Finite Group Databasebeta

← #11806913

Subgroups — #11806913

Order 1152.

1807 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63911C211yesmaximal, characteristic
2C2×#63904C211yesmaximal, characteristic, complemented
3C2×C4×#626C211yesmaximal, characteristic, complemented
4C2×#63881C211yesmaximal, characteristic, complemented
5C2×#63880C211yesmaximal, characteristic, complemented
6#10592364C211yesmaximal, characteristic, complemented
7C3×#4665C211yesmaximal, characteristic, complemented
8C3×#4649C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic, complemented
10#10591384C211yesmaximal, characteristic, complemented
11#10591383C211yesmaximal, characteristic, complemented
12#10591383C211yesmaximal, characteristic, complemented
13#10591380C211yesmaximal, characteristic, complemented
14#10591376C211yesmaximal, characteristic, complemented
15#10591242C211yesmaximal, characteristic, complemented
16#74679—31nomaximal
17#73653—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×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
49#63911C418yescomplemented
50#63904—24no—
51C4×#626—24no—
52#63881—24no—
53#63880—24no—
54C32×#95C2211yescharacteristic
55#63658C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57C3×C3⋊#95C2211yescharacteristic
58C2×#940—31no—
59C2×C4×#67—31no—
60C2×C4×#67—31no—
61C2×#893—31no—
62C2×#893—31no—
63C2×#67⋊C4—31no—
64C2×#67⋊C4—31no—
65C2×#874—31no—
66C2×C4×D12—31no—
67C2×C4×D12—31no—
68C3×#386—31no—
69C3×C4×C4⋊C4—31no—
70#5220—31no—
71#4988—31no—
72#4988—31no—
73#4957—31no—
74#4957—31no—
75#4957—31no—
76#4957—31no—
77#4939—31no—
78#4939—31no—
79C4×C4⋊Dic3—31no—
80#4665—31no—
81#4665—31no—
82#4665—31no—
83#4665—31no—
84#4665—31no—
85#4665—61no—
86#4665D311yescharacteristic, complemented
87#4649—31no—
88#4649D311yescharacteristic, complemented
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4⋊(C3⋊D3)—41no—
100C2×C4⋊(C3⋊D3)C2×C414yescomplemented
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—41no—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×D12—41no—
111C2×C3×D12—41no—
112C2×C3×D12C2×C414yescomplemented
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—41no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#626C2×C414yescomplemented
125C2×#626C2×C414yescomplemented
126C2×#626C2×C414yescomplemented
127C2×#626C2×C414yescomplemented
128C2×#624—22no—
129C2×#624—22no—
130C2×#624—41no—
131C2×D3×Dic3—22no—
132C2×D3×Dic3—22no—
133C2×D3×Dic3—41no—
134#3752—22no—
135#3752—22no—
136#3752—41no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—41no—
140C3×Dic3⋊C4—22no—
141C3×Dic3⋊C4D414yescomplemented
142C3×C4×Dic3—22no—
143C3×C4×Dic3—22no—
144C3×C4×Dic3C2×C414yescomplemented
145Dic3⋊Dic3—22no—
146Dic3⋊Dic3D414yescomplemented
147#3722—22no—
148#3722—22no—
149#3722—41no—
150(C2×D3)⋊Dic3—22no—
151(C2×D3)⋊Dic3—22no—
152(C2×D3)⋊Dic3—41no—
153Dic32—22no—
154Dic32—22no—
155#2366—91noSylow
156C22×C3×D4—31no—
157C23×C3×C4—31no—
158C22×#67—31no—
159C22×#67—31no—
160C22×#67—31no—
161C22×#67—31no—
162C23×Dic3—31no—
163C22×D12—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—31no—
168C22×D12—31no—
169C22×D12—61no—
170C22×D12C2×D311yescharacteristic
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—61no—
177C22×C4×D3C2×D311yescharacteristic
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C42—31no—
184C2×C3×C42—31no—
185C2×C3×C42—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189#940—38no—
190C4×#67—64no—
