Finite Group Databasebeta

← C2×#10595435 #11901352

Subgroups — C2×#10595435 #11901352

Order 1152.

2837 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×#64156C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic, complemented
4#10595435C2116yesmaximal, direct product factor
5C2×#63923C211yesmaximal, characteristic, complemented
6C2×#63922C211yesmaximal, characteristic, complemented
7C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×#63906C211yesmaximal, characteristic, complemented
10C2×#63902C211yesmaximal, characteristic, complemented
11C2×#63890C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63880C211yesmaximal, characteristic, complemented
14C2×#63868C211yesmaximal, characteristic, complemented
15C2×#63862C211yesmaximal, characteristic, complemented
16C2×#63854C211yesmaximal, characteristic, complemented
17C2×#5678—31nomaximal
18C2×#5644—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C32×Q8C2211yescharacteristic, complemented
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic, complemented
28C22×#625C2211yescharacteristic
29C22×#624C2211yescharacteristic, complemented
30C22×D3×Dic3C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic, complemented
32#64156C2218yescomplemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic, complemented
36C2×#3752C2211yescharacteristic, complemented
37C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
38C3×#947C2218yescomplemented
39C3×#946C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×C4×Dic3C2211yescharacteristic, complemented
50C2×#3724C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63923C2218yescomplemented
58#63922C2218yescomplemented
59D3×(C2×D3)⋊C4C2218yescomplemented
60#63910C2218yescomplemented
61#63906C2218yescomplemented
62#63902C2218yescomplemented
63#63890C2218yescomplemented
64#63886C2218yescomplemented
65#63880C2218yescomplemented
66#63868C2218yescomplemented
67#63862C2218yescomplemented
68#63854C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#947—31no—
72C2×#947—31no—
73C2×#947—61no—
74C2×#947D311yescharacteristic, complemented
75C2×#946D311yescharacteristic, complemented
76C2×#939—31no—
77C2×#937—31no—
78C2×#930—31no—
79C22×(C2×D3)⋊C4—31no—
80#5678—316no—
81#5644—316no—
82C2×#898—31no—
83C2×#898—31no—
84C2×#895—31no—
85C2×#895—31no—
86C2×#894—31no—
87C2×#894—31no—
88C2×#886—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#883—31no—
92C2×#882—31no—
93C2×#882—31no—
94C2×#882—31no—
95C2×#67⋊C4—31no—
96C2×#67⋊C4—31no—
97C2×#67⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×#879—31no—
100C2×#876—31no—
101C2×C4×D12—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—
111C2×C32×Q8—42no—
112C2×C32×Q8C2314yescomplemented
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C2×C4⋊(C3⋊D3)—42no—
119C2×C4⋊(C3⋊D3)C2314yes—
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×D3C2314yes—
129C2×#626—24no—
130C2×#626—42no—
131C2×#626—42no—
132C2×#626—42no—
133C2×#626C2314yes—
134C2×#626C2314yes—
135C2×#626C2314yes—
136C2×#626C2314yescomplemented
137C2×#625—24no—
138C2×#625C2314yes—
139C2×#624—42no—
140C2×#624C2314yescomplemented
141C2×D3×Dic3—42no—
142C2×D3×Dic3—42no—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yescomplemented
145#3752C2314yes—
146#3752C2314yes—
147#3752C2314yescomplemented
148#3752C2314yescomplemented
149C4×C3⋊Dic3C2314yescomplemented
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yescomplemented
155C3×(C2×D3)⋊C4C2314yescomplemented
156C3×C4⋊Dic3C2314yescomplemented
157C3×Dic3⋊C4C2314yescomplemented
158C3×Dic3⋊C4C2314yescomplemented
159C3×C4×Dic3C2314yescomplemented
160#3724C2314yescomplemented
161Dic3⋊Dic3C2314yescomplemented
162Dic3⋊Dic3C2314yescomplemented
163#3722C2314yes—
164#3722C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×Q8—21no—
171C22×C3×Q8C2×D311yescharacteristic, complemented
172C22×C3×Q8C2×D311yescharacteristic, complemented
173C22×C3×D4—31no—
174C23×C3×C4—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C23×Dic3—31no—
182C23×Dic3—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—31no—
189C22×D12—61no—
190C22×D12C2×D311yescharacteristic
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3C2×D311yescharacteristic
196C3×#124—38no—
197C3×C22⋊Q8—38no—
198C2×C3×C4⋊C4—31no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C22⋊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×C3×C42—31no—
208C2×#217—31no—
209C2×#217—31no—
210#947—38no—
211#947—38no—
212#947—68no—
213#947C2×D318yescomplemented
214#946C2×D318yescomplemented
215#939—38no—
216#937—38no—
217#930—38no—
218C2×(C2×D3)⋊C4—31no—
