Finite Group Databasebeta

← #11803604

Subgroups — #11803604

Order 1152.

1421 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63885C211yesmaximal, characteristic
2C2×#63879C211yesmaximal, characteristic, complemented
3C2×#63878C211yesmaximal, characteristic, complemented
4#10592675C211yesmaximal, characteristic, complemented
5C3×#4989C211yesmaximal, characteristic, complemented
6C3×#4988C211yesmaximal, characteristic, complemented
7#10591386C211yesmaximal, characteristic, complemented
8#10591385C211yesmaximal, characteristic, complemented
9#10591381C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591372C211yesmaximal, characteristic, complemented
12#10591369C211yesmaximal, characteristic, complemented
13#10591305C211yesmaximal, characteristic, complemented
14#10591284C211yesmaximal, characteristic, complemented
15#10591243C211yesmaximal, characteristic, complemented
16#76296—31nomaximal
17#74385—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63885C418yescomplemented
48#63879—24no—
49#63878—24no—
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#939—31no—
57C2×C4×#67—31no—
58C2×#892—31no—
59C2×#884—31no—
60C2×#67⋊C4—31no—
61C2×#877—31no—
62C3×#390—31no—
63C3×#385—31no—
64#5220—31no—
65#5213—31no—
66#4989—31no—
67#4989D311yescharacteristic, complemented
68#4988D311yescharacteristic, complemented
69#4976—31no—
70#4976—31no—
71#4976—61no—
72#4957—31no—
73#4957—31no—
74#4957—31no—
75#4957—31no—
76#4956—31no—
77#4951—31no—
78#4946—31no—
79#4945—31no—
80#4942—31no—
81#4940—31no—
82C4×Dic3⋊C4—31no—
83#4670—31no—
84#4667—31no—
85#4665—31no—
86#4649—31no—
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×D12—41no—
103C2×C3×D12—41no—
104C2×C3×D12C2×C414yescomplemented
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—41no—
107C2×C3×C4×D3—41no—
108C2×#625—22no—
109C2×#625—22no—
110C2×#625—41no—
111C2×#625—41no—
112C2×#625C2×C414yes—
113C2×#625C2×C414yescomplemented
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—41no—
118C2×D3×Dic3—41no—
119C2×D3×Dic3C2×C414yescomplemented
120C32×C4⋊C4—41no—
121#3750—22no—
122#3750—41no—
123#3750C2×C414yescomplemented
124C4×C3⋊Dic3—22no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4—41no—
130C3×(C2×D3)⋊C4C2×C414yescomplemented
131C3×Dic3⋊C4—22no—
132C3×C4×Dic3—41no—
133#3724—22no—
134Dic3⋊Dic3—22no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—41no—
138(C2×D3)⋊Dic3—41no—
139(C2×D3)⋊Dic3—41no—
140(C2×D3)⋊Dic3C2×C414yescomplemented
141Dic32—41no—
142Dic32D414yescomplemented
143#2324—91noSylow
144C22×C3×D4—31no—
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C23×Dic3—31no—
151C23×Dic3—31no—
152C22×D12C2×D311yescharacteristic
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3C2×D311yescharacteristic
156C2×C3×C4⋊C4—21no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4C2×D311yescharacteristic
159C2×C3×C4⋊C4C2×D311yescharacteristic
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C42—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173#939—38no—
174C4×#67—64no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4C2×D311yescharacteristic
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×(C2×D3)⋊C4C2×D311yescharacteristic
184C2×(C2×D3)⋊C4C2×D311yescharacteristic
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×C4⋊Dic3—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—61no—
198C2×Dic3⋊C4—61no—
199C2×Dic3⋊C4—61no—
200C2×Dic3⋊C4C2×D311yescharacteristic
