Finite Group Databasebeta

← #11803469

Subgroups — #11803469

Order 1152.

1207 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63895C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic, complemented
3C2×#63836C211yesmaximal, characteristic
4#10592639C211yesmaximal, characteristic
5C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C3×#4928C211yesmaximal, characteristic, complemented
7#10591367C211yesmaximal, characteristic
8#10591330C211yesmaximal, characteristic, complemented
9#10591289C211yesmaximal, characteristic
10#10591269C211yesmaximal, characteristic, complemented
11#10591266C211yesmaximal, characteristic
12#10591265C211yesmaximal, characteristic, complemented
13#10591259C211yesmaximal, characteristic
14#10591253C211yesmaximal, characteristic, complemented
15#10591235C211yesmaximal, characteristic, complemented
16#75971—31nomaximal
17#73762—31nomaximal
18C22×#627C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C32×C42C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63895C418yescomplemented
44#63837—24no—
45#63836—24no—
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#897—31no—
57C2×#896—31no—
58C2×#892—31no—
59C2×#887—31no—
60C2×#872—31no—
61C2×C4×Dic6—31no—
62C3×#389—31no—
63C3×C4×C4⋊C4—31no—
64#4990—31no—
65#4990—31no—
66#4987—31no—
67#4984—31no—
68#4980—31no—
69#4976—31no—
70#4976—31no—
71#4973—31no—
72#4940—31no—
73#4940—31no—
74#4940—31no—
75#4940—61no—
76C4×Dic3⋊C4D311yescharacteristic, complemented
77#4928—31no—
78#4928D311yescharacteristic, complemented
79#4670—31no—
80#4670—31no—
81#4669—31no—
82#4667—31no—
83#4655—31no—
84#4653—31no—
85#4653—31no—
86#4646—31no—
87C23×C3⋊D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
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
101C22×C3×Dic3C2311yescharacteristic
102C2×#627—22no—
103C2×#627—22no—
104C2×#627C2×C414yes—
105C2×#624—22no—
106C2×#624—22no—
107C2×#624C2×C414yes—
108C32×C42—41no—
109#3752—22no—
110#3752—41no—
111#3752C2×C414yes—
112#3750—22no—
113C3×C4⋊Dic3—41no—
114C3×C4⋊Dic3C2×C414yes—
115C3×Dic3⋊C4—22no—
116C3×Dic3⋊C4—22no—
117C3×Dic3⋊C4—22no—
118C3×Dic3⋊C4C2×C414yes—
119C3×C4×Dic3—41no—
120C3×C4×Dic3D414yes—
121Dic3⋊Dic3—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3C2×C414yes—
125#3722—22no—
126#3722—41no—
127#3722C2×C414yes—
128Dic32—22no—
129Dic32—22no—
130Dic32—22no—
131#2323—91noSylow
132C22×C4×D3—31no—
133C22×C4×D3—31no—
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×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C42—21no—
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×(C2×D3)⋊C4—61no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3C2×D311yescharacteristic
167C2×C4⋊Dic3C2×D311yescharacteristic
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—61no—
175C2×Dic3⋊C4C2×D311yescharacteristic
176C2×Dic3⋊C4C2×D311yescharacteristic
177C2×Dic3⋊C4C2×D311yescharacteristic
178C2×Dic3⋊C4C2×D311yescharacteristic
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3C2×D311yescharacteristic
186C2×C4×Dic3C2×D311yescharacteristic
187#897—38no—
188#896—38no—
189#892—64no—
190#887—64no—
191#872—64no—
192C4×Dic6—64no—
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⋊#95—61no—
210C3⋊#95—61no—
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⋊D3C22×C412yes—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4C22×C412yes—
231C2×C32×C4C2×D412yes—
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⋊Dic3—21no—
240C2×C3⋊Dic3C22×C412yes—
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×Dic3C22×C412yes—
259C2×C3×Dic3C22×C412yes—
260C2×C3×Dic3C22×C412yes—
261C2×C3×Dic3C22×C412yes—
262C2×C3×Dic3C2×D412yes—
263C2×C3×Dic3C2×D412yes—
264C2×C3×Dic3#4112yes—
265#627—28no—
266#624—28no—
267C2×C22⋊Q8—91no—
268C2×C4×Q8—91no—
269C2×#117—91no—
270#391—91no—
271#389—31no—
272#389—91no—
273#389—91no—
274#388—91no—
275#388—91no—
276#388—91no—
277#388—91no—
278#387—91no—
279#387—91no—
280#380—91no—
281C4×C4⋊C4—31no—
282C23×D3—31no—
283C23×D3—31no—
