Finite Group Databasebeta

← C2×#10594652 #11901342

Subgroups — C2×#10594652 #11901342

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#896C211yesmaximal, characteristic, complemented
4C2×#63923C211yesmaximal, characteristic, complemented
5C2×#63923C211yesmaximal, characteristic, complemented
6C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×#63910C211yesmaximal, characteristic, complemented
8C2×#63909C211yesmaximal, characteristic, complemented
9C2×#63907C211yesmaximal, characteristic, complemented
10C2×#63897C211yesmaximal, characteristic, complemented
11C2×#63881C211yesmaximal, characteristic, complemented
12C2×#63880C211yesmaximal, characteristic, complemented
13C2×#63864C211yesmaximal, characteristic, complemented
14C2×#63853C211yesmaximal, characteristic, complemented
15C2×#63848C211yesmaximal, characteristic, complemented
16#10594652C2116yesmaximal, direct product factor
17C2×#5704—31nomaximal
18C2×#5644—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#624C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic, complemented
35#64104C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×#898C2218yescomplemented
47C3×#896C2218yescomplemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic, complemented
53C2×#3722C2211yescharacteristic, complemented
54C2×#3722C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic, complemented
57#63923C2218yescomplemented
58#63923C2218yescomplemented
59D3×(C2×D3)⋊C4C2218yescomplemented
60#63910C2218yescomplemented
61#63909C2218yescomplemented
62#63907C2218yescomplemented
63#63897C2218yescomplemented
64#63881C2218yescomplemented
65#63880C2218yescomplemented
66#63864C2218yescomplemented
67#63853C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#947—31no—
72C2×#947—31no—
73C2×#930—31no—
74C22×(C2×D3)⋊C4—31no—
75#5704—316no—
76#5644—316no—
77C2×#898—31no—
78C2×#898—31no—
79C2×#898D311yescharacteristic, complemented
80C2×#896D311yescharacteristic, complemented
81C2×#895—31no—
82C2×#895—31no—
83C2×#895—31no—
84C2×#895—31no—
85C2×#895—61no—
86C2×#894—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#893—31no—
90C2×#885—31no—
91C2×#884—31no—
92C2×#883—31no—
93C2×#882—31no—
94C2×#882—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#67⋊C4—31no—
98C2×#67⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×#875—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—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4⋊(C3⋊D3)—42no—
116C2×C4⋊(C3⋊D3)—42no—
117C2×C4⋊(C3⋊D3)—42no—
118C2×C4⋊(C3⋊D3)C2314yes—
119C2×C4⋊(C3⋊D3)C2314yes—
120C2×C4⋊(C3⋊D3)C2314yescomplemented
121C2×C4×C3⋊D3—42no—
122C2×C4×C3⋊D3C2314yescomplemented
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×D3C2314yes—
131C2×C3×Dic6—42no—
132C2×C3×Dic6C2314yescomplemented
133C2×#626—24no—
134C2×#626—24no—
135C2×#626—42no—
136C2×#626—42no—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#624—42no—
142C2×#624C2314yescomplemented
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yes—
145C32×C4⋊C4C2314yescomplemented
146#3752C2314yes—
147#3752C2314yescomplemented
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×C4⋊Dic3C2314yescomplemented
154C3×Dic3⋊C4C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156C3×Dic3⋊C4C2314yescomplemented
157C3×C4×Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162#3722C2314yescomplemented
163#3722C2314yescomplemented
164#3722C2314yescomplemented
165(C2×D3)⋊Dic3C2314yes—
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×Q8—31no—