201C2×C4×Dic3—31no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—61no—
208C2×C4×Dic3C2×D311yescharacteristic
209#892—64no—
210#884—38no—
211#67⋊C4—64no—
212#877—64no—
213C3×#95—31no—
214C3×#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—61no—
224C3⋊#95—61no—
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C23×C32C2411yescharacteristic
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3C22×C412yes—
247C22×C3×D3C22×C412yes—
248C22×C3×D3C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C22×C412yes—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C22×C412yes—
267C2×C3⋊Dic3C22×C412yes—
268C2×C3⋊Dic3C2×D412yes—
269C2×C3⋊Dic3#4112yes—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C22×C412yes—
283C2×C3×Dic3C2×D412yes—
284C2×C3×Dic3C2×D412yes—
285C3×D12—44no—
286C3×C4×D3—44no—
287#625—28no—
288#625—44no—
289D3×Dic3—28no—
290D3×Dic3—44no—
291C2×#121—91no—
292C2×C4×D4—91no—
293C2×#117—91no—
294#390—31no—
295#390—91no—
296#390—91no—
297#389—91no—
298#388—91no—
299#388—91no—
300#386—91no—
301#386—91no—
302#385—31no—
303#385—91no—
304#380—91no—
305C4×C4⋊C4—91no—
306C24×C3—31no—
307C24×C3—31no—
308C24×C3—31no—
309C23×D3C22×D311yescharacteristic
310C23×D3C22×D311yescharacteristic
311C23×D3C22×D311yescharacteristic
312C2×C3×D4—34no—
313C2×C3×D4—121no—
314C2×C3×D4—121no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—62no—
324C22×C3×C4—121no—
325C22×C3×C4—121no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—34no—
333C2×#67—34no—
334C2×#67—34no—
335C2×#67—34no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—121no—
341C2×#67—121no—
342C2×#67—121no—
343C2×#67—121no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—34no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—62no—
358C22×Dic3—62no—
359C22×Dic3—62no—
360C22×Dic3—121no—
361C22×Dic3—121no—
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C2×D12—41no—
368C2×D12—41no—
369C2×D12C4×D314yescomplemented
370C2×C4×D3—22no—
371C2×C4×D3—34no—
372C2×C4×D3—41no—
373C2×C4×D3—41no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C3×C4⋊C4—41no—
380C3×C4⋊C4—41no—
381C3×C4⋊C4—42no—
382C3×C4⋊C4—62no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—62no—
385C3×C22⋊C4—62no—
386C3×C22⋊C4—121no—
387C3×C22⋊C4—121no—
388C3×C22⋊C4—121no—
389C3×C42—121no—
390#217—34no—
391#217—62no—
392#217—62no—
393#217—121no—
394#217—121no—
395#217—121no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—22no—
398(C2×D3)⋊C4—34no—
399(C2×D3)⋊C4—41no—
400(C2×D3)⋊C4—41no—
401(C2×D3)⋊C4—41no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4—121no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4C4×D314yescomplemented
408C4⋊Dic3—62no—
409Dic3⋊C4—22no—
410Dic3⋊C4—34no—
411Dic3⋊C4—34no—
412Dic3⋊C4—64no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—62no—
418Dic3⋊C4—122no—
419Dic3⋊C4—121no—
420Dic3⋊C4—121no—
421Dic3⋊C4—122no—
422C4×Dic3—34no—
423C4×Dic3—34no—
424C4×Dic3—41no—
425C4×Dic3—62no—
426C4×Dic3—62no—
427C4×Dic3—122no—
428C4×Dic3—121no—
429C4×Dic3—121no—
430C22×C32C23×C411yescharacteristic
431C22×C32C22×D411yescharacteristic
432C22×C32C2×#4111yescharacteristic
433C22×C32H(5,𝔽2)11yescharacteristic
434C22×C32H(5,𝔽2)11yescharacteristic
435C22×C32H(5,𝔽2)11yescharacteristic
436C22×C322−1+411yescharacteristic
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C32×C4—22no—
459C32×C4—41no—
460C32×C4—41no—
461C3⋊Dic3—22no—
462C3⋊Dic3—41no—
463C3⋊Dic3—41no—
