Finite Group Databasebeta

← #11803580

Subgroups — #11803580

Order 1152.

1479 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#877C211yesmaximal, characteristic, complemented
2C2×#63978C211yesmaximal, characteristic
3C2×C4×#626C211yesmaximal, characteristic, complemented
4#10592655C211yesmaximal, characteristic, complemented
5C3×#4956C211yesmaximal, characteristic, complemented
6#10591716C211yesmaximal, characteristic, complemented
7#10591707C211yesmaximal, characteristic, complemented
8#10591704C211yesmaximal, characteristic, complemented
9#10591383C211yesmaximal, characteristic, complemented
10#10591327C211yesmaximal, characteristic, complemented
11#10591290C211yesmaximal, characteristic, complemented
12#10591285C211yesmaximal, characteristic, complemented
13#10591277C211yesmaximal, characteristic, complemented
14#10591258C211yesmaximal, characteristic, complemented
15#10591242C211yesmaximal, characteristic, complemented
16#82236—31nomaximal
17#74665—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#877—24no—
35#63978C418yescomplemented
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49C4×#626—24no—
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×#117—31no—
57C2×#939—31no—
58C2×#930—31no—
59C2×C4×#67—31no—
60C2×#877D311yescharacteristic, complemented
61C2×C4×D12—31no—
62C3×#386—31no—
63#5221—31no—
64#5212—31no—
65#5210—31no—
66#4990—31no—
67#4990—31no—
68#4989—31no—
69#4989—31no—
70#4957—31no—
71#4957—31no—
72#4957—31no—
73#4957—31no—
74#4956—31no—
75#4956—31no—
76#4956—61no—
77#4956D311yescharacteristic, complemented
78#4944—31no—
79#4942—31no—
80#4939—31no—
81C4×C4⋊Dic3—31no—
82#4928—31no—
83#4669—31no—
84#4668—31no—
85#4649—31no—
86#4647—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638—41no—
93C2×#638—41no—
94C2×#638C2×C414yescomplemented
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—41no—
100C2×C4×C3⋊D3—41no—
101C2×C3×#67—41no—
102C2×C3×#67—41no—
103C2×C3×#67C2×C414yescomplemented
104C22×C3×Dic3—22no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3C2×C414yescomplemented
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626C2×C414yes—
120C32×C22⋊C4—22no—
121#3757—41no—
122#3752—41no—
123C3×#217—22no—
124C3×#217—41no—
125C3×(C2×D3)⋊C4—41no—
126C3×Dic3⋊C4—22no—
127C3×Dic3⋊C4—22no—
128C3×C4×Dic3—22no—
129C3×C4×Dic3D414yescomplemented
130#3724—41no—
131Dic3⋊Dic3—22no—
132Dic3⋊Dic3—22no—
133Dic3⋊Dic3—41no—
134Dic3⋊Dic3C2×C414yescomplemented
135#3722—22no—
136#3722—41no—
137#3722C2×C414yescomplemented
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—41no—
140(C2×D3)⋊Dic3C2×C414yescomplemented
141Dic32—41no—
142Dic32—41no—
143#2324—91noSylow
144C22×C3×D4—31no—
145C23×C3×C4—31no—
146C23×C3×C4—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—61no—
151C22×#67C2×D311yescharacteristic
152C23×Dic3C2×D311yescharacteristic
153C22×D12—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—61no—
157C22×C4×D3C2×D311yescharacteristic
158C3×#117—64no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—21no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4C2×D311yescharacteristic
166C2×C3×C22⋊C4C2×D311yescharacteristic
167C2×C3×C42—31no—
168C2×C3×C42—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—61no—
175C2×#217C2×D311yescharacteristic
176C2×#217C2×D311yescharacteristic
177#939—38no—
178#930—38no—
179C4×#67—64no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×Dic3⋊C4C2×D311yescharacteristic
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3C2×D311yescharacteristic
210C2×C4×Dic3C2×D311yescharacteristic
211#877—24no—
212C4×D12—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×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32C22×C412yes—
234C23×C32C2411yescharacteristic
