Finite Group Databasebeta

← #11808705

Subgroups — #11808705

Order 1152.

1185 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#627C211yesmaximal, characteristic, complemented
2C2×#63874C211yesmaximal, characteristic
3C4×#3752C211yesmaximal, characteristic
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#10591350C211yesmaximal, characteristic
7#10591347C211yesmaximal, characteristic
8#10591339C211yesmaximal, characteristic, complemented
9#10591338C211yesmaximal, characteristic, complemented
10C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
11#10591311C211yesmaximal, characteristic
12C4×#3722C211yesmaximal, characteristic
13#10591214C211yesmaximal, characteristic, complemented
14#10591209C211yesmaximal, characteristic, complemented
15#10591205C211yesmaximal, characteristic
16#73778—31nomaximal
17#73668—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C2×C32×C42C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C4×#627—24no—
44#63874—24no—
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#872—31no—
56C2×#872—31no—
57C2×C4×Dic6—31no—
58C2×C4×Dic6—31no—
59C3×C4×C4⋊C4—31no—
60C3×C4×C4⋊C4—31no—
61#4994—31no—
62#4994—31no—
63#4994—31no—
64#4993—31no—
65#4983—31no—
66#4981—31no—
67#4981—31no—
68#4979—31no—
69C4×(C2×D3)⋊C4—31no—
70C4×(C2×D3)⋊C4—31no—
71C4×(C2×D3)⋊C4—31no—
72C4×(C2×D3)⋊C4—31no—
73C4×(C2×D3)⋊C4—61no—
74C4×C4⋊Dic3—31no—
75C4×C4⋊Dic3D311yescharacteristic, complemented
76C4×Dic3⋊C4—31no—
77C4×Dic3⋊C4D311yescharacteristic, complemented
78#4677—31no—
79#4676—31no—
80#4673—31no—
81#4673—31no—
82#4659—31no—
83#4658—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
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3Q814yescomplemented
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×#627—22no—
105C2×#627—22no—
106C2×#627—22no—
107C32×C42—22no—
108#3752—22no—
109#3752—22no—
110C4×C3⋊Dic3—22no—
111C3×C4⋊Dic3—22no—
112C3×C4⋊Dic3—22no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4—22no—
115C3×C4×Dic3—22no—
116C3×C4×Dic3—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3D414yes—
119#3724—22no—
120#3724—22no—
121#3724—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—22no—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3—22no—
126#3722—22no—
127#3722—22no—
128#3722—22no—
129#3722—22no—
130#2396—91noSylow
131C22×C4×D3—31no—
132C22×C4×D3—31no—
133C22×C4×D3—61no—
134C22×Dic6—31no—
135C22×Dic6—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C42—21no—
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×C3×C42C2×D311yescharacteristic
146C2×C3×C42C2×D311yescharacteristic
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—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—61no—
160C2×(C2×D3)⋊C4—61no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3C2×D311yescharacteristic
166C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
177C2×Dic3⋊C4C2×D311yescharacteristic
178C2×Dic3⋊C4C2×D311yescharacteristic
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—61no—
182C2×C4×Dic3C2×D311yescharacteristic
183C2×C4×Dic3C2×D311yescharacteristic
184C2×C4×Dic3C2×D311yescharacteristic
185C2×C4×Dic3C2×D311yescharacteristic
186#872—64no—
187#872—64no—
188C4×Dic6—64no—
189C4×Dic6—64no—
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⋊#95C2×D311yescharacteristic
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×C4C2×D412yes—
226C2×C32×C4C2×Q812yes—
227C2×C32×C4#4112yes—
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⋊Dic3C2×Q812yes—
237C2×C3⋊Dic3#4112yes—
238C4×C3⋊D3—28no—
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×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×Dic3C2×D412yes—
260C2×C3×Dic3C2×D412yes—
261C2×C3×Dic3#4112yes—
262C2×C3×Dic3#4112yes—
263#627—28no—
264C2×C4×Q8—91no—
265C2×#117—91no—
266#400—91no—
267#399—91no—
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—31no—
276C4×C4⋊C4—91no—
277C4×C22⋊C4—91no—
278C4×C22⋊C4—91no—
279C23×D3—31no—
280C23×D3—31no—
281C23×D3—61no—
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—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—64no—
