Finite Group Databasebeta

← C2×#10594639 #11901303

Subgroups — C2×#10594639 #11901303

Order 1152.

2795 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64107C211yesmaximal, characteristic, complemented
2C2×C3×#894C211yesmaximal, characteristic, complemented
3C2×C3×#893C211yesmaximal, characteristic, complemented
4C2×#63922C211yesmaximal, characteristic, complemented
5C2×#63922C211yesmaximal, characteristic, complemented
6C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×#63915C211yesmaximal, characteristic, complemented
8C2×#63908C211yesmaximal, characteristic, complemented
9C2×#63906C211yesmaximal, characteristic, complemented
10C2×C4×#625C211yesmaximal, characteristic, complemented
11C2×#63893C211yesmaximal, characteristic, complemented
12C2×#63885C211yesmaximal, characteristic, complemented
13C2×#63859C211yesmaximal, characteristic, complemented
14C2×#63852C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594639C2116yesmaximal, direct product factor
17C2×#5657—31nomaximal
18C2×#5560—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic, complemented
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×#627C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37C2×#3750C2211yescharacteristic, complemented
38C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
39#64107C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47C3×#894C2218yescomplemented
48C3×#893C2218yescomplemented
49C2×#3724C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57#63922C2218yescomplemented
58#63922C2218yescomplemented
59D3×(C2×D3)⋊C4C2218yescomplemented
60#63915C2218yescomplemented
61#63908C2218yescomplemented
62#63906C2218yescomplemented
63C4×#625C2218yescomplemented
64#63893C2218yescomplemented
65#63885C2218yescomplemented
66#63859C2218yescomplemented
67#63852C2218yescomplemented
68#63850C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#938—31no—
73C2×#937—31no—
74C2×#937—31no—
75C2×#930—31no—
76C2×#930—31no—
77C2×#929—31no—
78C2×C4×#67—31no—
79C2×C4×#67—31no—
80C22×(C2×D3)⋊C4—31no—
81#5657—316no—
82#5560—316no—
83C2×#898—31no—
84C2×#898—31no—
85C2×#898—61no—
86C2×#897—31no—
87C2×#894—31no—
88C2×#894D311yescharacteristic, complemented
89C2×#893D311yescharacteristic, complemented
90C2×#885—31no—
91C2×#885—31no—
92C2×#885—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×D3×C22⋊C4—31no—
98C2×#879—31no—
99C2×#878—31no—
100C2×#876—31no—
101C2×#875—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
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×D12—24no—
122C2×C3×D12—42no—
123C2×C3×D12C2314yes—
124C2×C3×D12C2314yes—
125C2×C3×C4×D3—42no—
126C2×C3×C4×D3—42no—
127C2×C3×C4×D3—42no—
128C2×C3×C4×D3C2314yes—
129C2×C3×C4×D3C2314yescomplemented
130C2×C3×C4×D3C2314yescomplemented
131C2×#627—42no—
132C2×#627C2314yescomplemented
133C2×#626—42no—
134C2×#626—42no—
135C2×#626C2314yes—
136C2×#626C2314yes—
137C2×#625—24no—
138C2×#625—42no—
139C2×#625—42no—
140C2×#625C2314yes—
141C2×#625C2314yes—
142C2×#625C2314yescomplemented
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yes—
145C32×C4⋊C4C2314yescomplemented
146#3752C2314yes—
147#3752C2314yes—
148#3752C2314yes—
149C4⋊(C3⋊Dic3)C2314yescomplemented
150#3750C2314yescomplemented
151C4×C3⋊Dic3C2314yescomplemented
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yescomplemented
156C3×(C2×D3)⋊C4C2314yescomplemented
157C3×Dic3⋊C4C2314yescomplemented
158C3×C4×Dic3C2314yescomplemented
159#3724C2314yescomplemented
160Dic3⋊Dic3C2314yescomplemented
161#3722C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yescomplemented
