Finite Group Databasebeta

← #11808729

Subgroups — #11808729

Order 1152.

1131 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63877C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic, complemented
3#10592682C211yesmaximal, characteristic, complemented
4C3×#4993C211yesmaximal, characteristic
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic
7Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic
8#10591338C211yesmaximal, characteristic, complemented
9#10591309C211yesmaximal, characteristic
10#10591308C211yesmaximal, characteristic
11#10591293C211yesmaximal, characteristic
12#10591243C211yesmaximal, characteristic, complemented
13Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#10591199C211yesmaximal, characteristic, complemented
15#10591198C211yesmaximal, characteristic, complemented
16#78018—31nomaximal
17#73778—31nomaximal
18C22×#627C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63877—24no—
44#63837—24no—
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#887—31no—
56C2×#877—31no—
57C2×#872—31no—
58C2×C4×Dic6—31no—
59C3×#399—31no—
60C3×C4×C4⋊C4—31no—
61#4994—31no—
62#4993D311yescharacteristic
63#4985—31no—
64#4983—31no—
65#4983—31no—
66#4983—31no—
67#4983—61no—
68#4979—31no—
69Dic3×C4⋊C4—31no—
70Dic3×C4⋊C4D311yescharacteristic, complemented
71#4948—31no—
72#4948—31no—
73#4947—31no—
74Dic3×C22⋊C4—31no—
75Dic3×C22⋊C4—31no—
76C4×(C2×D3)⋊C4—31no—
77C4×(C2×D3)⋊C4—31no—
78C4×Dic3⋊C4—31no—
79C4×Dic3⋊C4—31no—
80#4676—31no—
81#4673—31no—
82#4658—31no—
83#4657—31no—
84#4656—31no—
85#4649—31no—
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×#627—22no—
102C2×#627—22no—
103C2×#627—22no—
104C2×D3×Dic3—22no—
105C2×D3×Dic3—22no—
106C2×D3×Dic3Q814yescomplemented
107C32×C4⋊C4—22no—
108#3750—22no—
109#3750—22no—
110#3750—22no—
111C3×(C2×D3)⋊C4—22no—
112C3×(C2×D3)⋊C4—22no—
113C3×(C2×D3)⋊C4—22no—
114C3×C4⋊Dic3—22no—
115C3×Dic3⋊C4—22no—
116C3×Dic3⋊C4—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120#3724—22no—
121#3724—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—22no—
124(C2×D3)⋊Dic3—22no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127Dic32—22no—
128Dic32—22no—
129Dic32D414yes—
130#2396—91noSylow
131C23×Dic3—31no—
132C22×C4×D3—31no—
133C22×Dic6—31no—
134C22×Dic6—31no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4C2×D311yescharacteristic
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C42—31no—
145C2×C3×C42—31no—
146C2×C3×C42—31no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4C2×D311yescharacteristic
154C2×(C2×D3)⋊C4C2×D311yescharacteristic
155C2×(C2×D3)⋊C4C2×D311yescharacteristic
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3C2×D311yescharacteristic
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—61no—
172C2×Dic3⋊C4—61no—
173C2×Dic3⋊C4—61no—
174C2×Dic3⋊C4C2×D311yescharacteristic
175C2×Dic3⋊C4C2×D311yescharacteristic
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3C2×D311yescharacteristic
183C2×C4×Dic3C2×D311yescharacteristic
184C2×C4×Dic3C2×D311yescharacteristic
185#887—64no—
186#877—64no—
187#872—64no—
188C4×Dic6—64no—
189C3×#95—31no—
190C3×#95—31no—
191C3×#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—61no—
207C3⋊#95—61no—
208C3⋊#95—61no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C23×C32C2411yescharacteristic
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3C2×Q812yes—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4#4112yes—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C2×D412yes—
239C2×C3⋊Dic3C2×Q812yes—
240C2×C3⋊Dic3#4112yes—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
257C2×C3×Dic3C2×D412yes—
258C2×C3×Dic3C2×Q812yes—
259C2×C3×Dic3#4112yes—
260C2×C3×Dic3#4112yes—
261C2×C3×Dic3#4112yes—
262#627—28no—
263D3×Dic3—28no—
264C2×C4×Q8—91no—
265C2×#117—91no—
266#400—91no—
267#399—31no—
268#398—91no—