191C4×#67—64no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—61no—
208C2×(C2×D3)⋊C4—61no—
209C2×(C2×D3)⋊C4—61no—
210C2×(C2×D3)⋊C4C2×D311yescharacteristic
211C2×(C2×D3)⋊C4C2×D311yescharacteristic
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4C2×D311yescharacteristic
218C2×Dic3⋊C4C2×D311yescharacteristic
219C2×C4×Dic3—31no—
220C2×C4×Dic3—31no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3—31no—
223C2×C4×Dic3C2×D311yescharacteristic
224C2×C4×Dic3C2×D311yescharacteristic
225C2×C4×Dic3C2×D311yescharacteristic
226#893—64no—
227#893—64no—
228#67⋊C4—64no—
229#67⋊C4—64no—
230#874—38no—
231C4×D12—64no—
232C4×D12—64no—
233C3×#95—21no—
234C3×#95—31no—
235C3×#95—31no—
236C3×#95C2×D311yescharacteristic
237C3×#95C2×D311yescharacteristic
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—61no—
241C3⋊#95C2×D311yescharacteristic
242C3⋊#95C2×D311yescharacteristic
243C23×C32C2411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C22×C412yes—
257C22×C3⋊D3C22×C412yes—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3C22×C412yes—
271C22×C3×D3C22×C412yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4C22×C412yes—
280C2×C32×C4C2×D412yes—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3C2×D412yes—
287C4⋊(C3⋊D3)—44no—
288C4×C3⋊D3—44no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3C22×C412yes—
300C2×C3×Dic3C22×C412yes—
301C2×C3×Dic3C2×D412yes—
302C2×C3×Dic3C2×D412yes—
303C2×C3×Dic3C2×D412yes—
304C2×C3×Dic3C2×D412yes—
305C2×C3×Dic3#4112yes—
306C2×C3×Dic3#4112yes—
307C3×D12—44no—
308C3×C4×D3—44no—
309#626—28no—
310#626—28no—
311#626—28no—
312#626—28no—
313#624—44no—
314D3×Dic3—44no—
315C2×#127—91no—
316C2×C4×D4—91no—
317C2×C4×D4—91no—
318C2×C4×D4—91no—
319C2×C4×D4—91no—
320#390—91no—
321#390—91no—
322#390—91no—
323#390—91no—
324#386—31no—
325#386—91no—
326#386—91no—
327#386—91no—
328C4×C4⋊C4—31no—
329C4×C4⋊C4—91no—
330C24×C3—31no—
331C24×C3—31no—
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—31no—
336C23×D3—61no—
337C23×D3—61no—
338C23×D3C22×D311yescharacteristic
339C23×D3C22×D311yescharacteristic
340C2×C3×D4—34no—
341C2×C3×D4—121no—
342C2×C3×D4—121no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—62no—
353C22×C3×C4—62no—
354C22×C3×C4—121no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—34no—
364C2×#67—34no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—62no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—62no—
380C22×Dic3—62no—
381C22×Dic3—121no—
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C2×D12—34no—
389C2×D12—34no—
390C2×D12—34no—
391C2×D12—34no—
392C2×D12—34no—
393C2×D12—34no—
394C2×D12—41no—
395C2×D12—41no—
396C2×D12—64no—
397C2×D12—62no—
398C2×D12—62no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—62no—
404C2×D12—62no—
405C2×D12—121no—
406C2×D12—121no—
407C2×D12—121no—
408C2×D12—121no—
409C2×D12—122no—
410C2×D12—122no—
411C2×D12C4×D314yescomplemented
412C2×C4×D3—22no—
413C2×C4×D3—22no—
414C2×C4×D3—41no—
415C2×C4×D3—62no—
416C2×C4×D3—62no—
417C2×C4×D3—62no—
418C2×C4×D3—62no—
419C2×C4×D3—62no—
420C2×C4×D3—62no—
421C2×C4×D3—62no—
422C2×C4×D3—62no—
423C2×C4×D3—62no—
424C2×C4×D3—62no—
425C2×C4×D3—122no—
426C2×C4×D3—122no—
427C2×C4×D3—121no—
428C2×C4×D3—121no—
429C2×C4×D3—121no—
430C2×C4×D3—121no—
431C2×C4×D3—121no—
432C2×C4×D3—122no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—62no—
435C3×C22⋊C4—62no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—121no—
438C3×C42—34no—
439C3×C42—62no—
440C3×C42—62no—
