Finite Group Databasebeta

← #11805434

Subgroups — #11805434

Order 1152.

1765 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic
4C2×#63952C211yesmaximal, characteristic
5C2×#63883C211yesmaximal, characteristic, complemented
6C3×#5210C211yesmaximal, characteristic, complemented
7#10591718C211yesmaximal, characteristic, complemented
8#10591716C211yesmaximal, characteristic, complemented
9#10591374C211yesmaximal, characteristic, complemented
10#10591367C211yesmaximal, characteristic, complemented
11#10591337C211yesmaximal, characteristic, complemented
12#10591290C211yesmaximal, characteristic, complemented
13#10591256C211yesmaximal, characteristic, complemented
14#10591244C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16C4⋊C4×#67—31nomaximal
17#74393—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C4×#638—24no—
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×Dic3⋊C4—24no—
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×#3724C2211yescharacteristic
40C2×#3724C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49#63952—24no—
50#63952C418yescomplemented
51#63883—24no—
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C22×C3×C4⋊C4—31no—
59C2×C4×#67—31no—
60C2×C4×#67—31no—
61C2×C4×#67—31no—
62C2×C4×#67—31no—
63C2×C4×#67—61no—
64C22×Dic3⋊C4D311yescharacteristic, complemented
65C2×D3×C4⋊C4—31no—
66C2×D3×C4⋊C4—31no—
67C2×#67⋊C4—31no—
68C2×#67⋊C4—31no—
69C3×#385—31no—
70#5212—31no—
71#5210—31no—
72#5210D311yescharacteristic, complemented
73#4989—31no—
74#4989—31no—
75#4989—31no—
76#4987—31no—
77#4976—31no—
78#4976—31no—
79#4976—31no—
80#4975—31no—
81#4975—31no—
82Dic3×C4⋊C4—31no—
83#4950—31no—
84#4942—31no—
85#4668—31no—
86#4667—31no—
87#4649—31no—
88#4647—31no—
89C24×C32C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638C2×C414yes—
97C2×#638D414yes—
98C2×#638Q814yes—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—22no—
104C2×C4×C3⋊D3—41no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3—22no—
107C22×C3×Dic3—22no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3—41no—
110C22×C3×Dic3C2×C414yescomplemented
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—22no—
123C2×#624—41no—
124C2×#624C2×C414yescomplemented
125#3757—22no—
126#3752—22no—
127#3750—22no—
128C4×C3⋊Dic3—22no—
129C3×#217—22no—
130C3×#217C2×C414yescomplemented
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4—41no—
136C3×Dic3⋊C4D414yescomplemented
137#3724—22no—
138#3724C2×C414yescomplemented
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—22no—
142Dic3⋊Dic3—41no—
143#3722—22no—
144#3722C2×C414yescomplemented
145Dic32—22no—
146Dic32C2×C414yescomplemented
147D4×C4⋊C4—91noSylow
148C23×C3×C4—21no—
149C23×C3×C4—31no—
150C23×C3×C4—31no—
151C23×C3×C4C2×D311yescharacteristic
152C23×C3×C4C2×D311yescharacteristic
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—61no—
156C23×Dic3C2×D311yescharacteristic
157C23×Dic3C2×D311yescharacteristic
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—61no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—64no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—61no—
177C2×#217C2×D311yescharacteristic
178C2×#217C2×D311yescharacteristic
179C4×#67—38no—
180C4×#67—64no—
181C4×#67—64no—
182C4×#67—64no—
183C4×#67—68no—
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—61no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×Dic3⋊C4—24no—
196C2×Dic3⋊C4—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⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—61no—
207C2×Dic3⋊C4C2×D311yescharacteristic
208C2×Dic3⋊C4C2×D311yescharacteristic
209C2×Dic3⋊C4C2×D311yescharacteristic
210C2×Dic3⋊C4C2×D311yescharacteristic
211C2×Dic3⋊C4C2×D311yescharacteristic
212C2×Dic3⋊C4C2×D311yescharacteristic
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218C2×C4×Dic3—31no—
219C2×C4×Dic3—61no—
220D3×C4⋊C4—64no—
221D3×C4⋊C4—64no—
222#67⋊C4—38no—
223#67⋊C4—64no—
224C3×#95—31no—
