Finite Group Databasebeta

← #11817743

Subgroups — #11817743

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2C2×#63861C211yesmaximal, characteristic, complemented
3C3×#4993C211yesmaximal, characteristic, complemented
4C3×#4983C211yesmaximal, characteristic, complemented
5#10591387C211yesmaximal, characteristic
6#10591384C211yesmaximal, characteristic
7#10591337C211yesmaximal, characteristic, complemented
8#10591292C211yesmaximal, characteristic
9#10591290C211yesmaximal, characteristic, complemented
10#10591286C211yesmaximal, characteristic, complemented
11#10591283C211yesmaximal, characteristic, complemented
12#10591271C211yesmaximal, characteristic, complemented
13#10591258C211yesmaximal, characteristic, complemented
14#10591241C211yesmaximal, characteristic, complemented
15#10591203C211yesmaximal, characteristic, complemented
16#78027—31nomaximal
17#77763—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#626C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64101—24no—
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46#63861—24no—
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#898—31no—
56C2×#892—31no—
57C2×#892—31no—
58C2×#892—61no—
59C2×#879—31no—
60C3×#399—31no—
61C3×#398—31no—
62#4993—31no—
63#4993—31no—
64#4993D311yescharacteristic, complemented
65#4990—31no—
66#4990—31no—
67#4989—31no—
68#4988—31no—
69#4983D311yescharacteristic, complemented
70#4976—31no—
71#4976—31no—
72Dic3×C4⋊C4—31no—
73#4959—31no—
74#4957—31no—
75#4956—31no—
76#4951—31no—
77#4945—31no—
78#4672—31no—
79#4669—31no—
80#4669—31no—
81#4668—31no—
82#4665—31no—
83#4654—31no—
84#4653—31no—
85#4649—31no—
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×#626—22no—
105C2×#626—22no—
106C2×#626—41no—
107C32×C4⋊C4—22no—
108#3752—22no—
109#3752—22no—
110C4⋊(C3⋊Dic3)D414yescomplemented
111C4×C3⋊Dic3—22no—
112C4×C3⋊Dic3—22no—
113C3×(C2×D3)⋊C4—22no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—41no—
116C3×Dic3⋊C4—22no—
117C3×Dic3⋊C4—22no—
118C3×Dic3⋊C4—41no—
119C3×Dic3⋊C4—41no—
120C3×Dic3⋊C4—41no—
121#3724—22no—
122#3724—22no—
123Dic3⋊Dic3—22no—
124#3722—22no—
125#3722—22no—
126#3722—41no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130Dic32—22no—
131Dic32—22no—
132#2479—91noSylow
133C22×#67—31no—
134C22×D12—31no—
135C22×C4×D3—31no—
136C22×C4×D3—31no—
137C22×C4×D3—61no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4C2×D311yescharacteristic
145C2×C3×C4⋊C4C2×D311yescharacteristic
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—61no—
166C2×(C2×D3)⋊C4—61no—
167C2×(C2×D3)⋊C4C2×D311yescharacteristic
168C2×(C2×D3)⋊C4C2×D311yescharacteristic
169C2×(C2×D3)⋊C4C2×D311yescharacteristic
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—61no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4C2×D311yescharacteristic
180C2×Dic3⋊C4C2×D311yescharacteristic
181C2×Dic3⋊C4C2×D311yescharacteristic
182C2×Dic3⋊C4C2×D311yescharacteristic
183C2×Dic3⋊C4C2×D311yescharacteristic
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—61no—
193C2×C4×Dic3—61no—
194#898—64no—
195#892—64no—
196#892—64no—
197#892—68no—
198#879—64no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C23×C32C2411yescharacteristic
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3#4112yes—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2×D412yes—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D412yes—
246C2×C3⋊Dic3C2×D412yes—
247C2×C3⋊Dic3#4112yes—
248C4×C3⋊D3—28no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
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×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3#4112yes—
269C2×C3×Dic3#4112yes—
270#626—44no—
271C2×#126—91no—
272C2×#117—91no—
273#399—31no—
274#399—91no—
275#398—31no—
276#394—91no—
277#390—91no—
278#389—91no—
279#388—91no—
280#388—91no—
281#388—91no—
282#387—91no—
283#386—91no—
284#385—91no—
285C4×C4⋊C4—91no—
286C24×C3—31no—
287C23×D3—31no—
