Finite Group Databasebeta

← C2×#10594243 #11901335

Subgroups — C2×#10594243 #11901335

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×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#878C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C22×#3722C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×#63909C211yesmaximal, characteristic, complemented
10C2×#63907C211yesmaximal, characteristic, complemented
11C2×#63897C211yesmaximal, characteristic, complemented
12C2×#63868C211yesmaximal, characteristic, complemented
13C2×#63864C211yesmaximal, characteristic, complemented
14C2×#63850C211yesmaximal, characteristic, complemented
15C2×#63848C211yesmaximal, characteristic, complemented
16#10594243C2116yesmaximal, direct product factor
17C2×#5644—31nomaximal
18C2×#5560—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×Dic6C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic, complemented
31C22×#624C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35#64091C2218yescomplemented
36C2×C3×#217C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
40C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×C4×Dic3C2211yescharacteristic, complemented
43C3×#67⋊C4C2218yescomplemented
44C3×#878C2218yescomplemented
45#63981C2218yescomplemented
46#63978C2218yescomplemented
47C2×#3724C2211yescharacteristic, complemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2218yescomplemented
56C2×#3722C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59C2×Dic32C2211yescharacteristic, complemented
60#63952C2218yescomplemented
61#63910C2218yescomplemented
62#63909C2218yescomplemented
63#63907C2218yescomplemented
64#63897C2218yescomplemented
65#63868C2218yescomplemented
66#63864C2218yescomplemented
67#63850C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C2×C3×C4×D4—31no—
71C2×#947—31no—
72C2×#947—31no—
73C2×#939—31no—
74C2×#937—31no—
75C2×#930—31no—
76C2×#930—31no—
77C2×#929—31no—
78C2×C4×#67—31no—
79C22×(C2×D3)⋊C4—31no—
80C22×(C2×D3)⋊C4—31no—
81#5644—316no—
82#5560—316no—
83C2×#898—31no—
84C2×#898—31no—
85C2×#898—31no—
86C2×#895—31no—
87C2×#895—31no—
88C2×#894—31no—
89C2×#894—31no—
90C2×#894—31no—
91C2×#885—31no—
92C2×#884—31no—
93C2×#882—31no—
94C2×#882—31no—
95C2×#882—31no—
96C2×#882—61no—
97C2×#67⋊C4—31no—
98C2×#67⋊C4D311yescharacteristic, complemented
99C2×#878D311yescharacteristic, complemented
100C2×#876—31no—
101C2×#875—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—24no—
114C2×#638C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C4⋊(C3⋊D3)—42no—
117C2×C4⋊(C3⋊D3)—42no—
118C2×C4⋊(C3⋊D3)C2314yes—
119C2×C4⋊(C3⋊D3)C2314yes—
120C2×C3×#67—24no—
121C2×C3×#67C2314yes—
122C22×C3×Dic3—42no—
123C22×C3×Dic3—42no—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2314yes—
132C22×C3×Dic3C2314yes—
133C2×C3×C4×D3—42no—
134C2×C3×C4×D3C2314yescomplemented
135C2×C3×Dic6—42no—
136C2×C3×Dic6C2314yescomplemented
137C2×#626—42no—
138C2×#626—42no—
139C2×#626—42no—
140C2×#626C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yescomplemented
143C2×#624—42no—
144C2×#624C2314yescomplemented
145C32×C22⋊C4C2314yes—
146#3752C2314yes—
147#3752C2314yes—
148C3×#217C2314yes—
149C3×(C2×D3)⋊C4C2314yescomplemented
150C3×C4⋊Dic3C2314yescomplemented
151C3×Dic3⋊C4C2314yescomplemented
152C3×Dic3⋊C4C2314yescomplemented
153C3×Dic3⋊C4C2314yescomplemented
154C3×C4×Dic3C2314yescomplemented
155#3724C2314yescomplemented