225C3×#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95C2×D311yescharacteristic
235C3⋊#95C2×D311yescharacteristic
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32C22×C412yes—
241C23×C32C2×D412yes—
242C23×C32C2×Q812yes—
243C23×C32C2411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3C22×C412yes—
249C22×C3⋊D3C2×D412yes—
250C22×C3⋊D3C2×Q812yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—44no—
257C2×C32×C4C2×D412yes—
258#638C4⋊C4116yescomplemented
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⋊Dic3C22×C412yes—
266C2×C3⋊Dic3C2×D412yes—
267C2×C3⋊Dic3C2×Q812yes—
268C4×C3⋊D3—44no—
269C2×C3×Dic3—21no—
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—28no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—44no—
288C2×C3×Dic3C22×C412yes—
289C2×C3×Dic3C22×C412yes—
290C2×C3×Dic3C22×C412yes—
291C2×C3×Dic3C22×C412yes—
292C2×C3×Dic3C2×D412yes—
293C2×C3×Dic3C2×D412yes—
294C2×C3×Dic3#4112yes—
295#624—28no—
296#624—44no—
297C2×C4×D4—91no—
298C2×C4×D4—91no—
299C2×C4×D4—91no—
300C22×C4⋊C4—31no—
301C22×C4⋊C4—91no—
302#389—91no—
303#389—91no—
304#385—31no—
305#385—91no—
306#385—91no—
307#385—91no—
308#384—91no—
309#380—91no—
310#380—91no—
311C4×C4⋊C4—91no—
312C24×C3—21no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C23×D3—31no—
316C23×D3—31no—
317C23×D3—61no—
318C22×C3×C4—24no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—34no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—42no—
335C22×C3×C4—41no—
336C22×C3×C4—41no—
337C22×C3×C4—42no—
338C22×C3×C4—62no—
339C22×C3×C4—62no—
340C22×C3×C4—62no—
341C22×C3×C4—62no—
342C22×C3×C4—121no—
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C2×#67—34no—
348C2×#67—34no—
349C2×#67—34no—
350C2×#67—34no—
351C2×#67—34no—
352C2×#67—34no—
353C2×#67—64no—
354C2×#67—64no—
355C2×#67—64no—
356C22×Dic3—22no—
357C22×Dic3—22no—
358C22×Dic3—22no—
359C22×Dic3—22no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—41no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3C4×D314yescomplemented
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C2×C4×D3—34no—
380C2×C4×D3—34no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—62no—
390C2×C4×D3—64no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—122no—
395C2×C4×D3—121no—
396C2×C4×D3—121no—
397C2×C4×D3—121no—
398C2×C4×D3—121no—
399C2×C4×D3—122no—
400C3×C4⋊C4—34no—
401C3×C4⋊C4—62no—
402C3×C4⋊C4—62no—
403C3×C4⋊C4—62no—
404C3×C4⋊C4—62no—
405C3×C4⋊C4—121no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—62no—
408#217—22no—
409#217—64no—
410#217—62no—
411#217—62no—
412#217C4×D314yescomplemented
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—64no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422C4⋊Dic3—62no—
423C4⋊Dic3—121no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—41no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434Dic3⋊C4—62no—
435Dic3⋊C4—62no—
436Dic3⋊C4—64no—
437Dic3⋊C4—62no—
438Dic3⋊C4—62no—
439Dic3⋊C4—121no—
440Dic3⋊C4#6714yescomplemented
441C4×Dic3—34no—
442C4×Dic3—34no—
443C4×Dic3—62no—
444C4×Dic3—62no—
445C4×Dic3—62no—
446C4×Dic3—62no—
447C4×Dic3—64no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—22no—
451C22×C32—22no—
452C22×C32—22no—
453C22×C32—22no—
454C22×C32C2×C4⋊C414yescomplemented
455C22×C32C23×C411yescharacteristic
456C22×C32C22×D411yescharacteristic
457C22×C32C22×D411yescharacteristic
458C22×C32C22×Q811yescharacteristic
459C22×C32C2×#4111yescharacteristic
460C22×C32H(5,𝔽2)11yescharacteristic
461C22×C322−1+411yescharacteristic
462C2×C3⋊D3—22no—
463C2×C3⋊D3—22no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—22no—
468C2×C3⋊D3C2×C4⋊C414yescomplemented
469C32×C4—22no—
470C32×C4—41no—
471C3⋊Dic3—41no—
472C3⋊Dic3—41no—
473C3⋊Dic3C2×C4⋊C414yescomplemented
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3C4×D414yescomplemented
482C22×D4—91no—
483C23×C4—31no—
484C23×C4—31no—
485C23×C4—91no—
486C23×C4—91no—
487C23×C4—91no—
488C23×C4D3211yescharacteristic
489C4×D4—98no—
490C4×D4—184no—