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—38no—
233C2×(C2×D3)⋊C4—61no—
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
241C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
242C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3C2×D311yescharacteristic, complemented
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4C2×D311yescharacteristic, complemented
251C2×Dic3⋊C4C2×D311yescharacteristic, complemented
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3—61no—
255C2×C4×Dic3C2×D311yescharacteristic, complemented
256#898—38no—
257#898—38no—
258#895—38no—
259#895—38no—
260#894—38no—
261#894—38no—
262#886—38no—
263#884—38no—
264#884—38no—
265#883—38no—
266#882—38no—
267#882—38no—
268#882—38no—
269#67⋊C4—38no—
270#67⋊C4—38no—
271#67⋊C4—38no—
272D3×C22⋊C4—38no—
273#879—38no—
274#876—38no—
275C4×D12—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—
301C32×Q8—44no—
302C2×C32×C4—22no—
303C2×C32×C4—22no—
304C2×C32×C4—22no—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307C2×C32×C4C2412yes—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
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—
325#626—28no—
326#626—44no—
327#626—44no—
328#626—44no—
329#625—28no—
330#624—44no—
331D3×Dic3—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—91no—
335C2×#126—91no—
336C2×#124—31no—
337C2×#124—91no—
338C2×#123—91no—
339C2×#123—91no—
340C2×C22⋊Q8—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—24no—
370C2×C3×Q8—42no—
371C2×C3×Q8—42no—
372C2×C3×Q8—44no—
373C2×C3×Q8C22×D314yescomplemented
374C2×C3×Q8C22×D314yescomplemented
375C2×C3×D4—34no—
376C2×C3×D4—122no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—34no—
386C22×C3×C4—122no—
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
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—64no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67—122no—
405C22×Dic3—31no—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—34no—
410C22×Dic3—34no—
411C22×Dic3—61no—
412C22×Dic3—61no—
413C22×Dic3—122no—
414C22×Dic3—122no—
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D311yescharacteristic
417C22×Dic3C22×D311yescharacteristic
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C2×D12—34no—
421C2×D12—34no—
422C2×D12—34no—
423C2×D12—34no—
424C2×D12—34no—
425C2×D12—34no—
426C2×D12—42no—
427C2×D12—64no—
428C2×D12—64no—
429C2×D12—122no—
430C2×D12—122no—
431C2×D12—124no—
432C2×D12—122no—
433C2×D12—122no—
434C2×D12—122no—
435C2×D12C22×D314yes—
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×D3C22×D314yes—
446C3×C4⋊C4—34no—
447C3×C4⋊C4—34no—
448C3×C4⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C42—34no—
456#217—34no—
457#217—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—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—64no—
473(C2×D3)⋊C4—64no—
474(C2×D3)⋊C4—64no—
475(C2×D3)⋊C4—64no—
476(C2×D3)⋊C4C22×D314yes—
477(C2×D3)⋊C4C22×D314yes—
478(C2×D3)⋊C4C22×D314yes—
479(C2×D3)⋊C4C22×D314yes—
480(C2×D3)⋊C4C22×D314yescomplemented
481(C2×D3)⋊C4C22×D314yescomplemented
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3C22×D314yescomplemented
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4C22×D314yescomplemented
490Dic3⋊C4C22×D314yescomplemented
491C4×Dic3—34no—
492C4×Dic3—34no—
493C4×Dic3—64no—
494C4×Dic3C22×D314yescomplemented
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×Q8D3211yescharacteristic, complemented
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—91no—
541C23×C4—91no—
542C23×C4—91no—
543#126—98no—
544#126—98no—
545#124—38no—
546#124—98no—
547#123—98no—
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⋊C4—91no—
563C2×C22⋊C4—31no—
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×C42—31no—
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—62no—
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—68no—
623C22×D3—122no—
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—44no—
640C3×Q8—44no—
641C3×Q8—48no—
642C3×D4—124no—
643C2×C3×C4—24no—
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—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—42no—
659C2×C3×C4—42no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4—124no—
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669C2×C3×C4C23×D312yes—
670C2×C3×C4C23×D312yes—
671C2×C3×C4C23×D312yes—
672#67—68no—
673#67—68no—
674#67—68no—
675#67—124no—
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—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—122no—
694C2×Dic3—122no—
695C2×Dic3—124no—
696C2×Dic3—124no—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701C2×Dic3C23×D312yes—
702D12—44no—