166(C2×D3)⋊Dic3C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C23×C3×C4—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—31no—
182C22×#67—31no—
183C23×Dic3—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12C2×D311yescharacteristic
187C22×D12C2×D311yescharacteristic
188C22×C4×D3—31no—
189C22×C4×D3C2×D311yescharacteristic
190C22×C4×D3C2×D311yescharacteristic, complemented
191C22×C4×D3C2×D311yescharacteristic, complemented
192C22×Dic6—31no—
193C22×Dic6—31no—
194C3×#123—38no—
195C3×C4×D4—38no—
196C2×C3×C4⋊C4—21no—
197C2×C3×C4⋊C4—31no—
198C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
199C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C42—31no—
206C2×#217—31no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—31no—
211#939—38no—
212#938—38no—
213#937—38no—
214#937—38no—
215#930—38no—
216#930—38no—
217#929—38no—
218C4×#67—38no—
219C4×#67—38no—
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—38no—
234C2×(C2×D3)⋊C4—61no—
235C2×(C2×D3)⋊C4—61no—
236C2×(C2×D3)⋊C4—61no—
237C2×(C2×D3)⋊C4C2×D311yescharacteristic
238C2×(C2×D3)⋊C4C2×D311yescharacteristic
239C2×(C2×D3)⋊C4C2×D311yescharacteristic
240C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
241C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3—61no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—61no—
252C2×Dic3⋊C4C2×D311yescharacteristic, complemented
253C2×C4×Dic3—31no—
254C2×C4×Dic3—31no—
255C2×C4×Dic3—61no—
256C2×C4×Dic3C2×D311yescharacteristic, complemented
257#898—38no—
258#898—38no—
259#898—68no—
260#897—38no—
261#894—38no—
262#894C2×D318yescomplemented
263#893C2×D318yescomplemented
264#885—38no—
265#885—38no—
266#885—38no—
267#884—38no—
268#884—38no—
269#882—38no—
270#882—38no—
271D3×C22⋊C4—38no—
272#879—38no—
273#878—38no—
274#876—38no—
275#875—38no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3—22no—
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3C2412yes—
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—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3#4114yes—
293C22×C3×D3C2412yes—
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⋊Dic3—22no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C3×D12—28no—
322C3×D12—44no—
323C3×C4×D3—44no—
324C3×C4×D3—44no—
325C3×C4×D3—44no—
326#627—44no—
327#626—44no—
328#626—44no—
329#625—28no—
330#625—44no—
331#625—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—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—31no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3—31no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—34no—
356C23×D3—34no—
357C23×D3—61no—
358C23×D3—64no—
359C23×D3—64no—
360C23×D3—122no—
361C23×D3—122no—
362C23×D3—122no—
363C23×D3—122no—
364C23×D3C22×D311yescharacteristic
365C23×D3C22×D311yescharacteristic
366C23×D3C22×D311yescharacteristic
367C23×D3C22×D311yescharacteristic
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—64no—
371C2×C3×D4—122no—
372C22×C3×C4—21no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—34no—
380C22×C3×C4—34no—
381C22×C3×C4—34no—
382C22×C3×C4—122no—
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—34no—
398C2×#67—34no—
399C2×#67—64no—
400C2×#67—64no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67—122no—
405C2×#67—122no—
406C2×#67—122no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—34no—
414C22×Dic3—61no—
415C22×Dic3—61no—
416C22×Dic3—61no—
417C22×Dic3—122no—
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C2×D12—24no—
423C2×D12—34no—
424C2×D12—34no—
425C2×D12—42no—
426C2×D12—122no—
427C2×D12—122no—
428C2×D12C22×D314yes—
429C2×D12C22×D314yes—
430C2×C4×D3—34no—
431C2×C4×D3—42no—
432C2×C4×D3—42no—
433C2×C4×D3—42no—