319C2×C4×D3—62no—
320C2×C4×D3—62no—
321C2×C4×D3—62no—
322C2×C4×D3—62no—
323C2×C4×D3—122no—
324C2×C4×D3—122no—
325C2×Dic6—62no—
326C2×Dic6—62no—
327C2×Dic6—62no—
328C2×Dic6—62no—
329C2×Dic6—62no—
330C2×Dic6—62no—
331C3×C4⋊C4—62no—
332C3×C4⋊C4—62no—
333C3×C4⋊C4—62no—
334C3×C4⋊C4—62no—
335C3×C42—22no—
336C3×C42—22no—
337C3×C42—34no—
338C3×C42—42no—
339C3×C42—62no—
340C3×C42—62no—
341C3×C42—62no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—62no—
344(C2×D3)⋊C4—62no—
345(C2×D3)⋊C4—62no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—64no—
349(C2×D3)⋊C4—64no—
350(C2×D3)⋊C4—62no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4—62no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356C4⋊Dic3—22no—
357C4⋊Dic3—22no—
358C4⋊Dic3—62no—
359C4⋊Dic3—62no—
360C4⋊Dic3—62no—
361C4⋊Dic3—62no—
362Dic3⋊C4—22no—
363Dic3⋊C4—22no—
364Dic3⋊C4—62no—
365Dic3⋊C4—62no—
366Dic3⋊C4—62no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374C4×Dic3—22no—
375C4×Dic3—22no—
376C4×Dic3—22no—
377C4×Dic3—62no—
378C4×Dic3—62no—
379C4×Dic3—122no—
380C4×Dic3D1214yes—
381C22×C32C22×D411yescharacteristic
382C22×C32C22×Q811yescharacteristic
383C22×C32C2×#4111yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C22×C32C2×#4111yescharacteristic
387C22×C32C2×#4111yescharacteristic
388C2×C3⋊D3—22no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—41no—
392C2×C3⋊D3—41no—
393C2×C3⋊D3—41no—
394C2×C3⋊D3—41no—
395C32×C4—22no—
396C32×C4—41no—
397C32×C4C22⋊Q814yes—
398C3⋊Dic3—22no—
399C3⋊Dic3—22no—
400C3⋊Dic3—41no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—91no—
410C23×C4—91no—
411C4×Q8—184no—
412#117—184no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—91no—
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×C22⋊C4—91no—
425C2×C22⋊C4—91no—
426C2×C22⋊C4—91no—
427C2×C22⋊C4—91no—
428C2×C22⋊C4—91no—
429C2×C22⋊C4—91no—
430C2×C42—31no—
431C2×C42—31no—
432C2×C42—31no—
433C2×C42—31no—
434C2×C42—91no—
435C2×C42D3211yescharacteristic
436#95—31no—
437#95—31no—
438#95—31no—
439#95—31no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95—91no—
444#95—91no—
445#95—91no—
446C23×C3—21no—
447C23×C3C23×D311yescharacteristic
448C23×C3C23×D311yescharacteristic
449C22×D3—32no—
450C22×D3—32no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—61no—
455C22×D3—61no—
456C22×D3—61no—
457C22×D3—61no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—61no—
465C22×D3—61no—
466C22×D3—121no—
467C22×D3—121no—
468C22×D3—121no—
469C22×D3—121no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
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—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4C2×D1212yes—
514C2×C3×C4#23512yes—
515C2×C3×C4#23512yes—
516C2×C3×C4#23512yes—
517C2×C3×C4D3×D412yes—
518C2×C3×C4#23712yes—
519C2×C3×C4D3×Q812yes—
520C2×C3×C4D3×Q812yes—
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—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—62no—
546C2×Dic3—62no—
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—62no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3C2×D1212yes—
569C2×Dic3C2×D1212yes—
570C2×Dic3#23512yes—
571C2×Dic3#23512yes—
572C4×D3—68no—
573C4×D3—68no—
574C4×D3—128no—
575Dic6—68no—
576Dic6—68no—
577C2×C32C2×C22⋊Q811yescharacteristic
578C2×C32#52511yescharacteristic
579C2×C32#52911yescharacteristic
580C2×C32#52911yescharacteristic
581C2×C32#53211yescharacteristic
582C2×C32#53311yescharacteristic
583C2×C32#53311yescharacteristic
584C3⋊D3—42no—
585C24—91no—
586C2×Q8—182no—
587C2×Q8—182no—
588C2×Q8—182no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—91no—
598C22×C4—91no—
599C22×C4—94no—
600C22×C4—91no—
601C22×C4—182no—
602C22×C4—182no—
603C22×C4C2×D3211yescharacteristic
604C22×C4C2×D3211yescharacteristic
605C22×C4C2×D3211yescharacteristic
606C4⋊C4—62no—
607C4⋊C4—62no—
608C4⋊C4—62no—
609C4⋊C4—62no—
610C4⋊C4—182no—
611C4⋊C4—182no—
612C4⋊C4—182no—
613C4⋊C4—182no—
614C4⋊C4—182no—
615C4⋊C4—182no—
616C4⋊C4—182no—
617C22⋊C4—182no—
618C22⋊C4—182no—
619C22⋊C4—182no—