171C23×C3×C4—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C23×Dic3—31no—
177C22×D12—31no—
178C22×D12—31no—
179C22×D12—31no—
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×D12—61no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3—61no—
196C22×C4×D3C2×D311yescharacteristic
197C22×Dic6C2×D311yescharacteristic, complemented
198C3×#126—38no—
199C3×C22⋊Q8—38no—
200C2×C3×C4⋊C4—21no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C4⋊C4—31no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
206C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4—31no—
210C2×C3×C22⋊C4—31no—
211C2×C3×C22⋊C4—31no—
212C2×C3×C42—31no—
213C2×#217—31no—
214#947—38no—
215#947—38no—
216#930—38no—
217C2×(C2×D3)⋊C4—31no—
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—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—38no—
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
242C2×C4⋊Dic3—31no—
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#898C2×D318yescomplemented
254#896C2×D318yescomplemented
255#895—38no—
256#895—38no—
257#895—38no—
258#895—38no—
259#895—68no—
260#894—38no—
261#894—38no—
262#894—38no—
263#893—38no—
264#885—38no—
265#884—38no—
266#883—38no—
267#882—38no—
268#882—38no—
269#882—38no—
270#882—38no—
271#67⋊C4—38no—
272#67⋊C4—38no—
273D3×C22⋊C4—38no—
274#875—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⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3C2412yes—
287C22×C3⋊D3C2412yes—
288C22×C3⋊D3C2412yes—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3#4114yes—
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⋊Dic3C2412yes—
309C4⋊(C3⋊D3)—44no—
310C4⋊(C3⋊D3)—44no—
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×Dic3—22no—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C3×C4×D3—44no—
326C3×Dic6—44no—
327#626—28no—
328#626—28no—
329#626—44no—
330#626—44no—
331#624—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—31no—
335C2×#126—91no—
336C2×#124—91no—
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—
351C23×D3—31no—
352C23×D3—31no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—34no—
358C23×D3—34no—
359C23×D3—61no—
360C23×D3—61no—
361C23×D3—61no—
362C23×D3—64no—
363C23×D3—64no—
364C23×D3—122no—
365C23×D3—122no—
366C23×D3—122no—
367C23×D3—122no—
368C23×D3C22×D311yescharacteristic
369C23×D3C22×D311yescharacteristic
370C2×C3×Q8—34no—
371C2×C3×Q8—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—31no—
380C22×C3×C4—31no—
381C22×C3×C4—34no—
382C22×C3×C4—122no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—64no—
394C2×#67—64no—
395C2×#67—122no—
396C2×#67—122no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—34no—
400C22×Dic3—61no—
401C22×Dic3—122no—
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C2×D12—34no—
409C2×D12—34no—
410C2×D12—34no—
411C2×D12—34no—
412C2×D12—34no—
413C2×D12—34no—
414C2×D12—34no—
415C2×D12—34no—
416C2×D12—34no—
417C2×D12—34no—
418C2×D12—64no—
419C2×D12—64no—
420C2×D12—64no—
421C2×D12—64no—
422C2×D12—64no—
423C2×D12—122no—
424C2×D12—122no—
425C2×D12—122no—
426C2×D12—122no—
427C2×D12—122no—
428C2×D12—122no—
429C2×D12—124no—
430C2×D12—124no—
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—42no—
440C2×C4×D3—64no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—122no—
446C2×C4×D3—124no—
447C2×C4×D3C22×D314yes—
448C2×Dic6—42no—
449C2×Dic6C22×D314yescomplemented
450C3×C4⋊C4—24no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4C22×D314yescomplemented
456C3×C4⋊C4C22×D314yescomplemented