441#217—62no—
442#217—62no—
443#217—121no—
444(C2×D3)⋊C4—22no—
445(C2×D3)⋊C4—22no—
446(C2×D3)⋊C4—41no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—62no—
456(C2×D3)⋊C4—62no—
457(C2×D3)⋊C4—122no—
458(C2×D3)⋊C4—122no—
459(C2×D3)⋊C4—121no—
460(C2×D3)⋊C4—121no—
461(C2×D3)⋊C4—121no—
462(C2×D3)⋊C4—121no—
463(C2×D3)⋊C4—121no—
464(C2×D3)⋊C4—122no—
465C4⋊Dic3—34no—
466C4⋊Dic3—62no—
467Dic3⋊C4—22no—
468Dic3⋊C4—34no—
469Dic3⋊C4—62no—
470Dic3⋊C4D1214yescomplemented
471C4×Dic3—22no—
472C4×Dic3—22no—
473C4×Dic3—62no—
474C4×Dic3—62no—
475C4×Dic3—62no—
476C4×Dic3—62no—
477C4×Dic3C4×D314yescomplemented
478C22×C32C23×C411yescharacteristic
479C22×C32C22×D411yescharacteristic
480C22×C32C22×D411yescharacteristic
481C22×C32C2×#4111yescharacteristic
482C22×C32C2×#4111yescharacteristic
483C22×C32H(5,𝔽2)11yescharacteristic
484C22×C32H(5,𝔽2)11yescharacteristic
485C2×C3⋊D3—22no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3—22no—
488C2×C3⋊D3—22no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—41no—
492C2×C3⋊D3—41no—
493C2×C3⋊D3—41no—
494C2×C3⋊D3—41no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—41no—
498C2×C3⋊D3—41no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3—41no—
508C2×C3×D3—41no—
509C2×C3×D3—41no—
510C2×C3×D3—41no—
511C2×C3×D3—41no—
512C2×C3×D3—41no—
513C32×C4—22no—
514C32×C4—22no—
515C32×C4—41no—
516C3⋊Dic3—22no—
517C3⋊Dic3—41no—
518C3×Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3—41no—
521C3×Dic3—41no—
522C3×Dic3C4×D414yescomplemented
523C3×Dic3C4×D414yescomplemented
524C22×D4—31no—
525C22×D4—91no—
526C22×D4—91no—
527C22×D4—91no—
528C22×D4—91no—
529C22×D4—91no—
530C23×C4—31no—
531C23×C4—91no—
532C23×C4—91no—
533C23×C4—91no—
534#127—98no—
535C4×D4—184no—
536C4×D4—184no—
537C4×D4—184no—
538C4×D4—184no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—91no—
547C2×C22⋊C4—91no—
548C2×C22⋊C4—91no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C42—31no—
556C2×C42—31no—
557C2×C42—31no—
558C2×C42—91no—
559C2×C42—91no—
560#95—31no—
561#95—31no—
562#95—91no—
563#95D3211yescharacteristic
564C23×C3—21no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3C23×D311yescharacteristic
580C23×C3C23×D311yescharacteristic
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—32no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—32no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3—121no—
632C22×D3—121no—
633C22×D3—121no—
634C22×D3—121no—
635C22×D3C2×C4×D312yes—
636C22×D3C2×C4×D312yes—
637C3×D4—124no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
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—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—124no—
680C2×C3×C4C2×C4×D312yes—
681C2×C3×C4C2×C4×D312yes—
682C2×C3×C4C2×D1212yes—
683C2×C3×C4D3×D412yes—
684#67—68no—
685#67—68no—
686#67—68no—
687#67—68no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—62no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—124no—
717C2×Dic3C2×C4×D312yes—
718C2×Dic3C2×C4×D312yes—
719C2×Dic3C2×D1212yes—
720C2×Dic3C2×D1212yes—
721C2×Dic3#23512yes—
722C2×Dic3D3×D412yes—
723C2×Dic3D3×D412yes—
724C2×Dic3#23912yes—
725D12—44no—
726D12—68no—
727D12—68no—
728D12—68no—
729D12—68no—
730D12—124no—
731D12—124no—
732D12—128no—
733C4×D3—44no—
734C4×D3—124no—
735C4×D3—124no—
736C4×D3—124no—
737C4×D3—124no—
738C4×D3—124no—
739C4×D3—128no—
740C2×C32C2×C4×D411yescharacteristic
741C2×C32C2×C4×D411yescharacteristic
742C2×C32#51811yescharacteristic