434C2×C4×D3—122no—
435C2×C4×D3C22×D314yes—
436C2×C4×D3C22×D314yescomplemented
437C2×C4×D3C22×D314yescomplemented
438C2×Dic6—34no—
439C2×Dic6—34no—
440C2×Dic6—122no—
441C2×Dic6—122no—
442C3×C4⋊C4—24no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4C22×D314yescomplemented
445C3×C4⋊C4C22×D314yescomplemented
446C3×C22⋊C4—34no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C42—34no—
452#217—34no—
453#217—34no—
454#217—34no—
455#217—34no—
456#217—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—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—64no—
471(C2×D3)⋊C4—64no—
472(C2×D3)⋊C4—64no—
473(C2×D3)⋊C4C22×D314yes—
474(C2×D3)⋊C4C22×D314yes—
475(C2×D3)⋊C4C22×D314yes—
476(C2×D3)⋊C4C22×D314yescomplemented
477(C2×D3)⋊C4C22×D314yescomplemented
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—64no—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—64no—
488Dic3⋊C4C22×D314yescomplemented
489C4×Dic3—34no—
490C4×Dic3—34no—
491C4×Dic3—64no—
492C4×Dic3C22×D314yescomplemented
493C22×C32C2×#4112yes—
494C22×C32H(5,𝔽2)12yes—
495C22×C32H(5,𝔽2)12yes—
496C22×C32C2511yescharacteristic
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—44no—
501C2×C3×D3—28no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
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—22no—
512C2×C3×D3—22no—
513C2×C3×D3—44no—
514C2×C3×D3—44no—
515C2×C3×D3—44no—
516C2×C3×D3C2×#4114yes—
517D32—416no—
518C32×C4—22no—
519C32×C4—22no—
520C32×C4—22no—
521C3⋊Dic3—22no—
522C3⋊Dic3—22no—
523C3⋊Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C25—91no—
529C22×Q8—91no—
530C22×D4—31no—
531C22×D4—31no—
532C22×D4—91no—
533C22×D4—91no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C23×C4—31no—
538C23×C4—31no—
539C23×C4—31no—
540C23×C4—91no—
541#126—98no—
542#126—98no—
543#124—98no—
544#124—98no—
545#123—38no—
546#123—98no—
547C22⋊Q8—98no—
548#121—98no—
549#121—98no—
550#121—98no—
551#120—98no—
552#120—98no—
553C4×D4—38no—
554C4×D4—98no—
555C2×C4⋊C4—31no—
556C2×C4⋊C4—91no—
557C2×C4⋊C4—91no—
558C2×C4⋊C4—91no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4D3211yescharacteristic, complemented
561C2×C22⋊C4—31no—
562C2×C22⋊C4—31no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—98no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—91no—
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×C42—31no—
577C2×C42—91no—
578C23×C3—21no—
579C23×C3—34no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—62no—
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×C3—62no—
594C23×C3—62no—
595C23×C3C23×D311yescharacteristic
596C23×C3C23×D311yescharacteristic
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—62no—
611C22×D3—68no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—68no—
619C22×D3—122no—
620C22×D3—122no—
621C22×D3—122no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3—124no—
625C22×D3—124no—
626C22×D3—1216no—
627C22×D3—1216no—
628C22×D3#23514yes—
629C22×D3C23×D312yes—
630C22×D3C23×D312yes—
631C22×D3C23×D312yes—
632C22×D3C23×D312yes—
633C3×D4—68no—
634C3×D4—124no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—42no—
649C2×C3×C4—42no—
650C2×C3×C4—42no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4—62no—
655C2×C3×C4—124no—
656C2×C3×C4—124no—
657C2×C3×C4—124no—
658C2×C3×C4C23×D312yes—
659C2×C3×C4C23×D312yes—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664#67—68no—
665#67—68no—
666#67—124no—
667#67—124no—
668#67—124no—
669#67—124no—
670#67—124no—
671#67—124no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—122no—
692C2×Dic3—122no—
693C2×Dic3—122no—
694C2×Dic3—124no—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699D12—28no—
