—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3—24no—
104C23×C3⋊D3—42no—
105C23×C3⋊D3—42no—
106C23×C3⋊D3C2311yescharacteristic
107C23×C3⋊D3C2311yescharacteristic
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2314yes—
110C23×C3×D3C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C2×#638—42no—
114C2×#638C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C4⋊(C3⋊D3)—24no—
117C2×C4⋊(C3⋊D3)—42no—
118C2×C4⋊(C3⋊D3)C2314yes—
119C2×C4⋊(C3⋊D3)C2314yes—
120C2×C3×#67—42no—
121C2×C3×#67C2314yes—
122C22×C3×Dic3C2311yescharacteristic
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×D3C2314yescomplemented
131C2×#627—42no—
132C2×#627C2314yescomplemented
133C2×#626—24no—
134C2×#626—42no—
135C2×#626—42no—
136C2×#626C2314yes—
137C2×#626C2314yes—
138C2×#626C2314yescomplemented
139C2×#624—42no—
140C2×#624—42no—
141C2×#624—42no—
142C2×#624C2314yes—
143C2×#624C2314yes—
144C2×#624C2314yescomplemented
145C32×C22⋊C4C2314yes—
146#3752C2314yes—
147#3752C2314yes—
148C3×#217C2314yes—
149C3×#217C2314yes—
150C3×#217C2314yes—
151C3×(C2×D3)⋊C4C2314yescomplemented
152C3×C4⋊Dic3C2314yescomplemented
153C3×C4⋊Dic3C2314yescomplemented
154C3×Dic3⋊C4C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156C3×Dic3⋊C4C2314yescomplemented
157C3×C4×Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162#3722C2314yes—
163#3722C2314yescomplemented
164#3722C2314yescomplemented
165(C2×D3)⋊Dic3C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C24×D3—61no—
171C22×C3×D4—31no—
172C23×C3×C4—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—61no—
179C22×#67C2×D311yescharacteristic
180C22×D12—31no—
181C22×D12—31no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—61no—
188C22×D12—61no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3C2×D311yescharacteristic, complemented
196C22×Dic6—31no—
197C22×Dic6—31no—
198C3×#126—38no—
199C3×#123—38no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C4⋊C4—31no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C22⋊C4—21no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4—31no—
210C2×C3×C22⋊C4C2×D311yescharacteristic
211C2×C3×C22⋊C4C2×D311yescharacteristic
212C2×C3×C42—31no—
213C2×#217—31no—
214C2×#217C2×D311yescharacteristic
215C2×#217C2×D311yescharacteristic
216C2×#217C2×D311yescharacteristic
217#938—38no—
218#937—38no—
219#930—38no—
220C4×#67—38no—
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—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—61no—
239C2×(C2×D3)⋊C4—61no—
240C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
241C2×C4⋊Dic3—31no—
242C2×C4⋊Dic3C2×D311yescharacteristic, complemented
243C2×C4⋊Dic3C2×D311yescharacteristic, complemented
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4C2×D311yescharacteristic, complemented
246C2×Dic3⋊C4C2×D311yescharacteristic, complemented
247C2×Dic3⋊C4C2×D311yescharacteristic, complemented
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3C2×D311yescharacteristic, complemented
251#898—38no—
252#898—38no—
253#897—38no—
254#896—38no—
255#895—38no—
256#895—38no—
257#894—38no—
258#894—38no—
259#893—38no—
260#893—38no—
261#885—38no—
262#885—38no—
263#885—38no—
264#884—38no—
265#884—38no—
266#883C2×D318yescomplemented
267#882—38no—
268#882—38no—
269#882—38no—
270#882—68no—
271D3×C22⋊C4—38no—
272D3×C22⋊C4—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⋊D3—22no—