284C23×D3—61no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3C22×D311yescharacteristic
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—34no—
321C2×C4×D3—62no—
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—62no—
325C2×Dic6—34no—
326C2×Dic6—34no—
327C2×Dic6—62no—
328C2×Dic6—62no—
329C2×Dic6—62no—
330C2×Dic6—62no—
331C3×C4⋊C4—34no—
332C3×C4⋊C4—34no—
333C3×C4⋊C4—62no—
334C3×C4⋊C4—62no—
335C3×C4⋊C4—62no—
336C3×C4⋊C4—121no—
337C3×C42—34no—
338C3×C42—41no—
339C3×C42—41no—
340C3×C42—42no—
341C3×C42—121no—
342(C2×D3)⋊C4—34no—
343(C2×D3)⋊C4—34no—
344(C2×D3)⋊C4—34no—
345(C2×D3)⋊C4—34no—
346(C2×D3)⋊C4—64no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—62no—
349(C2×D3)⋊C4—62no—
350(C2×D3)⋊C4—62no—
351(C2×D3)⋊C4—122no—
352(C2×D3)⋊C4—121no—
353(C2×D3)⋊C4—121no—
354(C2×D3)⋊C4—121no—
355(C2×D3)⋊C4—121no—
356(C2×D3)⋊C4—122no—
357C4⋊Dic3—34no—
358C4⋊Dic3—41no—
359C4⋊Dic3—62no—
360C4⋊Dic3—62no—
361C4⋊Dic3—121no—
362C4⋊Dic3C4×D314yes—
363Dic3⋊C4—22no—
364Dic3⋊C4—22no—
365Dic3⋊C4—22no—
366Dic3⋊C4—34no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—122no—
372Dic3⋊C4—121no—
373Dic3⋊C4C4×D314yes—
374C4×Dic3—41no—
375C4×Dic3—62no—
376C4×Dic3—62no—
377C4×Dic3—62no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C4×Dic3—62no—
381C4×Dic3D1214yes—
382C22×C32C23×C411yescharacteristic
383C22×C32C22×D411yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32H(5,𝔽2)11yescharacteristic
386C22×C322−1+411yescharacteristic
387C22×C322−1+411yescharacteristic
388C22×C322−1+411yescharacteristic
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—41no—
393C2×C3⋊D3—41no—
394C2×C3⋊D3—41no—
395C2×C3⋊D3—41no—
396C32×C4—22no—
397C32×C4—22no—
398C32×C4—41no—
399C3⋊Dic3—22no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3C4×D414yes—
410C22×Q8—91no—
411C23×C4—91no—
412C22⋊Q8—98no—
413C4×Q8—184no—
414#117—184no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—91no—
425C2×C4⋊C4—91no—
426C2×C22⋊C4—91no—
427C2×C22⋊C4—91no—
428C2×C22⋊C4—91no—
429C2×C22⋊C4—91no—
430C2×C22⋊C4—91no—
431C2×C22⋊C4—91no—
432C2×C42—31no—
433C2×C42—31no—
434C2×C42—91no—
435C2×C42—91no—
436C2×C42—91no—
437C2×C42D3211yescharacteristic
438#95—31no—
439#95—31no—
440#95—31no—
441#95—31no—
442#95—91no—
443#95—91no—
444#95—91no—
445#95—91no—
446#95—91no—
447#95—91no—
448C23×C3—21no—
449C23×C3C23×D311yescharacteristic
450C23×C3C23×D311yescharacteristic
451C22×D3—32no—
452C22×D3—32no—
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—
470C22×D3—121no—
471C22×D3—121no—
472C2×C3×C4—21no—
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—21no—
480C2×C3×C4—22no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—32no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
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×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4C2×C4×D312yes—
520C2×C3×C4C2×C4×D312yes—
521C2×C3×C4C2×D1212yes—
522C2×C3×C4D3×D412yes—
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—32no—
541C2×Dic3—32no—
542C2×Dic3—62no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
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—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3C2×C4×D312yes—
568C2×Dic3C2×C4×D312yes—
569C2×Dic3C2×C4×D312yes—
570C2×Dic3C2×C4×D312yes—
571C2×Dic3C2×D1212yes—
572C2×Dic3C2×D1212yes—
573C2×Dic3#23512yes—
574C4×D3—68no—
575C4×D3—68no—
576Dic6—68no—
577Dic6—68no—
578C2×C32C2×C4×D411yescharacteristic
579C2×C32#51911yescharacteristic
580C2×C32#52011yescharacteristic
581C2×C32#53611yescharacteristic
582C2×C32#53711yescharacteristic
583C2×C32#54111yescharacteristic
584C2×C32#54211yescharacteristic
585C3⋊D3—42no—
586C24—91no—
587C2×Q8—94no—
588C2×Q8—182no—
589C2×Q8—182no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—94no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—91no—
602C22×C4—182no—
603C22×C4—182no—
604C22×C4C2×D3211yescharacteristic
605C22×C4C2×D3211yescharacteristic
606C22×C4C2×D3211yescharacteristic
607C4⋊C4—34no—
608C4⋊C4—34no—
609C4⋊C4—62no—
610C4⋊C4—62no—
611C4⋊C4—62no—
612C4⋊C4—94no—
613C4⋊C4—121no—
614C4⋊C4—182no—