703D12—68no—
704D12—124no—
705D12—124no—
706D12—128no—
707D12—124no—
708D12—124no—
709D12—124no—
710C4×D3—44no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—124no—
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—42no—
734C2×Q8C2×D3214yescomplemented
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—94no—
756C22×C4—94no—
757C22×C4—94no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—122no—
761C22×C4—362no—
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⋊C4—94no—
773C22⋊C4—34no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—34no—
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—34no—
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—62no—
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—122no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—1216no—
843C2×D3—1216no—
844C2×D3—124no—
845C2×D3—124no—
846C2×D3—124no—
847C2×D3—124no—
848C2×D3—244no—
849C2×D3—244no—
850C2×D3C2×#23914yes—
851C3×C4—24no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—22no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—22no—
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—44no—
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—182no—
927C2×C4—182no—
928C2×C4—364no—
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#567814yescomplemented
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—122no—
953D3—122no—
954D3—122no—
955D3—122no—
956D3—242no—
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—
979C22D3×#23912yes—
980C22#6432012yes—
981C22#6433012yes—
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×#567811yescharacteristic, complemented
996C2—64no—
997C2—122no—
998C2—122no—
999C2—362no—
1000C2—362no—
1001C2#1059543514yesdirect product factor
1002C2C2×D3×#23911yescharacteristic
1003C2C2×#6432011yescharacteristic
1004C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64156C2semidirect
2. C2×C3×#947C2semidirect
3. C2×C3×#946C2semidirect
4. #10595435C2direct (N × H)
5. C2×#63923C2semidirect
6. C2×#63922C2semidirect
7. C2×D3×(C2×D3)⋊C4C2semidirect
8. C2×#63910C2semidirect
9. C2×#63906C2semidirect
10. C2×#63902C2semidirect
11. C2×#63890C2semidirect
12. C2×#63886C2semidirect
13. C2×#63880C2semidirect
14. C2×#63868C2semidirect
15. C2×#63862C2semidirect
16. C2×#63854C2semidirect
20. C22×C32×Q8C22semidirect
27. C22×#626C22semidirect
29. C22×#624C22semidirect
31. C22×D3×Dic3C22semidirect
32. #64156C22semidirect
35. C2×#3752C22semidirect
36. C2×#3752C22semidirect
37. C2×C4×C3⋊Dic3C22semidirect
38. C3×#947C22semidirect
39. C3×#946C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×C4⋊Dic3C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C2×C3×C4×Dic3C22semidirect
50. C2×#3724C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
57. #63923C22semidirect
58. #63922C22semidirect
59. D3×(C2×D3)⋊C4C22semidirect
60. #63910C22semidirect
61. #63906C22semidirect
62. #63902C22semidirect
63. #63890C22semidirect
64. #63886C22semidirect
65. #63880C22semidirect
66. #63868C22semidirect
67. #63862C22semidirect
68. #63854C22semidirect
74. C2×#947D3semidirect
75. C2×#946D3semidirect
112. C2×C32×Q8C23semidirect
136. C2×#626C23semidirect
140. C2×#624C23semidirect
144. C2×D3×Dic3C23semidirect
147. #3752C23semidirect
148. #3752C23semidirect
149. C4×C3⋊Dic3C23semidirect
154. C3×(C2×D3)⋊C4C23semidirect
155. C3×(C2×D3)⋊C4C23semidirect
156. C3×C4⋊Dic3C23semidirect
157. C3×Dic3⋊C4C23semidirect
158. C3×Dic3⋊C4C23semidirect
159. C3×C4×Dic3C23semidirect
160. #3724C23semidirect
161. Dic3⋊Dic3C23semidirect
162. Dic3⋊Dic3C23semidirect
171. C22×C3×Q8C2×D3semidirect
172. C22×C3×Q8C2×D3semidirect
213. #947C2×D3semidirect
214. #946C2×D3semidirect
241. C2×(C2×D3)⋊C4C2×D3semidirect
242. C2×(C2×D3)⋊C4C2×D3semidirect
245. C2×C4⋊Dic3C2×D3semidirect
250. C2×Dic3⋊C4C2×D3semidirect
251. C2×Dic3⋊C4C2×D3semidirect
255. C2×C4×Dic3C2×D3semidirect
373. C2×C3×Q8C22×D3semidirect
374. C2×C3×Q8C22×D3semidirect
480. (C2×D3)⋊C4C22×D3semidirect
481. (C2×D3)⋊C4C22×D3semidirect
484. C4⋊Dic3C22×D3semidirect
489. Dic3⋊C4C22×D3semidirect
490. Dic3⋊C4C22×D3semidirect
494. C4×Dic3C22×D3semidirect
531. C22×Q8D32semidirect
715. C2×C32#538semidirect
734. C2×Q8C2×D32semidirect
876. C32C2×#538semidirect
941. C2×C3#5644semidirect
942. C2×C3#5678semidirect
994. C3C2×#5644semidirect
995. C3C2×#5678semidirect
1001. C2#10595435direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641562
C2×C3×#9472
C2×C3×#9462
#105954352
C2×#639232
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639102
C2×#639062
C2×#639022
C2×#638902
C2×#638862
C2×#638802
C2×#638682
C2×#638622
C2×#638542
C2×#56783
C2×#56443