288C22×C3⋊D3—22no—
289C22×C3⋊D3—28no—
290C22×C3⋊D3—44no—
291C22×C3⋊D3—44no—
292C22×C3⋊D3—416no—
293C22×C3⋊D3#4114yes—
294C22×C3⋊D3C2412yes—
295C22×C3⋊D3C2412yes—
296C22×C3⋊D3C2412yes—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3C2412yes—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4C2412yes—
304C2×C32×C4C2412yes—
305#638—44no—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3C2412yes—
308C4⋊(C3⋊D3)—28no—
309C4⋊(C3⋊D3)—44no—
310C3×#67—44no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
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—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C3×C4×D3—44no—
326#627—44no—
327#626—28no—
328#626—44no—
329#626—44no—
330#624—44no—
331#624—44no—
332#624—44no—
333#538—916no—
334C2×#126—31no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—31no—
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—91no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3C22×D311yescharacteristic
352C24×C3C22×D311yescharacteristic
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—31no—
359C23×D3—34no—
360C23×D3—34no—
361C23×D3—61no—
362C23×D3—61no—
363C23×D3—64no—
364C23×D3—61no—
365C23×D3—64no—
366C23×D3—64no—
367C23×D3—124no—
368C23×D3—122no—
369C23×D3—122no—
370C23×D3—122no—
371C23×D3—122no—
372C23×D3—124no—
373C23×D3—124no—
374C23×D3C22×D311yescharacteristic
375C2×C3×D4—34no—
376C2×C3×D4—122no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—34no—
387C22×C3×C4—122no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—42no—
398C2×#67—64no—
399C2×#67—64no—
400C2×#67—122no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67—124no—
405C2×#67C22×D314yes—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—61no—
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
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—34no—
423C2×D12—64no—
424C2×D12—64no—
425C2×D12—64no—
426C2×D12—64no—
427C2×D12—64no—
428C2×D12—124no—
429C2×D12—122no—
430C2×D12—122no—
431C2×D12—124no—
432C2×D12—122no—
433C2×D12—122no—
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—42no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—122no—
446C2×C4×D3—122no—
447C2×C4×D3C22×D314yescomplemented
448C2×Dic6—34no—
449C2×Dic6—34no—
450C2×Dic6—122no—
451C2×Dic6—122no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—34no—
456C3×C4⋊C4—34no—
457C3×C22⋊C4—24no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4—34no—
460C3×C22⋊C4—34no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4C22×D314yes—
463C3×C22⋊C4C22×D314yes—
464C3×C42—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—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—64no—
487(C2×D3)⋊C4—64no—
488(C2×D3)⋊C4C22×D314yescomplemented
489C4⋊Dic3—34no—
490C4⋊Dic3C22×D314yescomplemented
491C4⋊Dic3C22×D314yescomplemented
492Dic3⋊C4—34no—
493Dic3⋊C4C22×D314yescomplemented
494Dic3⋊C4C22×D314yescomplemented
495Dic3⋊C4C22×D314yescomplemented
496C4×Dic3—34no—
497C4×Dic3—34no—
498C4×Dic3C22×D314yescomplemented
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—22no—
502C22×C32—44no—
503C22×C32C2×#4112yes—
504C22×C32H(5,𝔽2)12yes—
505C22×C32H(5,𝔽2)12yes—
506C22×C32C2511yescharacteristic
507C2×C3⋊D3—22no—
508C2×C3⋊D3—28no—
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—416no—
517C2×C3⋊D3—44no—
518C2×C3⋊D3—44no—
519C2×C3⋊D3C2×#4114yes—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—44no—