491C4×D4—184no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—64no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—91no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—184no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C42—91no—
514C2×C42—91no—
515C2×C42—91no—
516#95—31no—
517#95—31no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95—91no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3C2×C4×D312yes—
539C23×C3C2×C4×D312yes—
540C23×C3D3×D412yes—
541C23×C3D3×D412yes—
542C23×C3D3×Q812yes—
543C23×C3D3×Q812yes—
544C23×C3C23×D311yescharacteristic
545C23×C3C23×D311yescharacteristic
546C22×D3—32no—
547C22×D3—32no—
548C22×D3—32no—
549C22×D3—32no—
550C22×D3—32no—
551C22×D3—32no—
552C22×D3—62no—
553C22×D3—62no—
554C22×D3—62no—
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—121no—
564C22×D3—121no—
565C22×D3—121no—
566C22×D3—121no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—22no—
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—22no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—44no—
591C2×C3×C4—44no—
592C2×C3×C4—48no—
593C2×C3×C4—68no—
594C2×C3×C4—61no—
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—61no—
611C2×C3×C4—124no—
612C2×C3×C4D3×D412yes—
613C2×C3×C4C2×#6712yes—
614#67—316no—
615#67—316no—
616#67—616no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—28no—
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—21no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—32no—
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—44no—
642C2×Dic3—62no—
643C2×Dic3—62no—
644C2×Dic3—62no—
645C2×Dic3—62no—
646C2×Dic3—62no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—121no—
663C2×Dic3C2×C4×D312yes—
664C2×Dic3C2×C4×D312yes—
665C2×Dic3C2×C4×D312yes—
666C2×Dic3C2×C4×D312yes—
667C2×Dic3#23512yes—
668C2×Dic3C2×#6712yes—
669C2×Dic3C2×#6712yes—
670C4×D3—68no—
671C4×D3—68no—
672C4×D3—124no—
673C4×D3—124no—
674C4×D3—124no—
675C4×D3—124no—
676C4×D3—128no—
677C2×C32—24no—
678C2×C32C22×C4⋊C411yescharacteristic
679C2×C32C2×C4×D411yescharacteristic
680C2×C32#52011yescharacteristic
681C2×C32D4211yescharacteristic
682C2×C32#54711yescharacteristic
683C2×C32D4×Q811yescharacteristic
684C2×C32#55411yescharacteristic
685C3⋊D3—24no—
686C24—91no—
687C24C2×D3211yescharacteristic
688C2×D4—94no—
689C2×D4—94no—
690C2×D4—94no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—31no—
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—41no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—62no—
706C22×C4—62no—
707C22×C4—94no—
708C22×C4—91no—
709C22×C4—91no—
710C22×C4—91no—
711C22×C4—121no—
712C22×C4—182no—
713C22×C4—182no—
714C22×C4—182no—
715C22×C4—182no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—361no—
719C22×C4—361no—
720C22×C4C2×D3211yescharacteristic
721C22×C4C2×D3211yescharacteristic
722C4⋊C4—34no—
723C4⋊C4—62no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—94no—
728C4⋊C4—121no—
729C4⋊C4—182no—
730C4⋊C4—182no—
731C4⋊C4—182no—
732C4⋊C4—182no—
733C4⋊C4—182no—
734C4⋊C4—361no—
735C22⋊C4—34no—
736C22⋊C4—62no—
737C22⋊C4—94no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C42—94no—
742C42—182no—
743C42—182no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—24no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3D3×C4⋊C414yescomplemented
771C22×C3D3×C4⋊C414yescomplemented
772C22×C3C22×C4×D311yescharacteristic
773C22×C3C22×C4×D311yescharacteristic
774C22×C3C2×#23511yescharacteristic
775C22×C3C2×D3×D411yescharacteristic
776C22×C3C2×D3×D411yescharacteristic
777C22×C3C2×D3×D411yescharacteristic
778C22×C3#100411yescharacteristic
779C22×C3#100411yescharacteristic
780C22×C3C2×D3×Q811yescharacteristic
781C22×C3C2×D3×Q811yescharacteristic
782C22×C3#100711yescharacteristic
783C22×C3D3×#4111yescharacteristic
784C22×C3#101011yescharacteristic
785C22×C3C22×#6711yescharacteristic
786C2×D3—34no—
787C2×D3—34no—
788C2×D3—64no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