156Dic3⋊Dic3C2314yescomplemented
157#3722C2314yes—
158#3722C2314yes—
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×Q8—31no—
172C22×C3×D4—31no—
173C23×C3×C4—31no—
174C23×C3×C4—31no—
175C23×C3×C4—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—61no—
182C22×#67C2×D311yescharacteristic
183C23×Dic3C2×D311yescharacteristic
184C23×Dic3C2×D311yescharacteristic
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—31no—
189C22×D12—31no—
190C22×D12—31no—
191C22×D12—31no—
192C22×D12—61no—
193C22×D12—61no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3C2×D311yescharacteristic, complemented
197C22×Dic6C2×D311yescharacteristic, complemented
198C3×C22⋊Q8—38no—
199C3×C4×D4—38no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C4⋊C4—31no—
204C2×C3×C22⋊C4—21no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4C2×D311yescharacteristic
208C2×C3×C22⋊C4C2×D311yescharacteristic
209C2×C3×C42—31no—
210C2×#217—31no—
211C2×#217C2×D311yescharacteristic
212#947—38no—
213#947—38no—
214#939—38no—
215#937—38no—
216#930—38no—
217#930—38no—
218#929—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—38no—
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—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—38no—
243C2×(C2×D3)⋊C4—61no—
244C2×(C2×D3)⋊C4—61no—
245C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3C2×D311yescharacteristic, complemented
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4C2×D311yescharacteristic, complemented
252C2×Dic3⋊C4C2×D311yescharacteristic, complemented
253C2×Dic3⋊C4C2×D311yescharacteristic, complemented
254C2×C4×Dic3—31no—
255C2×C4×Dic3—31no—
256C2×C4×Dic3C2×D311yescharacteristic, complemented
257#898—38no—
258#898—38no—
259#898—38no—
260#895—38no—
261#895—38no—
262#894—38no—
263#894—38no—
264#894—38no—
265#885—38no—
266#884—38no—
267#882—38no—
268#882—38no—
269#882—38no—
270#882—68no—
271#67⋊C4—38no—
272#67⋊C4C2×D318yescomplemented
273#878C2×D318yescomplemented
274#876—38no—
275#875—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32#4114yes—
279C23×C32C2412yes—
280C23×C32C2411yescharacteristic
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—28no—
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—44no—
292C22×C3⋊D3—44no—
293C22×C3⋊D3—416no—
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—28no—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3C2412yes—
308C4⋊(C3⋊D3)—44no—
309C4⋊(C3⋊D3)—44no—
310C3×#67—28no—
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×Dic3—44no—
319C2×C3×Dic3—44no—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C3×C4×D3—44no—
328C3×Dic6—44no—
329#626—44no—
330#626—44no—
331#626—44no—
332#624—44no—
333#538—916no—
334C2×#126—91no—
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—31no—
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×Q8—34no—
376C2×C3×Q8—122no—
377C2×C3×D4—34no—
378C2×C3×D4—64no—
379C22×C3×C4—21no—
380C22×C3×C4—21no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—34no—
389C22×C3×C4—34no—
390C22×C3×C4—34no—
391C22×C3×C4—122no—
392C22×C3×C4—122no—
393C22×C3×C4—122no—
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C2×#67—24no—
399C2×#67—34no—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—64no—
405C2×#67—64no—
406C2×#67—64no—
407C2×#67—124no—
408C2×#67—122no—
409C2×#67—122no—
410C2×#67—122no—
411C2×#67C22×D314yes—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—42no—