524C32×C4—22no—
525C32×C4—22no—
526C3⋊Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—22no—
534C25—91no—
535C22×Q8—91no—
536C22×D4—31no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4—91no—
541C22×D4—91no—
542C22×D4—91no—
543C23×C4—31no—
544C23×C4—91no—
545C23×C4—91no—
546C23×C4—91no—
547#126—38no—
548#126—98no—
549#124—98no—
550#124—98no—
551#123—38no—
552#123—98no—
553C22⋊Q8—98no—
554#121—98no—
555#121—98no—
556#121—98no—
557#120—98no—
558#120—98no—
559C4×D4—98no—
560C4×D4—98no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—31no—
566C2×C4⋊C4—91no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—98no—
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⋊C4—91no—
580C2×C22⋊C4—91no—
581C2×C22⋊C4D3211yescharacteristic
582C2×C42—31no—
583C2×C42—91no—
584C23×C3—24no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—21no—
593C23×C3—32no—
594C23×C3—42no—
595C23×C3—42no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3C23×D312yes—
600C23×C3C23×D312yes—
601C23×C3C23×D311yescharacteristic
602C23×C3C23×D311yescharacteristic
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—34no—
607C22×D3—34no—
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—32no—
614C22×D3—64no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—68no—
619C22×D3—68no—
620C22×D3—62no—
621C22×D3—62no—
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—128no—
638C22×D3—122no—
639C22×D3—122no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3—122no—
643C22×D3—122no—
644C22×D3—122no—
645C22×D3—124no—
646C22×D3—124no—
647C22×D3—124no—
648C22×D3—124no—
649C22×D3—128no—
650C22×D3—1216no—
651C22×D3—1216no—
652C22×D3—128no—
653C22×D3—1232no—
654C22×D3C23×D312yes—
655C3×D4—124no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—42no—
670C2×C3×C4—42no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4—62no—
674C2×C3×C4—62no—
675C2×C3×C4—62no—
676C2×C3×C4—62no—
677C2×C3×C4—62no—
678C2×C3×C4—124no—
679C2×C3×C4C23×D312yes—
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D312yes—
682C2×C3×C4C23×D312yes—
683#67—44no—
684#67—68no—
685#67—124no—
686#67—124no—
687#67—124no—
688#67—124no—
689#67—128no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—62no—
702C2×Dic3—122no—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710D12—68no—
711D12—68no—
712D12—68no—
713D12—128no—
714D12—124no—
715D12—124no—
716D12—128no—
717D12—124no—
718D12—124no—
719C4×D3—44no—
720C4×D3—124no—
721C4×D3—124no—
722C4×D3—124no—
723C4×D3—124no—
724C4×D3—124no—
725C4×D3—124no—
726Dic6—124no—
727Dic6—124no—
728C2×C32—42no—
729C2×C32#53814yescomplemented
730C2×C32C22×#4111yescharacteristic
731C2×C32C2×H(5,𝔽2)11yescharacteristic
732C2×C32C2×H(5,𝔽2)11yescharacteristic
733C3⋊D3—24no—
734C3⋊D3—42no—
735C3⋊D3—42no—
736C3×D3—42no—
737C24—31no—
738C24—91no—
739C24—91no—
740C24—91no—
741C24—94no—
742C24—184no—
743C24—362no—
744C24—362no—
745C24C2×D3211yescharacteristic
746C2×Q8—94no—
747C2×Q8—362no—
748C2×D4—34no—
749C2×D4—94no—
750C2×D4—94no—
751C2×D4—94no—
752C2×D4—94no—
753C2×D4—94no—
754C2×D4—94no—
755C2×D4—122no—
756C2×D4—184no—
757C2×D4—184no—
758C2×D4—362no—
759C2×D4—362no—
760C2×D4—362no—
761C2×D4—362no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—34no—
770C22×C4—94no—
771C22×C4—94no—
772C22×C4—94no—
773C22×C4—91no—
774C22×C4—122no—