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—
807C3×C4—24no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—34no—
811C3×C4—42no—
812C3×C4—41no—
813C3×C4—41no—
814C3×C4—62no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—121no—
819C3×C4—121no—
820C3×C4—121no—
821Dic3—22no—
822Dic3—22no—
823Dic3—22no—
824Dic3—22no—
825Dic3—34no—
826Dic3—34no—
827Dic3—41no—
828Dic3—41no—
829Dic3—41no—
830Dic3—64no—
831Dic3—122no—
832Dic3—122no—
833Dic3—121no—
834Dic3—121no—
835Dic3—121no—
836Dic3—121no—
837Dic3C4×#6714yescomplemented
838C32D4×C4⋊C411yescharacteristic, complemented, Sylow
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—92no—
844C23—92no—
845C23—92no—
846C23—181no—
847C23—181no—
848C23—181no—
849C23—181no—
850C23#379712yes—
851C23C4×D3212yes—
852C23#381112yes—
853C23C22×D3211yescharacteristic
854D4—916no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—44no—
868C2×C4—68no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—92no—
887C2×C4—92no—
888C2×C4—92no—
889C2×C4—124no—
890C2×C4—188no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—181no—
896C2×C4—181no—
897C2×C4—364no—
898C2×C4—364no—
899C2×C4D3×#6712yes—
900C2×C3—24no—
901C2×C3—24no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—44no—
910C2×C3C2×D3×C4⋊C411yescharacteristic
911C2×C3C2×D3×C4⋊C411yescharacteristic
912C2×C3#550411yescharacteristic
913C2×C3#550711yescharacteristic
914C2×C3#551111yescharacteristic
915C2×C3C4×D3×D411yescharacteristic
916C2×C3#554611yescharacteristic
917C2×C3#559011yescharacteristic
918C2×C3#563211yescharacteristic
919C2×C3#563611yescharacteristic
920C2×C3#565511yescharacteristic
921C2×C3C2×C4×#6711yescharacteristic
922C2×C3D4×#6711yescharacteristic
923C2×C3Q8×#6711yescharacteristic
924D3—64no—
925D3—64no—
926D3—124no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—94no—
934C22—182no—
935C22—182no—
936C22—182no—
937C22—182no—
938C22—182no—
939C22—182no—
940C22#6388314yescomplemented
941C22#6429711yescharacteristic
942C22C2×#379711yescharacteristic
943C22C2×C4×D3211yescharacteristic
944C22D3×#23511yescharacteristic
945C22C2×D3×#6711yescharacteristic
946C22C2×#381111yescharacteristic
947C22#6433011yescharacteristic
948C4—22no—
949C4—34no—
950C4—41no—
951C4—62no—
952C4—62no—
953C4—62no—
954C4—62no—
955C4—94no—
956C4—121no—
957C4—121no—
958C4—121no—
959C4—361no—
960C4—361no—
961C3—21no—
962C3#7439311yescharacteristic, complemented
963C3C4⋊C4×#6711yescharacteristic, complemented
964C2—24no—
965C2—184no—
966C2#1059480311yescharacteristic
967C2#1059487411yescharacteristic
968C2C2×#6388311yescharacteristic
969C2#1059491711yescharacteristic
970C2#1059495611yescharacteristic
971C2C4×D3×#6711yescharacteristic
972C2#1059552611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic3⋊C4C2semidirect
5. C2×#63883C2semidirect
6. C3×#5210C2semidirect
7. #10591718C2semidirect
8. #10591716C2semidirect
9. #10591374C2semidirect
10. #10591367C2semidirect
11. #10591337C2semidirect
12. #10591290C2semidirect
13. #10591256C2semidirect
14. #10591244C2semidirect
15. #10591241C2semidirect
50. #63952C4semidirect
64. C22×Dic3⋊C4D3semidirect
72. #5210D3semidirect
110. C22×C3×Dic3C2×C4semidirect
124. C2×#624C2×C4semidirect
130. C3×#217C2×C4semidirect
136. C3×Dic3⋊C4D4semidirect
138. #3724C2×C4semidirect
144. #3722C2×C4semidirect
146. Dic32C2×C4semidirect
258. #638C4⋊C4semidirect
370. C22×Dic3C4×D3semidirect
412. #217C4×D3semidirect
440. Dic3⋊C4#67semidirect
454. C22×C32C2×C4⋊C4semidirect
468. C2×C3⋊D3C2×C4⋊C4semidirect
473. C3⋊Dic3C2×C4⋊C4semidirect
481. C3×Dic3C4×D4semidirect
770. C22×C3D3×C4⋊C4semidirect
771. C22×C3D3×C4⋊C4semidirect
837. Dic3C4×#67semidirect
838. C32D4×C4⋊C4semidirect
940. C22#63883semidirect
962. C3#74393semidirect
963. C3C4⋊C4×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C22×C3×Dic3⋊C42
C2×#639522
C2×#638832
C3×#52102
#105917182
#105917162
#105913742
#105913672
#105913372
#105912902
#105912562
#105912442
#105912412
C4⋊C4×#673
#743933