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⋊D3C22×C412yes—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
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×C4C2×D412yes—
255#638—44no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
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⋊Dic3C22×C412yes—
265C4×C3⋊D3—44no—
266C3×#67—44no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—28no—
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×Dic3—21no—
283C2×C3×Dic3C22×C412yes—
284C2×C3×Dic3C22×C412yes—
285C2×C3×Dic3C22×C412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3#4112yes—
289C3×C4×D3—44no—
290#626—28no—
291C2×#121—91no—
292C2×C4×D4—91no—
293C2×#117—31no—
294#390—91no—
295#390—91no—
296#390—91no—
297#389—91no—
298#388—91no—
299#388—91no—
300#386—31no—
301#386—91no—
302#385—91no—
303#385—91no—
304#380—91no—
305C4×C4⋊C4—91no—
306C24×C3—21no—
307C24×C3—31no—
308C24×C3C22×D311yescharacteristic
309C24×C3C22×D311yescharacteristic
310C23×D3—31no—
311C23×D3—31no—
312C23×D3—61no—
313C23×D3C22×D311yescharacteristic
314C2×C3×D4—34no—
315C2×C3×D4—121no—
316C2×C3×D4—121no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—34no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—121no—
331C22×C3×C4—121no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—34no—
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—41no—
340C2×#67—41no—
341C2×#67—64no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—121no—
345C2×#67—121no—
346C2×#67—121no—
347C2×#67—121no—
348C2×#67—122no—
349C2×#67—122no—
350C2×#67C4×D314yescomplemented
351C22×Dic3—22no—
352C22×Dic3—22no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3C4×D314yescomplemented
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C2×D12—34no—
371C2×D12—62no—
372C2×D12—62no—
373C2×C4×D3—22no—
374C2×C4×D3—41no—
375C2×C4×D3—41no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—122no—
379C2×C4×D3—121no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C2×C4×D3—121no—
383C2×C4×D3—122no—
384C2×C4×D3—122no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C22⋊C4—22no—
388C3×C22⋊C4—22no—
389C3×C22⋊C4—42no—
390C3×C22⋊C4—62no—
391C3×C22⋊C4—121no—
392C3×C22⋊C4—121no—
393C3×C42—34no—
394C3×C42—62no—
395#217—22no—
396#217—34no—
397#217—41no—
398#217—62no—
399#217—121no—
400#217—121no—
401#217—121no—
402#217—122no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—41no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—121no—
411(C2×D3)⋊C4—121no—
412(C2×D3)⋊C4—121no—
413(C2×D3)⋊C4—121no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4—122no—
416C4⋊Dic3—34no—
417C4⋊Dic3—62no—
418C4⋊Dic3—62no—
419C4⋊Dic3—121no—
420Dic3⋊C4—22no—
421Dic3⋊C4—22no—
422Dic3⋊C4—34no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—121no—
426Dic3⋊C4—121no—
427Dic3⋊C4—121no—
428C4×Dic3—22no—
429C4×Dic3—121no—
430C4×Dic3—121no—
431C4×Dic3—121no—
432C4×Dic3—121no—
433C4×Dic3#6714yescomplemented
434C22×C32—22no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32C23×C411yescharacteristic
442C22×C32C22×D411yescharacteristic
443C22×C32C2×#4111yescharacteristic
444C22×C32H(5,𝔽2)11yescharacteristic
445C22×C32H(5,𝔽2)11yescharacteristic
446C22×C32H(5,𝔽2)11yescharacteristic
447C22×C322−1+411yescharacteristic
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C32×C4—22no—
463C32×C4—41no—
464C3⋊Dic3—22no—
465C3⋊Dic3—41no—
466C3⋊Dic3—41no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3C4×D414yes—
474C22×D4—31no—
475C22×D4—91no—
476C22×D4—91no—
477C23×C4—31no—
478C23×C4—31no—
479C23×C4—91no—
480#121—98no—
481C4×D4—184no—
482#117—64no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—91no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4D3211yescharacteristic