700D12—44no—
701D12—124no—
702D12—124no—
703C4×D3—44no—
704C4×D3—44no—
705C4×D3—44no—
706C4×D3—124no—
707Dic6—124no—
708Dic6—124no—
709C2×C32#53814yescomplemented
710C2×C32C22×#4111yescharacteristic
711C2×C32C2×H(5,𝔽2)11yescharacteristic
712C2×C32C2×H(5,𝔽2)11yescharacteristic
713C3⋊D3—42no—
714C3×D3—24no—
715C3×D3—42no—
716C3×D3—42no—
717C3×D3—42no—
718C24—31no—
719C24—31no—
720C24—31no—
721C24—31no—
722C24—94no—
723C24—91no—
724C24—184no—
725C24—362no—
726C24—362no—
727C2×Q8—94no—
728C2×Q8—362no—
729C2×D4—34no—
730C2×D4—34no—
731C2×D4—64no—
732C2×D4—94no—
733C2×D4—94no—
734C2×D4—94no—
735C2×D4—94no—
736C2×D4—94no—
737C2×D4—122no—
738C2×D4—184no—
739C2×D4—362no—
740C2×D4—362no—
741C2×D4—362no—
742C2×D4—362no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—34no—
748C22×C4—34no—
749C22×C4—34no—
750C22×C4—94no—
751C22×C4—91no—
752C22×C4—91no—
753C22×C4—91no—
754C22×C4—122no—
755C22×C4—122no—
756C22×C4—122no—
757C22×C4—362no—
758C22×C4C2×D3211yescharacteristic
759C22×C4C2×D3211yescharacteristic
760C22×C4C2×D3211yescharacteristic
761C4⋊C4—34no—
762C4⋊C4—94no—
763C4⋊C4—94no—
764C4⋊C4—94no—
765C4⋊C4—94no—
766C4⋊C4C2×D3214yescomplemented
767C22⋊C4—34no—
768C22⋊C4—34no—
769C22⋊C4—34no—
770C22⋊C4—34no—
771C22⋊C4—34no—
772C22⋊C4—94no—
773C22⋊C4—94no—
774C22⋊C4—94no—
775C22⋊C4—94no—
776C22⋊C4—94no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C42—34no—
782C42—94no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—21no—
787C22×C3—34no—
788C22×C3—68no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—124no—
801C22×C3—124no—
802C22×C3—124no—
803C22×C3C2×#23512yes—
804C22×C3#100412yes—
805C22×C3#100412yes—
806C22×C3D3×#4112yes—
807C22×C3#100912yes—
808C22×C3#100912yes—
809C22×C3C24×D311yescharacteristic
810C22×C3C24×D311yescharacteristic
811C2×D3—22no—
812C2×D3—22no—
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—22no—
823C2×D3—44no—
824C2×D3—44no—
825C2×D3—44no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—122no—
833C2×D3—122no—
834C2×D3—122no—
835C2×D3—1216no—
836C2×D3—1216no—
837C2×D3—124no—
838C2×D3—124no—
839C2×D3—244no—
840C2×D3C2×#23514yes—
841C3×C4—22no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—42no—
848C3×C4—42no—
849C3×C4—42no—
850C3×C4—62no—
851C3×C4—62no—
852C3×C4—62no—
853C3×C4—62no—
854Dic3—22no—
855Dic3—22no—
856Dic3—22no—
857Dic3—22no—
858Dic3—62no—
859Dic3—62no—
860Dic3—62no—
861Dic3—62no—
862Dic3—62no—
863Dic3—62no—
864Dic3—122no—
865Dic3—122no—
866Dic3—122no—
867C32C2×#53811yescharacteristic, complemented, Sylow
868C23—34no—
869C23—32no—
870C23—32no—
871C23—32no—
872C23—32no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—92no—
885C23—188no—
886C23—182no—
887C23—182no—
888C23—182no—
889C23—364no—
890C23—364no—
891C23—3616no—
892C23C22×D3211yescharacteristic
893Q8—364no—
894D4—68no—
895D4—124no—
896D4—188no—
897D4—364no—
898D4—364no—
899D4—364no—
900D4—364no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—92no—
913C2×C4—92no—
914C2×C4—92no—
915C2×C4—124no—
916C2×C4—124no—
917C2×C4—124no—
918C2×C4—182no—
919C2×C4—182no—
920C2×C4—182no—
921C2×C4—364no—
922C2×C4C22×D3212yes—
923C2×C4C22×D3212yes—
924C2×C4C22×D3212yes—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—24no—
929C2×C3—64no—
930C2×C3—122no—
931C2×C3—122no—
932C2×C3—122no—
933C2×C3#556014yescomplemented
934C2×C3#565714yescomplemented
935C2×C3C22×#23511yescharacteristic
936C2×C3C2×#100411yescharacteristic
937C2×C3C2×#100411yescharacteristic
938C2×C3C2×D3×#4111yescharacteristic
939C2×C3C2×#100911yescharacteristic
940C2×C3C2×#100911yescharacteristic
941D3—24no—
942D3—42no—
943D3—42no—
944D3—42no—