269#398—91no—
270#396—91no—
271#396—91no—
272#395—91no—
273#393—91no—
274C4×C4⋊C4—31no—
275C4×C4⋊C4—91no—
276C4×C4⋊C4—91no—
277C4×C22⋊C4—91no—
278C4×C22⋊C4—91no—
279C24×C3—31no—
280C23×D3C22×D311yescharacteristic
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—34no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—62no—
311C22×Dic3—62no—
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C2×C4×D3—34no—
320C2×C4×D3—62no—
321C2×C4×D3—62no—
322C2×Dic6—62no—
323C2×Dic6—62no—
324C2×Dic6—62no—
325C2×Dic6—62no—
326C2×Dic6—62no—
327C2×Dic6—62no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—42no—
331C3×C4⋊C4—62no—
332C3×C4⋊C4—62no—
333C3×C4⋊C4—62no—
334C3×C22⋊C4—62no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4—62no—
337C3×C42—62no—
338C3×C42—62no—
339C3×C42—62no—
340#217—62no—
341#217—62no—
342#217—62no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—22no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—62no—
349C4⋊Dic3—22no—
350C4⋊Dic3—62no—
351C4⋊Dic3—62no—
352Dic3⋊C4—22no—
353Dic3⋊C4—22no—
354Dic3⋊C4—62no—
355Dic3⋊C4—62no—
356Dic3⋊C4—62no—
357Dic3⋊C4—62no—
358Dic3⋊C4—62no—
359Dic3⋊C4—62no—
360Dic3⋊C4—62no—
361Dic3⋊C4—62no—
362Dic3⋊C4—62no—
363Dic3⋊C4—62no—
364Dic3⋊C4—62no—
365Dic3⋊C4—62no—
366Dic3⋊C4—122no—
367Dic3⋊C4—122no—
368Dic3⋊C4—122no—
369C4×Dic3—22no—
370C4×Dic3—22no—
371C4×Dic3—22no—
372C4×Dic3—34no—
373C4×Dic3—34no—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C4×Dic3—62no—
377C4×Dic3—62no—
378C22×C32C22×D411yescharacteristic
379C22×C32C22×Q811yescharacteristic
380C22×C32C2×#4111yescharacteristic
381C22×C32C2×#4111yescharacteristic
382C22×C32C2×#4111yescharacteristic
383C22×C32C2×#4111yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C32×C4—22no—
393C32×C4—41no—
394C32×C4—41no—
395C3⋊Dic3—22no—
396C3⋊Dic3—22no—
397C3⋊Dic3—22no—
398C3⋊Dic3—41no—
399C3×Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3C22⋊Q814yes—
406C22×Q8—91no—
407C23×C4—91no—
408C4×Q8—184no—
409#117—184no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—91no—
414C2×C4⋊C4—91no—
415C2×C4⋊C4—91no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4D3211yescharacteristic
421C2×C22⋊C4—31no—
422C2×C22⋊C4—31no—
423C2×C22⋊C4—31no—
424C2×C22⋊C4—91no—
425C2×C22⋊C4—91no—
426C2×C22⋊C4—91no—
427C2×C42—31no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—91no—
431C2×C42—91no—
432C2×C42—91no—
433#95—31no—
434#95—31no—
435#95—31no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443C23×C3—21no—
444C23×C3—32no—
445C23×C3—61no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3—61no—
450C23×C3—61no—
451C23×C3C23×D311yescharacteristic
452C23×C3C23×D311yescharacteristic
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3D3×Q812yes—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4#23512yes—
507C2×C3×C4#23712yes—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—32no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—32no—
527C2×Dic3—32no—
528C2×Dic3—32no—
529C2×Dic3—62no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—68no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3#23512yes—
561C2×Dic3#23512yes—
562C2×Dic3D3×D412yes—
563C2×Dic3D3×D412yes—
564C2×Dic3#23712yes—
565C2×Dic3D3×Q812yes—
566C4×D3—68no—
567Dic6—68no—
568Dic6—68no—
569C2×C32C2×C22⋊Q811yescharacteristic
570C2×C32#52511yescharacteristic
571C2×C32#52911yescharacteristic
572C2×C32#52911yescharacteristic
573C2×C32#53211yescharacteristic
574C2×C32#53311yescharacteristic
575C2×C32#53311yescharacteristic
576C3×D3—42no—
577C24—31no—
578C2×Q8—182no—
579C2×Q8—182no—
580C2×Q8—182no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—94no—
589C22×C4—91no—
590C22×C4—91no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—182no—
594C22×C4—182no—
595C22×C4C2×D3211yescharacteristic
596C22×C4C2×D3211yescharacteristic