620C22⋊C4—182no—
621C22⋊C4—182no—
622C22⋊C4—182no—
623C42—22no—
624C42—34no—
625C42—62no—
626C42—62no—
627C42—62no—
628C42—182no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3C22×D1211yescharacteristic
637C22×C3C2×#23511yescharacteristic
638C22×C3C2×#23511yescharacteristic
639C22×C3C2×#23511yescharacteristic
640C22×C3C2×#23511yescharacteristic
641C22×C3C2×#23511yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×#23711yescharacteristic
644C22×C3C2×D3×Q811yescharacteristic
645C22×C3C2×D3×Q811yescharacteristic
646C22×C3D3×#4111yescharacteristic
647C22×C3D3×#4111yescharacteristic
648C22×C3D3×#4111yescharacteristic
649C22×C3D3×#4111yescharacteristic
650C2×D3—64no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—122no—
658C2×D3—122no—
659C2×D3—122no—
660C2×D3—122no—
661C2×D3—122no—
662C2×D3—122no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C3×C4—22no—
672C3×C4—22no—
673C3×C4—24no—
674C3×C4—42no—
675C3×C4—42no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—62no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—62no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4#89614yes—
687C3×C4#89714yes—
688Dic3—22no—
689Dic3—22no—
690Dic3—22no—
691Dic3—22no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—62no—
697Dic3—62no—
698Dic3—62no—
699Dic3—62no—
700Dic3—122no—
701Dic3—122no—
702Dic3—122no—
703Dic3—121no—
704Dic3—121no—
705C32#239611yescharacteristic, complemented, Sylow
706C23—92no—
707C23—181no—
708C23—181no—
709C23—181no—
710C23—181no—
711C23—181no—
712C23—181no—
713C23C22×D3211yescharacteristic
714Q8—188no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—32no—
723C2×C4—32no—
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—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—92no—
745C2×C4—92no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—188no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4#379712yes—
755C2×C4#379812yes—
756C2×C4D3×D1212yes—
757C2×C4#380412yes—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3#547711yescharacteristic
766C2×C3#547911yescharacteristic
767C2×C3C2×#89611yescharacteristic
768C2×C3C2×#89711yescharacteristic
769C2×C3#552411yescharacteristic
770C2×C3#552811yescharacteristic
771C2×C3#553811yescharacteristic
772C2×C3#553811yescharacteristic
773C2×C3#554711yescharacteristic
774C2×C3#554811yescharacteristic
775C2×C3#557811yescharacteristic
776C2×C3#557811yescharacteristic
777C2×C3#557811yescharacteristic
778C2×C3#557811yescharacteristic
779D3—124no—
780D3—122no—
781D3—122no—
782C22—182no—
783C22—182no—
784C22—182no—
785C22—361no—
786C22—361no—
787C22—361no—
788C22—361no—
789C22C2×#379711yescharacteristic
790C22C2×#379811yescharacteristic
791C22C2×D3×D1211yescharacteristic
792C22D3×#23511yescharacteristic
793C22D3×#23511yescharacteristic
794C22#6430611yescharacteristic
795C22C2×#380411yescharacteristic
796C4—22no—
797C4—41no—
798C4—62no—
799C4—62no—
800C4—62no—
801C4—62no—
802C4—121no—
803C4—121no—
804C4—121no—
805C4—121no—
806C4—182no—
807C4—182no—
808C4—361no—
809C4#6389514yes—
810C3—21no—
811C3#7366811yescharacteristic, complemented
812C3#7377811yescharacteristic, complemented
813C2—362no—
814C2#1059388211yescharacteristic
815C2#1059393511yescharacteristic
816C2#1059396811yescharacteristic
817C2#1059399711yescharacteristic
818C2#1059483911yescharacteristic
819C2C2×#6389511yescharacteristic
820C2#1059493311yescharacteristic
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×#627C2semidirect
4. C3×C4×C4⋊Dic3C2semidirect
5. C3×C4×Dic3⋊C4C2semidirect
8. #10591339C2semidirect
9. #10591338C2semidirect
10. C4×Dic3⋊Dic3C2semidirect
13. #10591214C2semidirect
14. #10591209C2semidirect
75. C4×C4⋊Dic3D3semidirect
77. C4×Dic3⋊C4D3semidirect
95. C2×C4×C3⋊D3Q8semidirect
705. C32#2396semidirect
811. C3#73668semidirect
812. C3#73778semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C2×#638742
C4×#37522
C3×C4×C4⋊Dic32
C3×C4×Dic3⋊C42
#105913502
#105913472
#105913392
#105913382
C4×Dic3⋊Dic32
#105913112
C4×#37222
#105912142
#105912092
#105912052
#737783
#736683