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4—34no—
460C3×C22⋊C4—34no—
461C3×C22⋊C4—34no—
462C3×C42—34no—
463#217—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—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—64no—
482(C2×D3)⋊C4—64no—
483(C2×D3)⋊C4C22×D314yes—
484(C2×D3)⋊C4C22×D314yes—
485(C2×D3)⋊C4C22×D314yes—
486(C2×D3)⋊C4C22×D314yes—
487(C2×D3)⋊C4C22×D314yes—
488C4⋊Dic3—34no—
489C4⋊Dic3C22×D314yescomplemented
490Dic3⋊C4—34no—
491Dic3⋊C4C22×D314yescomplemented
492Dic3⋊C4C22×D314yescomplemented
493Dic3⋊C4C22×D314yescomplemented
494C4×Dic3—34no—
495C4×Dic3—34no—
496C4×Dic3C22×D314yescomplemented
497C22×C32C2×#4112yes—
498C22×C32H(5,𝔽2)12yes—
499C22×C32H(5,𝔽2)12yes—
500C22×C32C2511yescharacteristic
501C2×C3⋊D3—22no—
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—44no—
511C2×C3⋊D3—44no—
512C2×C3⋊D3—44no—
513C2×C3×D3—28no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—44no—
520C2×C3×D3C2×#4114yes—
521D32—416no—
522C32×C4—22no—
523C32×C4—22no—
524C32×C4—22no—
525C3⋊Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C25—91no—
533C22×Q8—31no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4—91no—
541C23×C4—31no—
542C23×C4—91no—
543C23×C4—91no—
544C23×C4—91no—
545#126—38no—
546#126—98no—
547#124—98no—
548#124—98no—
549#123—98no—
550#123—98no—
551C22⋊Q8—38no—
552#121—98no—
553#121—98no—
554#121—98no—
555#120—98no—
556#120—98no—
557C4×D4—98no—
558C4×D4—98no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4D3211yescharacteristic, complemented
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—98no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—91no—
579C2×C22⋊C4—91no—
580C2×C42—31no—
581C2×C42—91no—
582C23×C3—21no—
583C23×C3—34no—
584C23×C3—32no—
585C23×C3—32no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3C23×D311yescharacteristic
592C23×C3C23×D311yescharacteristic
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—32no—
599C22×D3—32no—
600C22×D3—32no—
601C22×D3—32no—
602C22×D3—32no—
603C22×D3—32no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—62no—
607C22×D3—68no—
608C22×D3—64no—
609C22×D3—62no—
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—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—68no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—122no—
633C22×D3—122no—
634C22×D3—122no—
635C22×D3—122no—
636C22×D3—124no—
637C22×D3—124no—
638C22×D3—124no—
639C22×D3—124no—
640C22×D3—1216no—
641C22×D3—1216no—
642C22×D3#23914yes—
643C22×D3C23×D312yes—
644C22×D3C23×D312yes—
645C3×Q8—124no—
646C2×C3×C4—24no—
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—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—42no—
663C2×C3×C4—42no—
664C2×C3×C4—62no—
665C2×C3×C4—62no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—62no—
670C2×C3×C4—124no—
671C2×C3×C4C23×D312yes—
672C2×C3×C4C23×D312yes—
673C2×C3×C4C23×D312yes—
674C2×C3×C4C23×D312yes—
675C2×C3×C4C23×D312yes—
676C2×C3×C4C23×D312yes—
677#67—68no—
678#67—68no—
679#67—124no—
680#67—124no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—122no—
693C2×Dic3—124no—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700D12—68no—
701D12—68no—
702D12—124no—
703D12—124no—
704D12—124no—
705D12—124no—
706D12—124no—
707D12—124no—
708D12—128no—
709D12—128no—
710D12—128no—
711D12—124no—
712D12—124no—
713C4×D3—44no—
714C4×D3—124no—
715C4×D3—124no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—124no—
719C4×D3—128no—
720Dic6—44no—
721C2×C32#53814yescomplemented
722C2×C32C22×#4111yescharacteristic