743C2×C32D4211yescharacteristic
744C2×C32#55011yescharacteristic
745C2×C32#55011yescharacteristic
746C2×C32#55911yescharacteristic
747C3⋊D3—42no—
748C3⋊D3—42no—
749C3×D3—42no—
750C3×D3—42no—
751C24—31no—
752C24—31no—
753C24—91no—
754C24—91no—
755C2×D4—34no—
756C2×D4—94no—
757C2×D4—94no—
758C2×D4—94no—
759C2×D4—94no—
760C2×D4—94no—
761C2×D4—121no—
762C2×D4—121no—
763C2×D4—182no—
764C2×D4—182no—
765C2×D4—182no—
766C2×D4—182no—
767C2×D4—182no—
768C2×D4—182no—
769C2×D4—182no—
770C2×D4—182no—
771C2×D4—361no—
772C2×D4—361no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—31no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—62no—
780C22×C4—62no—
781C22×C4—91no—
782C22×C4—91no—
783C22×C4—121no—
784C22×C4—182no—
785C22×C4—182no—
786C22×C4—182no—
787C22×C4—182no—
788C22×C4—182no—
789C22×C4—182no—
790C22×C4—361no—
791C22×C4—361no—
792C22×C4—361no—
793C22×C4C2×D3211yescharacteristic
794C22×C4C2×D3211yescharacteristic
795C22×C4C2×D3211yescharacteristic
796C4⋊C4—34no—
797C4⋊C4—62no—
798C4⋊C4—94no—
799C4⋊C4—182no—
800C22⋊C4—62no—
801C22⋊C4—62no—
802C22⋊C4—121no—
803C22⋊C4—182no—
804C22⋊C4—182no—
805C22⋊C4—182no—
806C22⋊C4—182no—
807C22⋊C4—182no—
808C22⋊C4—182no—
809C22⋊C4—361no—
810C22⋊C4—361no—
811C22⋊C4—361no—
812C42—34no—
813C42—62no—
814C42—62no—
815C42—182no—
816C42—182no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3—121no—
837C22×C3—121no—
838C22×C3C22×C4×D311yescharacteristic
839C22×C3C22×C4×D311yescharacteristic
840C22×C3C22×D1211yescharacteristic
841C22×C3C2×#23511yescharacteristic
842C22×C3C2×D3×D411yescharacteristic
843C22×C3C2×D3×D411yescharacteristic
844C22×C3C2×D3×D411yescharacteristic
845C22×C3#100411yescharacteristic
846C22×C3#100411yescharacteristic
847C22×C3C2×#23911yescharacteristic
848C22×C3D3×#4111yescharacteristic
849C22×C3D3×#4111yescharacteristic
850C22×C3#100911yescharacteristic
851C22×C3#100911yescharacteristic
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—22no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—64no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—122no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3—122no—
883C2×D3—122no—
884C2×D3—122no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3—122no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—121no—
894C2×D3—121no—
895C2×D3—121no—
896C2×D3—121no—
897C2×D3—121no—
898C2×D3—121no—
899C2×D3—121no—
900C2×D3—121no—
901C2×D3—121no—
902C2×D3—121no—
903C2×D3—121no—
904C2×D3—241no—
905C2×D3—241no—
906C2×D3—241no—
907C2×D3—241no—
908C3×C4—22no—
909C3×C4—22no—
910C3×C4—22no—
911C3×C4—22no—
912C3×C4—34no—
913C3×C4—34no—
914C3×C4—42no—
915C3×C4—42no—
916C3×C4—41no—
917C3×C4—41no—
918C3×C4—62no—
919C3×C4—62no—
920C3×C4—81no—
921C3×C4—121no—
922C3×C4—121no—
923Dic3—22no—
924Dic3—22no—
925Dic3—41no—
926Dic3—41no—
927Dic3—62no—
928Dic3—62no—
929Dic3—122no—
930Dic3—121no—
931Dic3—121no—
932Dic3—241no—
933Dic3C4×D1214yescomplemented
934Dic3#89314yescomplemented
935C32#236611yescharacteristic, complemented, Sylow
936C23—32no—
937C23—32no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—92no—
951C23—92no—
952C23—181no—
953C23—181no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23—181no—
958C23—181no—
959C23—181no—
960C23—181no—
961C23—181no—
962C23—181no—
963C23—181no—
964C23C22×D3211yescharacteristic
965D4—124no—
966D4—188no—
967D4—188no—
968D4—188no—
969D4—188no—
970D4—364no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—32no—
979C2×C4—32no—