502C2×C42—31no—
503C2×C42—31no—
504C2×C42—91no—
505C2×C42—91no—
506#95—31no—
507#95—31no—
508#95—91no—
509#95—91no—
510#95—91no—
511#95—91no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—22no—
526C23×C3—32no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3C2×C4×D312yes—
540C23×C3C2×C4×D312yes—
541C23×C3C23×D311yescharacteristic
542C23×C3C23×D311yescharacteristic
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—32no—
550C22×D3—32no—
551C22×D3—62no—
552C22×D3—62no—
553C22×D3—62no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—61no—
561C22×D3—61no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—121no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—121no—
570C22×D3C2×C4×D312yes—
571C3×D4—124no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—22no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—68no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—124no—
611C2×C3×C4D3×D412yes—
612C2×C3×C4C2×#6712yes—
613#67—44no—
614#67—68no—
615#67—124no—
616#67—124no—
617#67—128no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—28no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—32no—
635C2×Dic3—32no—
636C2×Dic3—62no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—62no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—121no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3—121no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3C2×C4×D312yes—
662C2×Dic3C2×C4×D312yes—
663C2×Dic3C2×C4×D312yes—
664C2×Dic3#23512yes—
665C2×Dic3C2×#6712yes—
666C2×Dic3C2×#6712yes—
667D12—68no—
668C4×D3—44no—
669C4×D3—124no—
670C4×D3—124no—
671C4×D3—128no—
672C2×C32—42no—
673C2×C32C2×C4×D411yescharacteristic
674C2×C32#51811yescharacteristic
675C2×C32#52011yescharacteristic
676C2×C32#53511yescharacteristic
677C2×C32#53711yescharacteristic
678C2×C32#54011yescharacteristic
679C2×C32#54211yescharacteristic
680C3⋊D3—42no—
681C3×D3—42no—
682C24—31no—
683C24—91no—
684C24C2×D3211yescharacteristic
685C2×D4—34no—
686C2×D4—94no—
687C2×D4—94no—
688C2×D4—121no—
689C2×D4—121no—
690C2×D4—182no—
691C2×D4—182no—
692C2×D4—361no—
693C2×D4—361no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—34no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—62no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—91no—
706C22×C4—91no—
707C22×C4—91no—
708C22×C4—121no—
709C22×C4—121no—
710C22×C4—182no—
711C22×C4—361no—
712C22×C4—361no—
713C22×C4C2×D3211yescharacteristic
714C22×C4C2×D3211yescharacteristic
715C4⋊C4—62no—
716C4⋊C4—62no—
717C4⋊C4—94no—
718C4⋊C4—182no—
719C4⋊C4—182no—
720C4⋊C4—361no—
721C4⋊C4—361no—
722C22⋊C4—22no—
723C22⋊C4—62no—
724C22⋊C4—94no—
725C22⋊C4—94no—
726C22⋊C4—121no—
727C22⋊C4—121no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—361no—
731C22⋊C4—361no—
732C22⋊C4—361no—
733C22⋊C4—361no—
734C42—34no—
735C42—62no—
736C42—361no—
737C42—361no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3C22×C4×D311yescharacteristic
774C22×C3C22×C4×D311yescharacteristic
775C22×C3C2×#23511yescharacteristic
776C22×C3C2×D3×D411yescharacteristic
777C22×C3#100411yescharacteristic
778C22×C3#100411yescharacteristic
779C22×C3#100411yescharacteristic
780C22×C3D3×#4111yescharacteristic
781C22×C3#100911yescharacteristic
782C22×C3#100911yescharacteristic
783C22×C3#100911yescharacteristic
784C22×C3#101011yescharacteristic
785C22×C3#101011yescharacteristic
786C22×C3C22×#6711yescharacteristic
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—41no—
794C2×D3—64no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—122no—
802C2×D3—122no—
803C2×D3—122no—
804C2×D3—122no—
805C2×D3—122no—
806C2×D3—122no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3—121no—
814C2×D3—121no—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—34no—