775C22×C4—362no—
776C22×C4—362no—
777C22×C4—362no—
778C22×C4C2×D3211yescharacteristic
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—34no—
781C4⋊C4—34no—
782C4⋊C4—34no—
783C4⋊C4—34no—
784C4⋊C4—34no—
785C4⋊C4—94no—
786C22⋊C4—34no—
787C22⋊C4—34no—
788C22⋊C4—34no—
789C22⋊C4—34no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4—94no—
798C22⋊C4—94no—
799C22⋊C4C2×D3214yes—
800C42—34no—
801C42—94no—
802C22×C3—24no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—21no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—48no—
816C22×C3—44no—
817C22×C3—44no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—124no—
822C22×C3#100412yes—
823C22×C3D3×#4112yes—
824C22×C3D3×#4112yes—
825C22×C3#100912yes—
826C22×C3#100912yes—
827C22×C3#100912yes—
828C22×C3C24×D311yescharacteristic
829C22×C3C24×D311yescharacteristic
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—34no—
834C2×D3—34no—
835C2×D3—44no—
836C2×D3—64no—
837C2×D3—68no—
838C2×D3—62no—
839C2×D3—68no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—64no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—122no—
857C2×D3—122no—
858C2×D3—128no—
859C2×D3—122no—
860C2×D3—122no—
861C2×D3—122no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—1216no—
865C2×D3—1216no—
866C2×D3—128no—
867C2×D3—1232no—
868C2×D3—124no—
869C2×D3—124no—
870C2×D3—124no—
871C2×D3—124no—
872C2×D3—244no—
873C3×C4—22no—
874C3×C4—22no—
875C3×C4—22no—
876C3×C4—22no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—62no—
880C3×C4—62no—
881C3×C4—62no—
882C3×C4—62no—
883C3×C4—62no—
884C3×C4—62no—
885C3×C4—62no—
886Dic3—22no—
887Dic3—22no—
888Dic3—22no—
889Dic3—22no—
890Dic3—22no—
891Dic3—22no—
892Dic3—22no—
893Dic3—62no—
894Dic3—62no—
895Dic3—122no—
896C32C2×#53811yescharacteristic, complemented, Sylow
897C23—22no—
898C23—22no—
899C23—22no—
900C23—32no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—94no—
905C23—92no—
906C23—92no—
907C23—92no—
908C23—188no—
909C23—182no—
910C23—182no—
911C23—182no—
912C23—182no—
913C23—182no—
914C23—182no—
915C23—182no—
916C23—182no—
917C23—364no—
918C23—364no—
919C23—3616no—
920C23C22×D3212yes—
921C23C22×D3211yescharacteristic
922Q8—364no—
923D4—124no—
924D4—188no—
925D4—188no—
926D4—364no—
927D4—364no—
928D4—364no—
929D4—364no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—32no—
933C2×C4—32no—
934C2×C4—32no—
935C2×C4—32no—
936C2×C4—32no—
937C2×C4—32no—
938C2×C4—32no—
939C2×C4—62no—
940C2×C4—62no—
941C2×C4—62no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—62no—
945C2×C4—62no—
946C2×C4—92no—
947C2×C4—124no—
948C2×C4—182no—
949C2×C4—364no—
950C2×C4—364no—
951C2×C4—364no—
952C2×C4C22×D3212yes—
953C2×C4C22×D3212yes—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—24no—
958C2×C3—44no—
959C2×C3—42no—
960C2×C3—42no—
961C2×C3—122no—
962C2×C3#565714yescomplemented
963C2×C3#570414yescomplemented
964C2×C3C2×#100411yescharacteristic
965C2×C3C2×D3×#4111yescharacteristic
966C2×C3C2×D3×#4111yescharacteristic
967C2×C3C2×#100911yescharacteristic
968C2×C3C2×#100911yescharacteristic
969C2×C3C2×#100911yescharacteristic
970D3—42no—
971D3—64no—
972D3—64no—
973D3—124no—
974D3—124no—
975D3—122no—
976D3—122no—
977D3—122no—
978D3—122no—
979D3—242no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—44no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—94no—
988C22—124no—
989C22—182no—