415C22×Dic3—42no—
416C22×Dic3—61no—
417C22×Dic3C22×D311yescharacteristic
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D314yes—
425C22×Dic3C22×D314yes—
426C2×D12—34no—
427C2×D12—34no—
428C2×D12—34no—
429C2×D12—34no—
430C2×D12—34no—
431C2×D12—34no—
432C2×D12—34no—
433C2×D12—64no—
434C2×D12—64no—
435C2×D12—122no—
436C2×D12—122no—
437C2×D12—122no—
438C2×D12—122no—
439C2×D12—124no—
440C2×D12—124no—
441C2×D12—122no—
442C2×D12—122no—
443C2×D12—122no—
444C2×C4×D3—34no—
445C2×C4×D3—34no—
446C2×C4×D3—42no—
447C2×C4×D3—122no—
448C2×C4×D3—122no—
449C2×C4×D3C22×D314yescomplemented
450C2×Dic6—42no—
451C2×Dic6C22×D314yescomplemented
452C3×C4⋊C4—34no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—34no—
456C3×C22⋊C4—24no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4C22×D314yes—
460C3×C22⋊C4C22×D314yes—
461C3×C42—34no—
462#217—34no—
463#217C22×D314yes—
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—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—64no—
486(C2×D3)⋊C4—64no—
487(C2×D3)⋊C4C22×D314yescomplemented
488C4⋊Dic3—34no—
489C4⋊Dic3C22×D314yescomplemented
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4C22×D314yescomplemented
494Dic3⋊C4C22×D314yescomplemented
495Dic3⋊C4C22×D314yescomplemented
496C4×Dic3—34no—
497C4×Dic3—34no—
498C4×Dic3C22×D314yescomplemented
499C22×C32—28no—
500C22×C32—22no—
501C22×C32—22no—
502C22×C32C2×#4114yes—
503C22×C32C2×#4112yes—
504C22×C32H(5,𝔽2)12yes—
505C22×C32H(5,𝔽2)12yes—
506C22×C32C2511yescharacteristic
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—22no—
514C2×C3⋊D3—22no—
515C2×C3⋊D3—22no—
516C2×C3⋊D3—416no—
517C2×C3⋊D3—44no—
518C2×C3⋊D3—44no—
519C2×C3⋊D3—44no—
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—31no—
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—31no—
545C23×C4—31no—
546C23×C4—91no—
547#126—98no—
548#126—98no—
549#124—98no—
550#124—98no—
551#123—98no—
552#123—98no—
553C22⋊Q8—38no—
554#121—98no—
555#121—98no—
556#121—98no—
557#120—98no—
558#120—98no—
559C4×D4—38no—
560C4×D4—98no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—91no—
566C2×C4⋊C4—91no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—98no—
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—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—21no—
590C23×C3—24no—
591C23×C3—32no—
592C23×C3—42no—
593C23×C3—42no—
594C23×C3—62no—
595C23×C3—62no—
596C23×C3—62no—
597C23×C3#23514yes—
598C23×C3#23914yes—
599C23×C3C23×D312yes—
600C23×C3C23×D312yes—
601C23×C3C23×D311yescharacteristic
602C23×C3C23×D311yescharacteristic
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—32no—
607C22×D3—32no—
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—64no—
616C22×D3—64no—
617C22×D3—62no—
618C22×D3—68no—
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—62no—
628C22×D3—68no—
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—122no—
638C22×D3—122no—
639C22×D3—128no—
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—128no—
651C22×D3—1216no—
652C22×D3—1216no—
653C22×D3—1232no—
654C22×D3C23×D312yes—
655C3×Q8—124no—
656C3×D4—68no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
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—32no—
670C2×C3×C4—42no—
671C2×C3×C4—42no—
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—62no—
679C2×C3×C4—124no—
680C2×C3×C4—124no—
681C2×C3×C4—124no—
682C2×C3×C4C23×D312yes—