723C2×C32C2×H(5,𝔽2)11yescharacteristic
724C2×C32C2×H(5,𝔽2)11yescharacteristic
725C3⋊D3—42no—
726C3⋊D3—42no—
727C3⋊D3—42no—
728C3×D3—24no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24—94no—
733C24—91no—
734C24—91no—
735C24—91no—
736C24—184no—
737C24—362no—
738C24—362no—
739C2×Q8—34no—
740C2×Q8—122no—
741C2×D4—94no—
742C2×D4—94no—
743C2×D4—94no—
744C2×D4—94no—
745C2×D4—94no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—184no—
749C2×D4—184no—
750C2×D4—362no—
751C2×D4—362no—
752C2×D4—362no—
753C2×D4—362no—
754C2×D4—362no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—34no—
762C22×C4—94no—
763C22×C4—94no—
764C22×C4—91no—
765C22×C4—94no—
766C22×C4—122no—
767C22×C4—362no—
768C22×C4—362no—
769C22×C4—362no—
770C22×C4C2×D3211yescharacteristic
771C22×C4C2×D3211yescharacteristic
772C22×C4C2×D3211yescharacteristic
773C4⋊C4—34no—
774C4⋊C4—34no—
775C4⋊C4—34no—
776C4⋊C4—34no—
777C4⋊C4—94no—
778C4⋊C4C2×D3214yescomplemented
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C42—34no—
794C42—94no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—21no—
799C22×C3—34no—
800C22×C3—68no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—124no—
807C22×C3#100412yes—
808C22×C3C2×#23912yes—
809C22×C3D3×#4112yes—
810C22×C3#100912yes—
811C22×C3#100912yes—
812C22×C3#100912yes—
813C22×C3C24×D311yescharacteristic
814C22×C3C24×D311yescharacteristic
815C2×D3—28no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—44no—
822C2×D3—64no—
823C2×D3—62no—
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—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—122no—
842C2×D3—122no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—122no—
848C2×D3—122no—
849C2×D3—1216no—
850C2×D3—1216no—
851C2×D3—128no—
852C2×D3—124no—
853C2×D3—124no—
854C2×D3—124no—
855C2×D3—124no—
856C2×D3—124no—
857C2×D3—124no—
858C2×D3—244no—
859C2×D3—244no—
860C2×D3C2×#23914yes—
861C3×C4—24no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—22no—
866C3×C4—22no—
867C3×C4—22no—
868C3×C4—42no—
869C3×C4—42no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—62no—
873C3×C4—62no—
874C3×C4—62no—
875C3×C4—62no—
876Dic3—22no—
877Dic3—22no—
878Dic3—22no—
879Dic3—22no—
880Dic3—22no—
881Dic3—22no—
882Dic3—62no—
883Dic3—62no—
884Dic3—122no—
885C32C2×#53811yescharacteristic, complemented, Sylow
886C23—34no—
887C23—32no—
888C23—32no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—92no—
895C23—92no—
896C23—92no—
897C23—188no—
898C23—182no—
899C23—182no—
900C23—182no—
901C23—182no—
902C23—182no—
903C23—182no—
904C23—182no—
905C23—182no—
906C23—182no—
907C23—364no—
908C23—364no—
909C23—3616no—
910C23C22×D3211yescharacteristic
911Q8—124no—
912D4—188no—
913D4—188no—
914D4—364no—
915D4—364no—
916D4—364no—
917D4—364no—
918D4—364no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—62no—
929C2×C4—62no—
930C2×C4—62no—
931C2×C4—62no—
932C2×C4—62no—
933C2×C4—62no—
934C2×C4—92no—
935C2×C4—124no—
936C2×C4—182no—
937C2×C4—364no—
938C2×C4—364no—
939C2×C4—364no—
940C2×C4C22×D3212yes—
941C2×C4C22×D3212yes—
942C2×C4C22×D3212yes—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—24no—
947C2×C3—64no—
948C2×C3—122no—
949C2×C3#564414yescomplemented
950C2×C3#570414yescomplemented
951C2×C3C2×#100411yescharacteristic
952C2×C3C22×#23911yescharacteristic
953C2×C3C2×D3×#4111yescharacteristic
954C2×C3C2×#100911yescharacteristic
955C2×C3C2×#100911yescharacteristic
956C2×C3C2×#100911yescharacteristic
957D3—24no—
958D3—42no—
959D3—124no—
960D3—122no—
961D3—122no—
962D3—122no—