980C2×C4—32no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—32no—
984C2×C4—32no—
985C2×C4—32no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—92no—
997C2×C4—124no—
998C2×C4—181no—
999C2×C4—181no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4—364no—
1004C2×C4—364no—
1005C2×C4—364no—
1006C2×C4C4×D3212yes—
1007C2×C4D3×D1212yes—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—122no—
1016C2×C3—122no—
1017C2×C3C2×C4×D1211yescharacteristic
1018C2×C3#548611yescharacteristic
1019C2×C3C2×#89311yescharacteristic
1020C2×C3#552111yescharacteristic
1021C2×C3C4×D3×D411yescharacteristic
1022C2×C3C4×D3×D411yescharacteristic
1023C2×C3D4×D1211yescharacteristic
1024C2×C3#555311yescharacteristic
1025C2×C3#557711yescharacteristic
1026C2×C3#558511yescharacteristic
1027C2×C3#559011yescharacteristic
1028C2×C3#559911yescharacteristic
1029C2×C3#559911yescharacteristic
1030C2×C3#566411yescharacteristic
1031D3—42no—
1032D3—42no—
1033D3—124no—
1034D3—122no—
1035D3—122no—
1036D3—122no—
1037D3—122no—
1038D3—242no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—121no—
1046C22—121no—
1047C22—121no—
1048C22—121no—
1049C22—121no—
1050C22—121no—
1051C22—121no—
1052C22—121no—
1053C22—182no—
1054C22—182no—
1055C22—182no—
1056C22—182no—
1057C22—182no—
1058C22—182no—
1059C22—361no—
1060C22—361no—
1061C22—361no—
1062C22—361no—
1063C22—361no—
1064C22—361no—
1065C22—361no—
1066C22—361no—
1067C22C2×C4×D3211yescharacteristic
1068C22C2×D3×D1211yescharacteristic
1069C22D3×#23511yescharacteristic
1070C22D32×D411yescharacteristic
1071C22#6431411yescharacteristic
1072C22#6431411yescharacteristic
1073C22D3×#23911yescharacteristic
1074C4—22no—
1075C4—22no—
1076C4—34no—
1077C4—34no—
1078C4—41no—
1079C4—62no—
1080C4—62no—
1081C4—121no—
1082C4—121no—
1083C4—182no—
1084C4—361no—
1085C3—21no—
1086C3#7365311yescharacteristic, complemented
1087C3#7467911yescharacteristic, complemented
1088C2—122no—
1089C2—122no—
1090C2—362no—
1091C2—362no—
1092C2C4×D3×D1211yescharacteristic
1093C2#1059418211yescharacteristic
1094C2#1059424611yescharacteristic
1095C2#1059427711yescharacteristic
1096C2#1059452411yescharacteristic
1097C2#1059454911yescharacteristic
1098C2D3×#89311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63911C2
hypercenter#95D32
hypocenterC32#2366
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63904C2semidirect
3. C2×C4×#626C2semidirect
4. C2×#63881C2semidirect
5. C2×#63880C2semidirect
6. #10592364C2semidirect
7. C3×#4665C2semidirect
8. C3×#4649C2semidirect
9. #10591384C2semidirect
10. #10591384C2semidirect
11. #10591383C2semidirect
12. #10591383C2semidirect
13. #10591380C2semidirect
14. #10591376C2semidirect
15. #10591242C2semidirect
49. #63911C4semidirect
86. #4665D3semidirect
88. #4649D3semidirect
100. C2×C4⋊(C3⋊D3)C2×C4semidirect
112. C2×C3×D12C2×C4semidirect
124. C2×#626C2×C4semidirect
125. C2×#626C2×C4semidirect
126. C2×#626C2×C4semidirect
127. C2×#626C2×C4semidirect
141. C3×Dic3⋊C4D4semidirect
144. C3×C4×Dic3C2×C4semidirect
146. Dic3⋊Dic3D4semidirect
411. C2×D12C4×D3semidirect
470. Dic3⋊C4D12semidirect
477. C4×Dic3C4×D3semidirect
522. C3×Dic3C4×D4semidirect
523. C3×Dic3C4×D4semidirect
933. Dic3C4×D12semidirect
934. Dic3#893semidirect
935. C32#2366semidirect
1086. C3#73653semidirect
1087. C3#74679semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
C2×#639042
C2×C4×#6262
C2×#638812
C2×#638802
#105923642
C3×#46652
C3×#46492
#105913842
#105913832
#105913802
#105913762
#105912422
#746793
#736533