464C3⋊Dic3C4×D414yes—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—41no—
469C3×Dic3—41no—
470C22×D4—31no—
471C22×D4—91no—
472C22×D4—91no—
473C23×C4—31no—
474C23×C4—91no—
475C23×C4—91no—
476#121—98no—
477C4×D4—184no—
478#117—184no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—91no—
481C2×C4⋊C4—91no—
482C2×C4⋊C4—91no—
483C2×C4⋊C4—91no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4D3211yescharacteristic
486C2×C22⋊C4—31no—
487C2×C22⋊C4—31no—
488C2×C22⋊C4—31no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—91no—
493C2×C22⋊C4—91no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C42—31no—
499C2×C42—91no—
500C2×C42—91no—
501C2×C42—91no—
502#95—31no—
503#95—31no—
504#95—91no—
505#95—91no—
506#95—91no—
507#95—91no—
508C23×C3—21no—
509C23×C3—32no—
510C23×C3—32no—
511C23×C3—32no—
512C23×C3—61no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3C23×D311yescharacteristic
531C23×C3C23×D311yescharacteristic
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3C2×C4×D312yes—
551C22×D3C2×C4×D312yes—
552C22×D3C2×C4×D312yes—
553C3×D4—124no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—124no—
595C2×C3×C4C2×C4×D312yes—
596C2×C3×C4C2×C4×D312yes—
597#67—68no—
598#67—68no—
599#67—124no—
600#67—124no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—62no—
622C2×Dic3—62no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—68no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—62no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—124no—
651C2×Dic3C2×C4×D312yes—
652C2×Dic3D3×D412yes—
653C2×Dic3D3×D412yes—
654D12—44no—
655C4×D3—44no—
656C4×D3—68no—
657C4×D3—124no—
658C2×C32C2×C4×D411yescharacteristic
659C2×C32#51811yescharacteristic
660C2×C32#52011yescharacteristic
661C2×C32#53511yescharacteristic
662C2×C32#53711yescharacteristic
663C2×C32#54011yescharacteristic
664C2×C32#54211yescharacteristic
665C3×D3—42no—
666C3×D3—42no—
667C3×D3—42no—
668C24—31no—
669C24—31no—
670C24—31no—
671C2×D4—34no—
672C2×D4—94no—
673C2×D4—94no—
674C2×D4—121no—
675C2×D4—121no—
676C2×D4—182no—
677C2×D4—182no—
678C2×D4—361no—
679C2×D4—361no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—62no—
686C22×C4—94no—
687C22×C4—91no—
688C22×C4—91no—
689C22×C4—91no—
690C22×C4—91no—
691C22×C4—121no—
692C22×C4—121no—
693C22×C4—182no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4—361no—
697C22×C4—361no—
698C22×C4C2×D3211yescharacteristic
699C22×C4C2×D3211yescharacteristic
700C22×C4C2×D3211yescharacteristic
701C4⋊C4—41no—
702C4⋊C4—62no—
703C4⋊C4—94no—
704C4⋊C4—182no—
705C4⋊C4—182no—
706C4⋊C4—182no—
707C4⋊C4—361no—
708C22⋊C4—34no—
709C22⋊C4—62no—
710C22⋊C4—62no—
711C22⋊C4—94no—
712C22⋊C4—121no—
713C22⋊C4—121no—
714C22⋊C4—121no—
715C22⋊C4—182no—
716C22⋊C4—182no—
717C22⋊C4—361no—
718C22⋊C4—361no—
719C22⋊C4—361no—
720C42—94no—
721C42—121no—
722C42—182no—
723C42—361no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3C22×C4×D311yescharacteristic
753C22×C3C22×C4×D311yescharacteristic
754C22×C3C2×D3×D411yescharacteristic
755C22×C3C2×D3×D411yescharacteristic
756C22×C3#100411yescharacteristic
757C22×C3#100411yescharacteristic
758C22×C3#100411yescharacteristic
759C22×C3#100411yescharacteristic
760C22×C3#100411yescharacteristic
761C22×C3#100711yescharacteristic
762C22×C3D3×#4111yescharacteristic
763C22×C3D3×#4111yescharacteristic
764C22×C3#100911yescharacteristic
765C22×C3#101011yescharacteristic
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C3×C4—22no—
