Finite Group Databasebeta

← #11808699

Subgroups — #11808699

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×#63855C211yesmaximal, characteristic
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10591354C211yesmaximal, characteristic, complemented
6#10591351C211yesmaximal, characteristic, complemented
7C4×#3724C211yesmaximal, characteristic, complemented
8C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
9#10591322C211yesmaximal, characteristic
10#10591319C211yesmaximal, characteristic
11#10591309C211yesmaximal, characteristic
12#10591303C211yesmaximal, characteristic
13C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic
14#10591210C211yesmaximal, characteristic, complemented
15#10591198C211yesmaximal, characteristic, complemented
16#73778—31nomaximal
17#73480—31nomaximal
18C22×#634C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C2×C32×C42C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C4×#634—24no—
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44#63855—24no—
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#926—31no—
56C2×#872—31no—
57C2×C4×Dic6—31no—
58C2×C4×Dic6—31no—
59C2×C4×Dic6—61no—
60C3×C4×C4⋊C4—31no—
61C3×C4×C22⋊C4—31no—
62C4×#217—31no—
63#4994—31no—
64#4993—31no—
65#4983—31no—
66#4979—31no—
67#4949—31no—
68#4948—31no—
69#4948—31no—
70#4947—31no—
71C4×(C2×D3)⋊C4—31no—
72C4×(C2×D3)⋊C4D311yescharacteristic
73C4×C4⋊Dic3—31no—
74C4×Dic3⋊C4—31no—
75C4×Dic3⋊C4—31no—
76C4×Dic3⋊C4—31no—
77C4×Dic3⋊C4D311yescharacteristic, complemented
78#4676—31no—
79#4673—31no—
80#4661—31no—
81#4660—31no—
82#4658—31no—
83#4657—31no—
84#4657—31no—
85#4656—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
94C2×#634—22no—
95C2×#634—22no—
96C2×#634—22no—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3Q814yescomplemented
107C32×C42—22no—
108C4⋊(C3⋊Dic3)—22no—
109#3750—22no—
110#3750—22no—
111C4×C3⋊Dic3—22no—
112C4×C3⋊Dic3D414yes—
113C3×(C2×D3)⋊C4—22no—
114C3×(C2×D3)⋊C4—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—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130#2396—91noSylow
131C23×C3×C4—31no—
132C22×C4×D3C2×D311yescharacteristic
133C22×Dic6—31no—
134C22×Dic6—31no—
135C22×Dic6—61no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C42—21no—
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42C2×D311yescharacteristic
145C2×C3×C42C2×D311yescharacteristic
146C2×#217—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)⋊C4—31no—
154C2×(C2×D3)⋊C4C2×D311yescharacteristic
155C2×(C2×D3)⋊C4C2×D311yescharacteristic
156#926—64no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—61no—
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—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—61no—
177C2×Dic3⋊C4—61no—
178C2×Dic3⋊C4C2×D311yescharacteristic
179C2×Dic3⋊C4C2×D311yescharacteristic
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—61no—
185C2×C4×Dic3—61no—
186C2×C4×Dic3C2×D311yescharacteristic
187C2×C4×Dic3C2×D311yescharacteristic
188C2×C4×Dic3C2×D311yescharacteristic
189#872—64no—
190C4×Dic6—64no—
191C4×Dic6—64no—
192C4×Dic6—68no—
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—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C23×C32C2411yescharacteristic
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3C2×Q812yes—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4C2×D412yes—
227C2×C32×C4C2×Q812yes—
228C2×C32×C4#4112yes—
229C2×C32×C4#4112yes—
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⋊Dic3—21no—
239C2×C3⋊Dic3C2×D412yes—
240C2×C3⋊Dic3C2×D412yes—
241C2×C3⋊Dic3#4112yes—
242#634—28no—
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×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×Q812yes—
262C2×C3×Dic3#4112yes—
263C2×C3×Dic3#4112yes—
264C3×C4×D3—28no—
265C2×C4×Q8—91no—
266C2×#117—91no—
267#400—91no—
268#399—91no—
269#398—91no—
270#398—91no—
271#396—91no—
272#396—91no—
273#395—91no—
274#393—91no—
275C4×C4⋊C4—31no—
276C4×C4⋊C4—91no—
277C4×C4⋊C4—91no—