683C2×C3×C4C23×D312yes—
684C2×C3×C4C23×D312yes—
685C2×C3×C4C23×D312yes—
686#67—28no—
687#67—68no—
688#67—68no—
689#67—128no—
690#67—124no—
691#67—124no—
692#67—124no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—44no—
703C2×Dic3—44no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—122no—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D312yes—
711C2×Dic3C23×D312yes—
712C2×Dic3C23×D312yes—
713C2×Dic3C23×D312yes—
714C2×Dic3C23×D312yes—
715D12—124no—
716D12—124no—
717D12—124no—
718D12—124no—
719D12—128no—
720D12—128no—
721D12—124no—
722D12—124no—
723D12—124no—
724C4×D3—44no—
725C4×D3—124no—
726C4×D3—124no—
727Dic6—44no—
728C2×C32—24no—
729C2×C32#53814yescomplemented
730C2×C32C22×#4111yescharacteristic
731C2×C32C2×H(5,𝔽2)11yescharacteristic
732C2×C32C2×H(5,𝔽2)11yescharacteristic
733C3⋊D3—42no—
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—34no—
747C2×Q8—122no—
748C2×D4—34no—
749C2×D4—64no—
750C2×D4—94no—
751C2×D4—94no—
752C2×D4—94no—
753C2×D4—94no—
754C2×D4—94no—
755C2×D4—94no—
756C2×D4—184no—
757C2×D4—362no—
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—34no—
771C22×C4—34no—
772C22×C4—94no—
773C22×C4—91no—
774C22×C4—122no—
775C22×C4—122no—
776C22×C4—122no—
777C22×C4—362no—
778C22×C4C2×D3211yescharacteristic
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—34no—
781C4⋊C4—34no—
782C4⋊C4—34no—
783C4⋊C4—34no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C22⋊C4—34no—
787C22⋊C4—34no—
788C22⋊C4—94no—
789C22⋊C4—94no—
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—28no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—28no—
808C22×C3—22no—
809C22×C3—24no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—21no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—48no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—124no—
820C22×C3C2×#23514yes—
821C22×C3C2×#23512yes—
822C22×C3#100412yes—
823C22×C3#100412yes—
824C22×C3C2×#23914yes—
825C22×C3C2×#23912yes—
826C22×C3#100912yes—
827C22×C3#100912yes—
828C22×C3C24×D311yescharacteristic
829C22×C3C24×D311yescharacteristic
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—44no—
834C2×D3—64no—
835C2×D3—64no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
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—122no—
855C2×D3—122no—
856C2×D3—122no—
857C2×D3—122no—
858C2×D3—122no—
859C2×D3—122no—
860C2×D3—122no—
861C2×D3—1216no—
862C2×D3—1216no—
863C2×D3—128no—
864C2×D3—128no—
865C2×D3—1232no—
866C2×D3—124no—
867C2×D3—124no—
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—32no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—92no—
904C23—92no—
905C23—92no—
906C23—182no—
907C23—188no—
908C23—182no—
909C23—182no—
910C23—182no—
911C23—182no—
912C23—182no—
913C23—182no—
914C23—182no—
915C23—182no—
916C23—364no—
917C23—364no—
918C23—3616no—
919C23#379914yes—
920C23C22×D3212yes—
921C23C22×D3211yescharacteristic
922Q8—124no—
923D4—68no—
924D4—188no—
925D4—364no—
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—124no—
949C2×C4—124no—
950C2×C4—182no—
951C2×C4—364no—
952C2×C4C22×D3212yes—
953C2×C4C22×D3212yes—
954C2×C3—24no—
955C2×C3—24no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—21no—
959C2×C3—24no—
960C2×C3—44no—
961C2×C3—122no—
962C2×C3#556014yescomplemented
963C2×C3#564414yescomplemented
964C2×C3C22×#23511yescharacteristic
965C2×C3C2×#100411yescharacteristic
966C2×C3C2×#100411yescharacteristic