788C3×C4—22no—
789C3×C4—42no—
790C3×C4—42no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4—62no—
796C3×C4—62no—
797C3×C4—62no—
798C3×C4—81no—
799C3×C4—121no—
800C3×C4—121no—
801Dic3—22no—
802Dic3—22no—
803Dic3—22no—
804Dic3—34no—
805Dic3—34no—
806Dic3—41no—
807Dic3—41no—
808Dic3—64no—
809Dic3—62no—
810Dic3—62no—
811Dic3—122no—
812Dic3—122no—
813Dic3—121no—
814Dic3—121no—
815Dic3—121no—
816Dic3—121no—
817Dic3—241no—
818C32#232411yescharacteristic, complemented, Sylow
819C23—32no—
820C23—32no—
821C23—32no—
822C23—61no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23C22×D3211yescharacteristic
841D4—124no—
842D4—188no—
843D4—364no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—92no—
868C2×C4—92no—
869C2×C4—92no—
870C2×C4—92no—
871C2×C4—124no—
872C2×C4—188no—
873C2×C4—181no—
874C2×C4—181no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—364no—
882C2×C4C4×D3212yes—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—122no—
891C2×C3—122no—
892C2×C3—122no—
893C2×C3#548611yescharacteristic
894C2×C3#550411yescharacteristic
895C2×C3C4×D3×D411yescharacteristic
896C2×C3C4×D3×D411yescharacteristic
897C2×C3#554511yescharacteristic
898C2×C3#554611yescharacteristic
899C2×C3#559211yescharacteristic
900C2×C3#559711yescharacteristic
901C2×C3#561511yescharacteristic
902C2×C3#562911yescharacteristic
903C2×C3#564011yescharacteristic
904C2×C3#566311yescharacteristic
905C2×C3#566911yescharacteristic
906C2×C3#571511yescharacteristic
907D3—42no—
908D3—42no—
909D3—42no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22C2×C4×D3211yescharacteristic
932C22#6430711yescharacteristic
933C22D32×D411yescharacteristic
934C22#6431311yescharacteristic
935C22#6431511yescharacteristic
936C22#6431911yescharacteristic
937C22#6433011yescharacteristic
938C4—22no—
939C4—41no—
940C4—41no—
941C4—62no—
942C4—62no—
943C4—62no—
944C4—94no—
945C4—121no—
946C4—121no—
947C4—182no—
948C4—361no—
949C4—361no—
950C3—21no—
951C3#7438511yescharacteristic, complemented
952C3#7629611yescharacteristic, complemented
953C2—122no—
954C2—122no—
955C2—122no—
956C2#1059435911yescharacteristic
957C2#1059436811yescharacteristic
958C2#1059458011yescharacteristic
959C2#1059460511yescharacteristic
960C2#1059505611yescharacteristic
961C2#1059528611yescharacteristic
962C2#1059539111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63885C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63879C2semidirect
3. C2×#63878C2semidirect
4. #10592675C2semidirect
5. C3×#4989C2semidirect
6. C3×#4988C2semidirect
7. #10591386C2semidirect
8. #10591385C2semidirect
9. #10591381C2semidirect
10. #10591376C2semidirect
11. #10591372C2semidirect
12. #10591369C2semidirect
13. #10591305C2semidirect
14. #10591284C2semidirect
15. #10591243C2semidirect
47. #63885C4semidirect
67. #4989D3semidirect
68. #4988D3semidirect
104. C2×C3×D12C2×C4semidirect
113. C2×#625C2×C4semidirect
119. C2×D3×Dic3C2×C4semidirect
123. #3750C2×C4semidirect
130. C3×(C2×D3)⋊C4C2×C4semidirect
140. (C2×D3)⋊Dic3C2×C4semidirect
142. Dic32D4semidirect
369. C2×D12C4×D3semidirect
407. (C2×D3)⋊C4C4×D3semidirect
818. C32#2324semidirect
951. C3#74385semidirect
952. C3#76296semidirect

Maximal subgroups

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

subgroupindex
C2×#638852
C2×#638792
C2×#638782
#105926752
C3×#49892
C3×#49882
#105913862
#105913852
#105913812
#105913762
#105913722
#105913692
#105913052
#105912842
#105912432
#762963
#743853