288C23×D3—31no—
289C23×D3—61no—
290C23×D3C22×D311yescharacteristic
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—62no—
308C2×#67—62no—
309C2×#67—121no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C2×D12—62no—
327C2×D12—62no—
328C2×D12—121no—
329C2×C4×D3—62no—
330C2×C4×D3—62no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—64no—
334C2×C4×D3—64no—
335C2×C4×D3—64no—
336C2×C4×D3—62no—
337C2×C4×D3—62no—
338C3×C4⋊C4—24no—
339C3×C4⋊C4—22no—
340C3×C4⋊C4—22no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—121no—
344C3×C4⋊C4—121no—
345C3×C4⋊C4—121no—
346C3×C22⋊C4—62no—
347C3×C22⋊C4—62no—
348C3×C22⋊C4—121no—
349#217—62no—
350#217—62no—
351#217—62no—
352(C2×D3)⋊C4—22no—
353(C2×D3)⋊C4—22no—
354(C2×D3)⋊C4—41no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—64no—
366(C2×D3)⋊C4—64no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—121no—
369(C2×D3)⋊C4—121no—
370C4⋊Dic3—34no—
371C4⋊Dic3—34no—
372C4⋊Dic3—64no—
373C4⋊Dic3—62no—
374Dic3⋊C4—22no—
375Dic3⋊C4—22no—
376Dic3⋊C4—41no—
377Dic3⋊C4—41no—
378Dic3⋊C4—41no—
379Dic3⋊C4—62no—
380Dic3⋊C4—62no—
381Dic3⋊C4—62no—
382Dic3⋊C4—62no—
383Dic3⋊C4—62no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C4×Dic3—62no—
391C4×Dic3—64no—
392C4×Dic3—64no—
393C4×Dic3—62no—
394C22×C32C22×D411yescharacteristic
395C22×C32C2×#4111yescharacteristic
396C22×C32C2×#4111yescharacteristic
397C22×C32C2×#4111yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32H(5,𝔽2)11yescharacteristic
400C22×C322−1+411yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—22no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C32×C4—22no—
416C32×C4—41no—
417C32×C4—41no—
418C3⋊Dic3—22no—
419C3⋊Dic3—22no—
420C3⋊Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×D4—91no—
429C23×C4—91no—
430#126—184no—
431#117—184no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—91no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4—91no—
440C2×C4⋊C4—91no—
441C2×C4⋊C4D3211yescharacteristic
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C22⋊C4—91no—
448C2×C22⋊C4—91no—
449C2×C22⋊C4—91no—
450C2×C22⋊C4—91no—
451C2×C22⋊C4—91no—
452C2×C22⋊C4—91no—
453C2×C42—91no—
454C2×C42—91no—
455C2×C42—91no—
456C2×C42—91no—
457#95—31no—
458#95—31no—
459#95—31no—
460#95—31no—
461#95—91no—
462#95—91no—
463#95—91no—
464#95—91no—
465C23×C3—21no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3C23×D311yescharacteristic
474C23×C3C23×D311yescharacteristic
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—32no—
483C22×D3—32no—
484C22×D3—62no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—121no—
500C22×D3—121no—
501C22×D3—121no—
502C22×D3—121no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—22no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4D3×D412yes—
550C2×C3×C4D3×D412yes—
551#67—124no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—32no—
572C2×Dic3—32no—
573C2×Dic3—32no—
574C2×Dic3—32no—
575C2×Dic3—32no—
576C2×Dic3—32no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—62no—
580C2×Dic3—62no—
581C2×Dic3—62no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3#23712yes—
599C2×Dic3#23912yes—
600D12—124no—
601C4×D3—616no—
602C4×D3—68no—
603C4×D3—68no—
604C2×C32#52511yescharacteristic
605C2×C32#52911yescharacteristic
606C2×C32#54211yescharacteristic
607C2×C32#54711yescharacteristic
608C2×C32#55011yescharacteristic
609C2×C32#55111yescharacteristic
610C2×C32#55211yescharacteristic
611C3⋊D3—42no—
612C3×D3—81no—
613C24—31no—
614C24—91no—
615C2×D4—182no—
616C2×D4—182no—
617C2×D4—361no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—91no—
626C22×C4—91no—
627C22×C4—91no—
628C22×C4—182no—
629C22×C4—182no—
630C22×C4—182no—
631C22×C4C2×D3211yescharacteristic
632C22×C4C2×D3211yescharacteristic
633C22×C4C2×D3211yescharacteristic
634C4⋊C4—22no—
635C4⋊C4—62no—
636C4⋊C4—62no—
637C4⋊C4—94no—
638C4⋊C4—121no—
639C4⋊C4—121no—
640C4⋊C4—121no—
641C4⋊C4—182no—
642C4⋊C4—182no—
643C4⋊C4—182no—