278C4×C22⋊C4—31no—
279C4×C22⋊C4—91no—
280C24×C3—31no—
281C23×D3C22×D311yescharacteristic
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—34no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—62no—
294C22×C3×C4—62no—
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C2×C4×D3—22no—
321C2×C4×D3—22no—
322C2×C4×D3Dic614yescomplemented
323C2×Dic6—62no—
324C2×Dic6—62no—
325C2×Dic6—62no—
326C2×Dic6—62no—
327C2×Dic6—64no—
328C2×Dic6—64no—
329C2×Dic6—64no—
330C2×Dic6—62no—
331C2×Dic6—62no—
332C3×C4⋊C4—62no—
333C3×C4⋊C4—62no—
334C3×C22⋊C4—62no—
335C3×C22⋊C4—62no—
336C3×C42—24no—
337C3×C42—22no—
338C3×C42—22no—
339C3×C42—62no—
340C3×C42—62no—
341C3×C42—62no—
342#217—62no—
343#217—62no—
344#217—62no—
345#217—62no—
346(C2×D3)⋊C4—22no—
347(C2×D3)⋊C4—22no—
348(C2×D3)⋊C4—62no—
349(C2×D3)⋊C4—62no—
350(C2×D3)⋊C4—62no—
351(C2×D3)⋊C4—62no—
352C4⋊Dic3—62no—
353C4⋊Dic3—62no—
354C4⋊Dic3—62no—
355C4⋊Dic3—62no—
356C4⋊Dic3—62no—
357C4⋊Dic3—62no—
358C4⋊Dic3—64no—
359Dic3⋊C4—22no—
360Dic3⋊C4—22no—
361Dic3⋊C4—62no—
362Dic3⋊C4—62no—
363Dic3⋊C4—62no—
364Dic3⋊C4—62no—
365Dic3⋊C4—62no—
366Dic3⋊C4—62no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—64no—
371Dic3⋊C4—64no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375C4×Dic3—22no—
376C4×Dic3—22no—
377C4×Dic3—22no—
378C4×Dic3—34no—
379C4×Dic3—34no—
380C4×Dic3—64no—
381C4×Dic3—64no—
382C4×Dic3—62no—
383C4×Dic3—62no—
384C22×C32C22×D411yescharacteristic
385C22×C32C22×Q811yescharacteristic
386C22×C32C2×#4111yescharacteristic
387C22×C32C2×#4111yescharacteristic
388C22×C32C2×#4111yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C2×C3×D3—22no—
392C2×C3×D3—22no—
393C2×C3×D3—22no—
394C2×C3×D3—41no—
395C2×C3×D3—41no—
396C2×C3×D3—41no—
397C2×C3×D3—41no—
398C32×C4—22no—
399C32×C4—41no—
400C32×C4C22⋊Q814yes—
401C3⋊Dic3—22no—
402C3⋊Dic3—22no—
403C3⋊Dic3—22no—
404C3⋊Dic3—41no—
405C3×Dic3—22no—
406C3×Dic3—22no—
407C3×Dic3—22no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C22×Q8—91no—
413C23×C4—31no—
414C4×Q8—184no—
415#117—184no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—91no—
425C2×C4⋊C4—91no—
426C2×C4⋊C4—91no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—31no—
429C2×C22⋊C4—91no—
430C2×C22⋊C4—91no—
431C2×C22⋊C4—91no—
432C2×C22⋊C4—91no—
433C2×C42—31no—
434C2×C42—31no—
435C2×C42—31no—
436C2×C42—91no—
437C2×C42—91no—
438C2×C42D3211yescharacteristic
439#95—31no—
440#95—31no—
441#95—31no—
442#95—31no—
443#95—91no—
444#95—91no—
445#95—91no—
446#95—91no—
447#95—91no—
448#95—91no—
449C23×C3—21no—
450C23×C3—32no—
451C23×C3—61no—
452C23×C3—61no—
453C23×C3—61no—
454C23×C3—61no—
455C23×C3—61no—
456C23×C3—61no—
457C23×C3C23×D311yescharacteristic
458C23×C3C23×D311yescharacteristic
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3C2×Dic612yes—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—68no—
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—61no—
507C2×C3×C4C2×Dic612yes—
508C2×C3×C4#23512yes—
509C2×C3×C4#23512yes—
510C2×C3×C4#23512yes—
511C2×C3×C4D3×D412yes—
512C2×C3×C4D3×D412yes—
513C2×C3×C4#23712yes—
514C2×C3×C4D3×Q812yes—
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—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—62no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—62no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3C2×Dic612yes—
570C2×Dic3#23512yes—
571C2×Dic3#23512yes—
572C4×D3—28no—
573Dic6—616no—
574Dic6—68no—
575Dic6—68no—
576C2×C32C2×C22⋊Q811yescharacteristic
577C2×C32#52511yescharacteristic
578C2×C32#52911yescharacteristic
579C2×C32#52911yescharacteristic
580C2×C32#53211yescharacteristic
581C2×C32#53311yescharacteristic
582C2×C32#53311yescharacteristic
583C3×D3—42no—
584C24—31no—
585C2×Q8—182no—
586C2×Q8—182no—
587C2×Q8—182no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—34no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—91no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—91no—
602C22×C4C2×D3211yescharacteristic