945D3—122no—
946D3—122no—
947D3—242no—
948C22—34no—
949C22—62no—
950C22—62no—
951C22—68no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—124no—
962C22—124no—
963C22—124no—
964C22—182no—
965C22—182no—
966C22—182no—
967C22—3616no—
968C22—364no—
969C22D3×#23512yes—
970C22#6431312yes—
971C22#6432012yes—
972C22C23×D3211yescharacteristic
973C4—22no—
974C4—22no—
975C4—22no—
976C4—62no—
977C4—62no—
978C4—62no—
979C4—62no—
980C4—182no—
981C4—182no—
982C4—182no—
983C3—21no—
984C3C2×#556011yescharacteristic, complemented
985C3C2×#565711yescharacteristic, complemented
986C2—64no—
987C2—122no—
988C2—122no—
989C2—122no—
990C2—362no—
991C2#1059463914yesdirect product factor
992C2C2×D3×#23511yescharacteristic
993C2C2×#6431311yescharacteristic
994C2C2×#6432011yescharacteristic
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×#64107C2semidirect
2. C2×C3×#894C2semidirect
3. C2×C3×#893C2semidirect
4. C2×#63922C2semidirect
5. C2×#63922C2semidirect
6. C2×D3×(C2×D3)⋊C4C2semidirect
7. C2×#63915C2semidirect
8. C2×#63908C2semidirect
9. C2×#63906C2semidirect
10. C2×C4×#625C2semidirect
11. C2×#63893C2semidirect
12. C2×#63885C2semidirect
13. C2×#63859C2semidirect
14. C2×#63852C2semidirect
15. C2×#63850C2semidirect
16. #10594639C2direct (N × H)
23. C22×C3×C4×D3C22semidirect
24. C22×C3×C4×D3C22semidirect
25. C22×#627C22semidirect
30. C22×#625C22semidirect
32. C2×C32×C4⋊C4C22semidirect
36. C2×C4⋊(C3⋊Dic3)C22semidirect
37. C2×#3750C22semidirect
38. C2×C4×C3⋊Dic3C22semidirect
39. #64107C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×C4×Dic3C22semidirect
47. C3×#894C22semidirect
48. C3×#893C22semidirect
49. C2×#3724C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
55. C2×(C2×D3)⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. #63922C22semidirect
58. #63922C22semidirect
59. D3×(C2×D3)⋊C4C22semidirect
60. #63915C22semidirect
61. #63908C22semidirect
62. #63906C22semidirect
63. C4×#625C22semidirect
64. #63893C22semidirect
65. #63885C22semidirect
66. #63859C22semidirect
67. #63852C22semidirect
68. #63850C22semidirect
88. C2×#894D3semidirect
89. C2×#893D3semidirect
129. C2×C3×C4×D3C23semidirect
130. C2×C3×C4×D3C23semidirect
132. C2×#627C23semidirect
142. C2×#625C23semidirect
145. C32×C4⋊C4C23semidirect
149. C4⋊(C3⋊Dic3)C23semidirect
150. #3750C23semidirect
151. C4×C3⋊Dic3C23semidirect
155. C3×(C2×D3)⋊C4C23semidirect
156. C3×(C2×D3)⋊C4C23semidirect
157. C3×Dic3⋊C4C23semidirect
158. C3×C4×Dic3C23semidirect
159. #3724C23semidirect
160. Dic3⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. (C2×D3)⋊Dic3C23semidirect
190. C22×C4×D3C2×D3semidirect
191. C22×C4×D3C2×D3semidirect
198. C2×C3×C4⋊C4C2×D3semidirect
199. C2×C3×C4⋊C4C2×D3semidirect
240. C2×(C2×D3)⋊C4C2×D3semidirect
241. C2×(C2×D3)⋊C4C2×D3semidirect
252. C2×Dic3⋊C4C2×D3semidirect
256. C2×C4×Dic3C2×D3semidirect
262. #894C2×D3semidirect
263. #893C2×D3semidirect
436. C2×C4×D3C22×D3semidirect
437. C2×C4×D3C22×D3semidirect
444. C3×C4⋊C4C22×D3semidirect
445. C3×C4⋊C4C22×D3semidirect
476. (C2×D3)⋊C4C22×D3semidirect
477. (C2×D3)⋊C4C22×D3semidirect
488. Dic3⋊C4C22×D3semidirect
492. C4×Dic3C22×D3semidirect
560. C2×C4⋊C4D32semidirect
709. C2×C32#538semidirect
766. C4⋊C4C2×D32semidirect
867. C32C2×#538semidirect
933. C2×C3#5560semidirect
934. C2×C3#5657semidirect
984. C3C2×#5560semidirect
985. C3C2×#5657semidirect
991. C2#10594639direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641072
C2×C3×#8942
C2×C3×#8932
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639152
C2×#639082
C2×#639062
C2×C4×#6252
C2×#638932
C2×#638852
C2×#638592
C2×#638522
C2×#638502
#105946392
C2×#56573
C2×#55603