597C22×C4C2×D3211yescharacteristic
598C4⋊C4—22no—
599C4⋊C4—62no—
600C4⋊C4—62no—
601C4⋊C4—62no—
602C4⋊C4—182no—
603C4⋊C4—182no—
604C4⋊C4—182no—
605C4⋊C4—182no—
606C4⋊C4—182no—
607C4⋊C4—182no—
608C4⋊C4—182no—
609C22⋊C4—62no—
610C22⋊C4—62no—
611C22⋊C4—62no—
612C22⋊C4—182no—
613C22⋊C4—182no—
614C22⋊C4—182no—
615C42—62no—
616C42—62no—
617C42—62no—
618C42—94no—
619C42—182no—
620C42—182no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—62no—
629C22×C3—62no—
630C22×C3—62no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×#23511yescharacteristic
636C22×C3C2×#23511yescharacteristic
637C22×C3C2×#23511yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×#23711yescharacteristic
641C22×C3C2×#23711yescharacteristic
642C22×C3C2×D3×Q811yescharacteristic
643C22×C3C2×D3×Q811yescharacteristic
644C22×C3D3×#4111yescharacteristic
645C22×C3D3×#4111yescharacteristic
646C22×C3D3×#4111yescharacteristic
647C22×C3D3×#4111yescharacteristic
648C22×C3D3×#4111yescharacteristic
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—34no—
659C3×C4—42no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672Dic3—22no—
673Dic3—22no—
674Dic3—22no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—62no—
679Dic3—62no—
680Dic3—62no—
681Dic3—62no—
682Dic3—62no—
683Dic3—62no—
684Dic3—122no—
685Dic3—122no—
686Dic3—122no—
687Dic3—121no—
688Dic3—121no—
689Dic3—241no—
690Dic3#89614yes—
691C32#239611yescharacteristic, complemented, Sylow
692C23—32no—
693C23—61no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23C22×D3211yescharacteristic
700Q8—188no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—32no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—92no—
731C2×C4—92no—
732C2×C4—92no—
733C2×C4—188no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4#380412yes—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—122no—
752C2×C3#547911yescharacteristic
753C2×C3C2×#89611yescharacteristic
754C2×C3#552811yescharacteristic
755C2×C3#554711yescharacteristic
756C2×C3#554811yescharacteristic
757C2×C3#557811yescharacteristic
758C2×C3#557811yescharacteristic
759C2×C3#562211yescharacteristic
760C2×C3#562211yescharacteristic
761C2×C3D3×C22⋊Q811yescharacteristic
762C2×C3#564911yescharacteristic
763C2×C3#564911yescharacteristic
764C2×C3#565611yescharacteristic
765C2×C3#571611yescharacteristic
766D3—42no—
767C22—62no—
768C22—62no—
769C22—62no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22D3×#23511yescharacteristic
775C22D3×#23511yescharacteristic
776C22D32×D411yescharacteristic
777C22D3×#23711yescharacteristic
778C22D32×Q811yescharacteristic
779C22#6431911yescharacteristic
780C22C2×#380411yescharacteristic
781C4—22no—
782C4—34no—
783C4—41no—
784C4—41no—
785C4—62no—
786C4—62no—
787C4—62no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—182no—
792C4—182no—
793C4—182no—
794C4—361no—
795C3—21no—
796C3#7377811yescharacteristic, complemented
797C3#7801811yescharacteristic, complemented
798C2—122no—
799C2#1059438611yescharacteristic
800C2#1059440411yescharacteristic
801C2D3×#89611yescharacteristic
802C2#1059461411yescharacteristic
803C2#1059494811yescharacteristic
804C2#1059513911yescharacteristic
805C2#1059536711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63837C2semidirect
3. #10592682C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
8. #10591338C2semidirect
12. #10591243C2semidirect
13. Dic3×Dic3⋊C4C2semidirect
14. #10591199C2semidirect
15. #10591198C2semidirect
70. Dic3×C4⋊C4D3semidirect
106. C2×D3×Dic3Q8semidirect
691. C32#2396semidirect
796. C3#73778semidirect
797. C3#78018semidirect

Maximal subgroups

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

subgroupindex
C2×#638772
C2×#638372
#105926822
C3×#49932
C3×Dic3×C4⋊C42
Dic3×(C2×D3)⋊C42
#105913382
#105913092
#105913082
#105912932
#105912432
Dic3×Dic3⋊C42
#105911992
#105911982
#780183
#737783