603C22×C4C2×D3211yescharacteristic
604C22×C4C2×D3211yescharacteristic
605C4⋊C4—62no—
606C4⋊C4—62no—
607C4⋊C4—182no—
608C4⋊C4—182no—
609C4⋊C4—182no—
610C4⋊C4—182no—
611C4⋊C4—182no—
612C4⋊C4—182no—
613C4⋊C4—182no—
614C4⋊C4—182no—
615C4⋊C4—182no—
616C22⋊C4—62no—
617C22⋊C4—62no—
618C22⋊C4—182no—
619C22⋊C4—182no—
620C22⋊C4—182no—
621C22⋊C4—182no—
622C42—22no—
623C42—62no—
624C42—62no—
625C42—62no—
626C42—94no—
627C42—182no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C22×Dic611yescharacteristic
643C22×C3C2×#23511yescharacteristic
644C22×C3C2×#23511yescharacteristic
645C22×C3C2×#23511yescharacteristic
646C22×C3C2×#23511yescharacteristic
647C22×C3C2×#23511yescharacteristic
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×#23711yescharacteristic
651C22×C3C2×D3×Q811yescharacteristic
652C22×C3D3×#4111yescharacteristic
653C22×C3D3×#4111yescharacteristic
654C22×C3D3×#4111yescharacteristic
655C22×C3D3×#4111yescharacteristic
656C2×D3—22no—
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C3×C4—24no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—24no—
667C3×C4—42no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—62no—
671C3×C4—62no—
672C3×C4—62no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4#87814yes—
678C3×C4#89614yes—
679Dic3—22no—
680Dic3—22no—
681Dic3—22no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—64no—
687Dic3—64no—
688Dic3—62no—
689Dic3—62no—
690Dic3—62no—
691Dic3—62no—
692Dic3—62no—
693Dic3—62no—
694Dic3—122no—
695Dic3—122no—
696Dic3—121no—
697Dic3—121no—
698C32#239611yescharacteristic, complemented, Sylow
699C23—32no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23C22×D3211yescharacteristic
707Q8—188no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—68no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—92no—
736C2×C4—92no—
737C2×C4—92no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4D3×Dic612yes—
748C2×C4#379512yes—
749C2×C4#379812yes—
750C2×C4#381112yes—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—122no—
759C2×C3#547011yescharacteristic
760C2×C3#547911yescharacteristic
761C2×C3C2×#87811yescharacteristic
762C2×C3C2×#89611yescharacteristic
763C2×C3#551711yescharacteristic
764C2×C3#552811yescharacteristic
765C2×C3#553811yescharacteristic
766C2×C3#554711yescharacteristic
767C2×C3#554711yescharacteristic
768C2×C3#554811yescharacteristic
769C2×C3#554811yescharacteristic
770C2×C3#555711yescharacteristic
771C2×C3#557811yescharacteristic
772C2×C3#557811yescharacteristic
773D3—42no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22C2×D3×Dic611yescharacteristic
782C22C2×#379511yescharacteristic
783C22C2×#379811yescharacteristic
784C22D3×#23511yescharacteristic
785C22D3×#23511yescharacteristic
786C22#6430611yescharacteristic
787C22C2×#381111yescharacteristic
788C4—22no—
789C4—41no—
790C4—62no—
791C4—62no—
792C4—62no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—121no—
797C4—182no—
798C4—182no—
799C4—182no—
800C4—361no—
801C4#6389614yes—
802C3—21no—
803C3#7348011yescharacteristic, complemented
804C3#7377811yescharacteristic, complemented
805C2—122no—
806C2#1059387311yescharacteristic
807C2#1059391011yescharacteristic
808C2#1059392611yescharacteristic
809C2#1059397411yescharacteristic
810C2C2×#6389611yescharacteristic
811C2#1059501611yescharacteristic
812C2#1059501711yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
4. C3×C4×Dic3⋊C4C2semidirect
5. #10591354C2semidirect
6. #10591351C2semidirect
7. C4×#3724C2semidirect
8. C4×Dic3⋊Dic3C2semidirect
14. #10591210C2semidirect
15. #10591198C2semidirect
77. C4×Dic3⋊C4D3semidirect
106. C2×C3×C4×D3Q8semidirect
322. C2×C4×D3Dic6semidirect
698. C32#2396semidirect
803. C3#73480semidirect
804. C3#73778semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×#638552
C3×C4×(C2×D3)⋊C42
C3×C4×Dic3⋊C42
#105913542
#105913512
C4×#37242
C4×Dic3⋊Dic32
#105913222
#105913192
#105913092
#105913032
C4×(C2×D3)⋊Dic32
#105912102
#105911982
#737783
#734803