644C22⋊C4—62no—
645C22⋊C4—62no—
646C22⋊C4—121no—
647C22⋊C4—182no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—361no—
655C42—182no—
656C42—182no—
657C42—182no—
658C42—182no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3C2×D3×D411yescharacteristic
674C22×C3C2×D3×D411yescharacteristic
675C22×C3C2×#23711yescharacteristic
676C22×C3#100411yescharacteristic
677C22×C3#100411yescharacteristic
678C22×C3C2×#23911yescharacteristic
679C22×C3#100711yescharacteristic
680C22×C3#100711yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3D3×#4111yescharacteristic
683C22×C3D3×#4111yescharacteristic
684C22×C3D3×#4111yescharacteristic
685C22×C3D3×#4111yescharacteristic
686C22×C3D3×#4111yescharacteristic
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—64no—
695C2×D3—62no—
696C2×D3—62no—
697C2×D3—62no—
698C2×D3—62no—
699C2×D3—62no—
700C2×D3—62no—
701C2×D3—122no—
702C2×D3—122no—
703C2×D3—122no—
704C2×D3—122no—
705C2×D3—122no—
706C2×D3—122no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C3×C4—24no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731Dic3—22no—
732Dic3—22no—
733Dic3—41no—
734Dic3—41no—
735Dic3—41no—
736Dic3—41no—
737Dic3—41no—
738Dic3—64no—
739Dic3—62no—
740Dic3—62no—
741Dic3—62no—
742Dic3—62no—
743Dic3—62no—
744Dic3—62no—
745Dic3—122no—
746Dic3—122no—
747C32#247911yescharacteristic, complemented, Sylow
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—92no—
756C23—181no—
757C23—181no—
758C23—181no—
759C23—181no—
760C23—181no—
761C23—181no—
762C23C22×D3211yescharacteristic
763D4—364no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—92no—
794C2×C4—92no—
795C2×C4—92no—
796C2×C4—188no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4#381112yes—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—241no—
812C2×C3#559911yescharacteristic
813C2×C3#563111yescharacteristic
814C2×C3#563711yescharacteristic
815C2×C3#563911yescharacteristic
816C2×C3#564011yescharacteristic
817C2×C3#564011yescharacteristic
818C2×C3#564911yescharacteristic
819C2×C3#565611yescharacteristic
820C2×C3#565611yescharacteristic
821C2×C3#565911yescharacteristic
822C2×C3#569111yescharacteristic
823C2×C3#569311yescharacteristic
824C2×C3#571811yescharacteristic
825C2×C3#572611yescharacteristic
826D3—81no—
827D3—124no—
828D3—122no—
829D3—122no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—182no—
838C22—182no—
839C22—182no—
840C22—361no—
841C22—361no—
842C22—361no—
843C22—361no—
844C22#6430611yescharacteristic
845C22#6430611yescharacteristic
846C22D3×#23711yescharacteristic
847C22#6431311yescharacteristic
848C22#6431611yescharacteristic
849C22D3×#23911yescharacteristic
850C22C2×#381111yescharacteristic
851C4—22no—
852C4—41no—
853C4—41no—
854C4—62no—
855C4—62no—
856C4—121no—
857C4—121no—
858C4—121no—
859C4—121no—
860C4—121no—
861C4—182no—
862C4—182no—
863C4—182no—
864C3—21no—
865C3#7776311yescharacteristic, complemented
866C3#7802711yescharacteristic, complemented
867C2—241no—
868C2—362no—
869C2#1059433411yescharacteristic
870C2#1059444111yescharacteristic
871C2#1059456911yescharacteristic
872C2#1059465311yescharacteristic
873C2#1059492011yescharacteristic
874C2#1059516411yescharacteristic
875C2#1059534111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64101C2semidirect
2. C2×#63861C2semidirect
3. C3×#4993C2semidirect
4. C3×#4983C2semidirect
7. #10591337C2semidirect
9. #10591290C2semidirect
10. #10591286C2semidirect
11. #10591283C2semidirect
12. #10591271C2semidirect
13. #10591258C2semidirect
14. #10591241C2semidirect
15. #10591203C2semidirect
64. #4993D3semidirect
69. #4983D3semidirect
110. C4⋊(C3⋊Dic3)D4semidirect
747. C32#2479semidirect
865. C3#77763semidirect
866. C3#78027semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#638612
C3×#49932
C3×#49832
#105913872
#105913842
#105913372
#105912922
#105912902
#105912862
#105912832
#105912712
#105912582
#105912412
#105912032
#780273
#777633