990C22—182no—
991C22—188no—
992C22—182no—
993C22—182no—
994C22—182no—
995C22—182no—
996C22—182no—
997C22—182no—
998C22—3616no—
999C22—364no—
1000C22—364no—
1001C22#6430812yes—
1002C22#6431212yes—
1003C22#6431412yes—
1004C22C23×D3211yescharacteristic
1005C4—22no—
1006C4—22no—
1007C4—62no—
1008C4—62no—
1009C4—62no—
1010C4—62no—
1011C4—62no—
1012C4—62no—
1013C4—62no—
1014C4—182no—
1015C3—21no—
1016C3C2×#565711yescharacteristic, complemented
1017C3C2×#570411yescharacteristic, complemented
1018C2—42no—
1019C2—122no—
1020C2—184no—
1021C2—362no—
1022C2—362no—
1023C2#1059423214yesdirect product factor
1024C2C2×#6430811yescharacteristic
1025C2C2×#6431211yescharacteristic
1026C2C2×#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×#64091C2semidirect
2. C2×C3×#883C2semidirect
3. C2×C3×#879C2semidirect
4. C2×#63981C2semidirect
5. C2×#63974C2semidirect
6. C2×#63958C2semidirect
7. C2×#63953C2semidirect
8. C2×#63910C2semidirect
9. C2×#63909C2semidirect
10. C2×#63904C2semidirect
11. C2×#63897C2semidirect
12. C2×#63895C2semidirect
13. C2×#63894C2semidirect
14. C2×#63852C2semidirect
15. C2×#63848C2semidirect
16. #10594232C2direct (N × H)
24. C22×C3×C4×D3C22semidirect
25. C22×#627C22semidirect
28. C22×#626C22semidirect
31. C22×#624C22semidirect
35. #64091C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
41. C2×C3×C4⋊Dic3C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×C4×Dic3C22semidirect
46. C3×#883C22semidirect
47. C3×#879C22semidirect
48. #63981C22semidirect
49. #63974C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
55. C2×#3722C22semidirect
56. C2×#3722C22semidirect
57. C2×(C2×D3)⋊Dic3C22semidirect
58. #63958C22semidirect
59. C2×Dic32C22semidirect
60. #63953C22semidirect
61. #63910C22semidirect
62. #63909C22semidirect
63. #63904C22semidirect
64. #63897C22semidirect
65. #63895C22semidirect
66. #63894C22semidirect
67. #63852C22semidirect
68. #63848C22semidirect
92. C2×#883D3semidirect
99. C2×#879D3semidirect
130. C2×C3×C4×D3C23semidirect
132. C2×#627C23semidirect
138. C2×#626C23semidirect
144. C2×#624C23semidirect
151. C3×(C2×D3)⋊C4C23semidirect
152. C3×C4⋊Dic3C23semidirect
153. C3×C4⋊Dic3C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. C3×Dic3⋊C4C23semidirect
157. C3×C4×Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
163. #3722C23semidirect
164. #3722C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
195. C22×C4×D3C2×D3semidirect
240. C2×(C2×D3)⋊C4C2×D3semidirect
242. C2×C4⋊Dic3C2×D3semidirect
243. C2×C4⋊Dic3C2×D3semidirect
245. C2×Dic3⋊C4C2×D3semidirect
246. C2×Dic3⋊C4C2×D3semidirect
247. C2×Dic3⋊C4C2×D3semidirect
250. C2×C4×Dic3C2×D3semidirect
266. #883C2×D3semidirect
273. #879C2×D3semidirect
447. C2×C4×D3C22×D3semidirect
488. (C2×D3)⋊C4C22×D3semidirect
490. C4⋊Dic3C22×D3semidirect
491. C4⋊Dic3C22×D3semidirect
493. Dic3⋊C4C22×D3semidirect
494. Dic3⋊C4C22×D3semidirect
495. Dic3⋊C4C22×D3semidirect
498. C4×Dic3C22×D3semidirect
729. C2×C32#538semidirect
896. C32C2×#538semidirect
962. C2×C3#5657semidirect
963. C2×C3#5704semidirect
1016. C3C2×#5657semidirect
1017. C3C2×#5704semidirect
1023. C2#10594232direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640912
C2×C3×#8832
C2×C3×#8792
C2×#639812
C2×#639742
C2×#639582
C2×#639532
C2×#639102
C2×#639092
C2×#639042
C2×#638972
C2×#638952
C2×#638942
C2×#638522
C2×#638482
#105942322
C2×#57043
C2×#56573