967C2×C3C22×#23911yescharacteristic
968C2×C3C2×#100911yescharacteristic
969C2×C3C2×#100911yescharacteristic
970D3—42no—
971D3—124no—
972D3—124no—
973D3—122no—
974D3—122no—
975D3—122no—
976D3—122no—
977D3—122no—
978D3—122no—
979D3—242no—
980C22—22no—
981C22—22no—
982C22—28no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—124no—
987C22—182no—
988C22—182no—
989C22—182no—
990C22—182no—
991C22—182no—
992C22—182no—
993C22—182no—
994C22—182no—
995C22—182no—
996C22—3616no—
997C22—364no—
998C22—364no—
999C22—364no—
1000C22C2×#379914yes—
1001C22C2×#379912yes—
1002C22#6431412yes—
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×#556011yescharacteristic, complemented
1017C3C2×#564411yescharacteristic, complemented
1018C2—24no—
1019C2—122no—
1020C2—362no—
1021C2—362no—
1022C2—362no—
1023C2#1059424314yesdirect product factor
1024C2C22×#379911yescharacteristic
1025C2C2×#6431411yescharacteristic
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×#67⋊C4C2semidirect
3. C2×C3×#878C2semidirect
4. C2×#63981C2semidirect
5. C2×#63978C2semidirect
6. C22×#3722C2semidirect
7. C2×#63952C2semidirect
8. C2×#63910C2semidirect
9. C2×#63909C2semidirect
10. C2×#63907C2semidirect
11. C2×#63897C2semidirect
12. C2×#63868C2semidirect
13. C2×#63864C2semidirect
14. C2×#63850C2semidirect
15. C2×#63848C2semidirect
16. #10594243C2direct (N × H)
26. C22×C3×C4×D3C22semidirect
27. C22×C3×Dic6C22semidirect
30. C22×#626C22semidirect
31. C22×#624C22semidirect
35. #64091C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C2×C3×C4×Dic3C22semidirect
43. C3×#67⋊C4C22semidirect
44. C3×#878C22semidirect
45. #63981C22semidirect
46. #63978C22semidirect
47. C2×#3724C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
55. C2×#3722C22semidirect
56. C2×#3722C22semidirect
57. C2×#3722C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×Dic32C22semidirect
60. #63952C22semidirect
61. #63910C22semidirect
62. #63909C22semidirect
63. #63907C22semidirect
64. #63897C22semidirect
65. #63868C22semidirect
66. #63864C22semidirect
67. #63850C22semidirect
68. #63848C22semidirect
98. C2×#67⋊C4D3semidirect
99. C2×#878D3semidirect
134. C2×C3×C4×D3C23semidirect
136. C2×C3×Dic6C23semidirect
142. C2×#626C23semidirect
144. C2×#624C23semidirect
149. C3×(C2×D3)⋊C4C23semidirect
150. C3×C4⋊Dic3C23semidirect
151. C3×Dic3⋊C4C23semidirect
152. C3×Dic3⋊C4C23semidirect
153. C3×Dic3⋊C4C23semidirect
154. C3×C4×Dic3C23semidirect
155. #3724C23semidirect
156. Dic3⋊Dic3C23semidirect
163. #3722C23semidirect
164. #3722C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
196. C22×C4×D3C2×D3semidirect
197. C22×Dic6C2×D3semidirect
245. C2×(C2×D3)⋊C4C2×D3semidirect
247. C2×C4⋊Dic3C2×D3semidirect
251. C2×Dic3⋊C4C2×D3semidirect
252. C2×Dic3⋊C4C2×D3semidirect
253. C2×Dic3⋊C4C2×D3semidirect
256. C2×C4×Dic3C2×D3semidirect
272. #67⋊C4C2×D3semidirect
273. #878C2×D3semidirect
449. C2×C4×D3C22×D3semidirect
451. C2×Dic6C22×D3semidirect
487. (C2×D3)⋊C4C22×D3semidirect
489. 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#5560semidirect
963. C2×C3#5644semidirect
1016. C3C2×#5560semidirect
1017. C3C2×#5644semidirect
1023. C2#10594243direct (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×#67⋊C42
C2×C3×#8782
C2×#639812
C2×#639782
C22×#37222
C2×#639522
C2×#639102
C2×#639092
C2×#639072
C2×#638972
C2×#638682
C2×#638642
C2×#638502
C2×#638482
#105942432
C2×#56443
C2×#55603