818C3×C4—42no—
819C3×C4—41no—
820C3×C4—41no—
821C3×C4—62no—
822C3×C4—62no—
823C3×C4—62no—
824C3×C4—81no—
825C3×C4—121no—
826C3×C4—121no—
827C3×C4—121no—
828Dic3—22no—
829Dic3—22no—
830Dic3—22no—
831Dic3—41no—
832Dic3—41no—
833Dic3—41no—
834Dic3—62no—
835Dic3—62no—
836Dic3—122no—
837Dic3—122no—
838Dic3—121no—
839Dic3—121no—
840Dic3—121no—
841Dic3—121no—
842Dic3—241no—
843Dic3C4×#6714yes—
844C32#232411yescharacteristic, complemented, Sylow
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—32no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—92no—
859C23—181no—
860C23—181no—
861C23—181no—
862C23—181no—
863C23—181no—
864C23—181no—
865C23C4×D3212yes—
866C23C22×D3211yescharacteristic
867D4—124no—
868D4—188no—
869D4—364no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—32no—
881C2×C4—68no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—92no—
898C2×C4—124no—
899C2×C4—181no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—364no—
908C2×C4D3×#6712yes—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—42no—
917C2×C3—42no—
918C2×C3—82no—
919C2×C3—122no—
920C2×C3#548611yescharacteristic
921C2×C3#552111yescharacteristic
922C2×C3#552311yescharacteristic
923C2×C3#553411yescharacteristic
924C2×C3#553511yescharacteristic
925C2×C3C4×D3×D411yescharacteristic
926C2×C3#554611yescharacteristic
927C2×C3#559211yescharacteristic
928C2×C3#560811yescharacteristic
929C2×C3#561511yescharacteristic
930C2×C3#566211yescharacteristic
931C2×C3C2×C4×#6711yescharacteristic
932C2×C3#583011yescharacteristic
933C2×C3#583311yescharacteristic
934D3—42no—
935D3—124no—
936D3—122no—
937D3—122no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—121no—
949C22—121no—
950C22—121no—
951C22—121no—
952C22—182no—
953C22—182no—
954C22—182no—
955C22—361no—
956C22—361no—
957C22—361no—
958C22—361no—
959C22C2×C4×D3211yescharacteristic
960C22D3×#23511yescharacteristic
961C22#6430911yescharacteristic
962C22#6431411yescharacteristic
963C22#6431411yescharacteristic
964C22#6431411yescharacteristic
965C22C2×D3×#6711yescharacteristic
966C4—22no—
967C4—34no—
968C4—41no—
969C4—62no—
970C4—62no—
971C4—62no—
972C4—121no—
973C4—121no—
974C4—121no—
975C4—182no—
976C4—361no—
977C4—361no—
978C3—21no—
979C3#7466511yescharacteristic, complemented
980C3#8223611yescharacteristic, complemented
981C2—42no—
982C2—122no—
983C2—362no—
984C2#1059404911yescharacteristic
985C2#1059418211yescharacteristic
986C2#1059420511yescharacteristic
987C2#1059420611yescharacteristic
988C2C4×D3×#6711yescharacteristic
989C2#1059523211yescharacteristic
990C2#1059523811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63978C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2324
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×C3×#877C2semidirect
3. C2×C4×#626C2semidirect
4. #10592655C2semidirect
5. C3×#4956C2semidirect
6. #10591716C2semidirect
7. #10591707C2semidirect
8. #10591704C2semidirect
9. #10591383C2semidirect
10. #10591327C2semidirect
11. #10591290C2semidirect
12. #10591285C2semidirect
13. #10591277C2semidirect
14. #10591258C2semidirect
15. #10591242C2semidirect
35. #63978C4semidirect
60. C2×#877D3semidirect
77. #4956D3semidirect
94. C2×#638C2×C4semidirect
103. C2×C3×#67C2×C4semidirect
106. C22×C3×Dic3C2×C4semidirect
129. C3×C4×Dic3D4semidirect
134. Dic3⋊Dic3C2×C4semidirect
137. #3722C2×C4semidirect
140. (C2×D3)⋊Dic3C2×C4semidirect
350. C2×#67C4×D3semidirect
362. C22×Dic3C4×D3semidirect
433. C4×Dic3#67semidirect
844. C32#2324semidirect
979. C3#74665semidirect
980. C3#82236semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
C2×#639782
C2×C4×#6262
#105926552
C3×#49562
#105917162
#105917072
#105917042
#105913832
#105913272
#105912902
#105912852
#105912772
#105912582
#105912422
#822363
#746653