963D3—122no—
964D3—122no—
965D3—122no—
966D3—242no—
967D3—242no—
968C22—34no—
969C22—62no—
970C22—62no—
971C22—68no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—124no—
976C22—182no—
977C22—182no—
978C22—182no—
979C22—182no—
980C22—182no—
981C22—182no—
982C22—182no—
983C22—182no—
984C22—182no—
985C22—3616no—
986C22—364no—
987C22—364no—
988C22—364no—
989C22#6430812yes—
990C22#6431412yes—
991C22D3×#23912yes—
992C22C23×D3211yescharacteristic
993C4—22no—
994C4—22no—
995C4—22no—
996C4—62no—
997C4—62no—
998C4—62no—
999C4—62no—
1000C4—62no—
1001C4—62no—
1002C4—182no—
1003C3—21no—
1004C3C2×#564411yescharacteristic, complemented
1005C3C2×#570411yescharacteristic, complemented
1006C2—64no—
1007C2—122no—
1008C2—362no—
1009C2—362no—
1010C2—362no—
1011C2#1059465214yesdirect product factor
1012C2C2×#6430811yescharacteristic
1013C2C2×#6431411yescharacteristic
1014C2C2×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×#64104C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#896C2semidirect
4. C2×#63923C2semidirect
5. C2×#63923C2semidirect
6. C2×D3×(C2×D3)⋊C4C2semidirect
7. C2×#63910C2semidirect
8. C2×#63909C2semidirect
9. C2×#63907C2semidirect
10. C2×#63897C2semidirect
11. C2×#63881C2semidirect
12. C2×#63880C2semidirect
13. C2×#63864C2semidirect
14. C2×#63853C2semidirect
15. C2×#63848C2semidirect
16. #10594652C2direct (N × H)
22. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C4×C3⋊D3C22semidirect
25. C22×C3×Dic6C22semidirect
30. C22×#624C22semidirect
32. C2×C32×C4⋊C4C22semidirect
34. C2×#3752C22semidirect
35. #64104C22semidirect
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×#898C22semidirect
47. C3×#896C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
52. C2×#3722C22semidirect
53. C2×#3722C22semidirect
54. C2×#3722C22semidirect
56. C2×Dic32C22semidirect
57. #63923C22semidirect
58. #63923C22semidirect
59. D3×(C2×D3)⋊C4C22semidirect
60. #63910C22semidirect
61. #63909C22semidirect
62. #63907C22semidirect
63. #63897C22semidirect
64. #63881C22semidirect
65. #63880C22semidirect
66. #63864C22semidirect
67. #63853C22semidirect
68. #63848C22semidirect
79. C2×#898D3semidirect
80. C2×#896D3semidirect
120. C2×C4⋊(C3⋊D3)C23semidirect
122. C2×C4×C3⋊D3C23semidirect
132. C2×C3×Dic6C23semidirect
142. C2×#624C23semidirect
145. C32×C4⋊C4C23semidirect
147. #3752C23semidirect
153. C3×C4⋊Dic3C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. C3×Dic3⋊C4C23semidirect
157. C3×C4×Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
162. #3722C23semidirect
163. #3722C23semidirect
164. #3722C23semidirect
166. Dic32C23semidirect
197. C22×Dic6C2×D3semidirect
205. C2×C3×C4⋊C4C2×D3semidirect
206. C2×C3×C4⋊C4C2×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
253. #898C2×D3semidirect
254. #896C2×D3semidirect
449. C2×Dic6C22×D3semidirect
455. C3×C4⋊C4C22×D3semidirect
456. C3×C4⋊C4C22×D3semidirect
489. C4⋊Dic3C22×D3semidirect
491. Dic3⋊C4C22×D3semidirect
492. Dic3⋊C4C22×D3semidirect
493. Dic3⋊C4C22×D3semidirect
496. C4×Dic3C22×D3semidirect
564. C2×C4⋊C4D32semidirect
721. C2×C32#538semidirect
778. C4⋊C4C2×D32semidirect
885. C32C2×#538semidirect
949. C2×C3#5644semidirect
950. C2×C3#5704semidirect
1004. C3C2×#5644semidirect
1005. C3C2×#5704semidirect
1011. C2#10594652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C3×#8982
C2×C3×#8962
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639102
C2×#639092
C2×#639072
C2×#638972
C2×#638812
C2×#638802
C2×#638642
C2×#638532
C2×#638482
#105946522
C2×#57043
C2×#56443