615C4⋊C4—182no—
616C4⋊C4—182no—
617C4⋊C4—361no—
618C22⋊C4—94no—
619C22⋊C4—94no—
620C22⋊C4—182no—
621C22⋊C4—182no—
622C22⋊C4—361no—
623C22⋊C4—361no—
624C42—34no—
625C42—41no—
626C42—121no—
627C42—182no—
628C42—182no—
629C42—182no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3C22×C4×D311yescharacteristic
638C22×C3C22×C4×D311yescharacteristic
639C22×C3C22×D1211yescharacteristic
640C22×C3C2×#23511yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C22×C3#100411yescharacteristic
643C22×C3#100411yescharacteristic
644C22×C3#100711yescharacteristic
645C22×C3#100711yescharacteristic
646C22×C3#100711yescharacteristic
647C22×C3D3×#4111yescharacteristic
648C22×C3#101011yescharacteristic
649C22×C3#101011yescharacteristic
650C22×C3#101011yescharacteristic
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—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—241no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—241no—
672C3×C4—22no—
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—34no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—42no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—62no—
683C3×C4—62no—
684C3×C4—62no—
685C3×C4—62no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689Dic3—22no—
690Dic3—22no—
691Dic3—22no—
692Dic3—22no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—62no—
697Dic3—62no—
698Dic3—122no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3—241no—
705Dic3C4×D1214yes—
706C32#232311yescharacteristic, complemented, Sylow
707C23—92no—
708C23—181no—
709C23—181no—
710C23—181no—
711C23—181no—
712C23—181no—
713C23—181no—
714C23C22×D3211yescharacteristic
715Q8—188no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—32no—
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—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—92no—
748C2×C4—188no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4C4×D3212yes—
758C2×C4D3×D1212yes—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3C2×C4×D1211yescharacteristic
767C2×C3#550411yescharacteristic
768C2×C3#551011yescharacteristic
769C2×C3#552611yescharacteristic
770C2×C3C4×D3×D411yescharacteristic
771C2×C3#554611yescharacteristic
772C2×C3#556111yescharacteristic
773C2×C3#557211yescharacteristic
774C2×C3#557211yescharacteristic
775C2×C3#558311yescharacteristic
776C2×C3#559711yescharacteristic
777C2×C3#564011yescharacteristic
778C2×C3#569611yescharacteristic
779C2×C3#572411yescharacteristic
780D3—122no—
781D3—122no—
782D3—242no—
783C22—182no—
784C22—182no—
785C22—182no—
786C22—361no—
787C22—361no—
788C22—361no—
789C22—361no—
790C22#6429711yescharacteristic
791C22#6429711yescharacteristic
792C22#6429711yescharacteristic
793C22C2×C4×D3211yescharacteristic
794C22C2×D3×D1211yescharacteristic
795C22D3×#23511yescharacteristic
796C22#6433011yescharacteristic
797C4—22no—
798C4—22no—
799C4—34no—
800C4—41no—
801C4—62no—
802C4—62no—
803C4—62no—
804C4—62no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—182no—
809C4—361no—
810C4—361no—
811C3—21no—
812C3#7376211yescharacteristic, complemented
813C3#7597111yescharacteristic, complemented
814C2—362no—
815C2#1059384811yescharacteristic
816C2#1059384911yescharacteristic
817C2#1059389311yescharacteristic
818C2C4×D3×D1211yescharacteristic
819C2#1059483711yescharacteristic
820C2#1059487411yescharacteristic
821C2#1059491111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63837C2semidirect
5. C3×C4×Dic3⋊C4C2semidirect
6. C3×#4928C2semidirect
8. #10591330C2semidirect
10. #10591269C2semidirect
12. #10591265C2semidirect
14. #10591253C2semidirect
15. #10591235C2semidirect
43. #63895C4semidirect
76. C4×Dic3⋊C4D3semidirect
78. #4928D3semidirect
706. C32#2323semidirect
812. C3#73762semidirect
813. C3#75971semidirect

Maximal subgroups

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

subgroupindex
C2×#638952
C2×#638372
C2×#638362
#105926392
C3×C4×Dic3⋊C42
C3×#49282
#105913672
#105913302
#105912892
#105912692
#105912662
#105912652
#105912592
#105912532
#105912352
#759713
#737623