Finite Group Databasebeta

← #11803471

Subgroups — #11803471

Order 1152.

1197 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63893C211yesmaximal, characteristic
2C2×#63877C211yesmaximal, characteristic
3C2×#63837C211yesmaximal, characteristic, complemented
4#10592627C211yesmaximal, characteristic, complemented
5C3×#4940C211yesmaximal, characteristic
6C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
7#10591366C211yesmaximal, characteristic
8#10591330C211yesmaximal, characteristic, complemented
9#10591316C211yesmaximal, characteristic
10#10591284C211yesmaximal, characteristic
11#10591280C211yesmaximal, characteristic
12#10591271C211yesmaximal, characteristic, complemented
13#10591268C211yesmaximal, characteristic, complemented
14#10591250C211yesmaximal, characteristic, complemented
15#10591235C211yesmaximal, characteristic, complemented
16#75459—31nomaximal
17#73762—31nomaximal
18C22×#627C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C2×C32×C42C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
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#63893C418yescomplemented
44#63877—24no—
45#63837—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×#887—31no—
58C2×#878—31no—
59C2×#877—31no—
60C2×#872—31no—
61C2×C4×Dic6—31no—
62C3×#388—31no—
63C3×C4×C4⋊C4—31no—
64#4987—31no—
65#4984—31no—
66#4976—31no—
67#4973—31no—
68#4951—31no—
69#4945—31no—
70#4945—31no—
71#4942—31no—
72#4940—31no—
73#4940D311yescharacteristic
74C4×Dic3⋊C4D311yescharacteristic, complemented
75#4928—31no—
76#4928—31no—
77#4928—31no—
78#4928—61no—
79#4670—31no—
80#4670—31no—
81#4654—31no—
82#4653—31no—
83#4653—31no—
84#4652—31no—
85#4647—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×D3×Dic3—22no—
106C2×D3×Dic3—22no—
107C2×D3×Dic3C2×C414yes—
108C32×C42—41no—
109C4⋊(C3⋊Dic3)—41no—
110C4⋊(C3⋊Dic3)C2×C414yes—
111#3750—22no—
112#3750—22no—
113C3×(C2×D3)⋊C4—22no—
114C3×(C2×D3)⋊C4—41no—
115C3×(C2×D3)⋊C4C2×C414yes—
116C3×Dic3⋊C4—22no—
117C3×Dic3⋊C4—22no—
118C3×Dic3⋊C4C2×C414yes—
119C3×C4×Dic3—41no—
120C3×C4×Dic3D414yes—
121#3724—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3C2×C414yes—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—41no—
127(C2×D3)⋊Dic3C2×C414yes—
128Dic32—22no—
129Dic32—22no—
130Dic32—22no—
131#2323—91noSylow
132C23×Dic3—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×C22⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C42—21no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×C3×C42C2×D311yescharacteristic
146C2×C3×C42C2×D311yescharacteristic
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⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—61no—
164C2×C4⋊Dic3—61no—
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—61no—
175C2×Dic3⋊C4—61no—
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#887—64no—
189#878—38no—
190#877—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⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3C22×C412yes—
243C2×C3⋊Dic3C22×C412yes—
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×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—
266D3×Dic3—28no—
267C2×C22⋊Q8—91no—
268C2×C4×Q8—91no—
269C2×#117—91no—
270#391—91no—
271#389—91no—
272#389—91no—
273#389—91no—
274#388—31no—
275#388—91no—
276#388—91no—
277#388—91no—
278#387—91no—
279#387—91no—
280#380—91no—
281C4×C4⋊C4—31no—
282C24×C3—31no—
283C23×D3C22×D311yescharacteristic
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
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×C4—31no—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—34no—
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×Dic3—62no—
314C22×Dic3—62no—
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C2×C4×D3—34no—
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—62no—
333C3×C4⋊C4—62no—
334C3×C22⋊C4—34no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4—121no—
337C3×C42—34no—
338C3×C42—41no—
339C3×C42—41no—
340C3×C42—42no—
341C3×C42—121no—
342#217—34no—
343#217—62no—
344#217—121no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4—34no—
347(C2×D3)⋊C4—41no—
348(C2×D3)⋊C4—62no—
349(C2×D3)⋊C4—121no—
350(C2×D3)⋊C4C4×D314yes—
351C4⋊Dic3—34no—
352C4⋊Dic3—34no—
353C4⋊Dic3—34no—
354C4⋊Dic3—64no—
355C4⋊Dic3—62no—
356C4⋊Dic3—121no—
357C4⋊Dic3—121no—
358C4⋊Dic3—121no—
359C4⋊Dic3—122no—
360Dic3⋊C4—22no—
361Dic3⋊C4—22no—
362Dic3⋊C4—34no—
363Dic3⋊C4—62no—
364Dic3⋊C4—62no—
365Dic3⋊C4—62no—
366Dic3⋊C4—62no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—122no—
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—22no—
401C3⋊Dic3—41no—
402C3⋊Dic3—41no—
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—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×C22⋊C4—31no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—31no—
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×C3—32no—
450C23×C3—61no—
451C23×C3—61no—
452C23×C3—61no—
453C23×C3—61no—
454C23×C3—61no—
455C23×C3—61no—
456C23×C3C23×D311yescharacteristic
457C23×C3C23×D311yescharacteristic
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3C2×C4×D312yes—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
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—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
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×C4C2×C4×D312yes—
510C2×C3×C4C2×C4×D312yes—
511C2×C3×C4C2×D1212yes—
512C2×C3×C4D3×D412yes—
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—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—62no—
533C2×Dic3—62no—
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—68no—
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—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3C2×C4×D312yes—
566C2×Dic3C2×C4×D312yes—
567C2×Dic3C2×C4×D312yes—
568C2×Dic3C2×D1212yes—
569C2×Dic3C2×D1212yes—
570C2×Dic3#23512yes—
571C4×D3—68no—
572Dic6—68no—
573Dic6—68no—
574C2×C32C2×C4×D411yescharacteristic
575C2×C32#51911yescharacteristic
576C2×C32#52011yescharacteristic
577C2×C32#53611yescharacteristic
578C2×C32#53711yescharacteristic
579C2×C32#54111yescharacteristic
580C2×C32#54211yescharacteristic
581C3×D3—42no—
582C24—31no—
583C2×Q8—94no—
584C2×Q8—182no—
585C2×Q8—182no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—94no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—182no—
599C22×C4—182no—
600C22×C4C2×D3211yescharacteristic
601C22×C4C2×D3211yescharacteristic
602C22×C4C2×D3211yescharacteristic
603C4⋊C4—34no—
604C4⋊C4—62no—
605C4⋊C4—62no—
606C4⋊C4—94no—
607C4⋊C4—94no—
608C4⋊C4—182no—
609C4⋊C4—182no—
610C4⋊C4—182no—
611C4⋊C4—182no—
612C4⋊C4—361no—
613C4⋊C4—361no—
614C22⋊C4—34no—
615C22⋊C4—62no—
616C22⋊C4—94no—
617C22⋊C4—121no—
618C22⋊C4—182no—
619C22⋊C4—361no—
620C42—34no—
621C42—41no—
622C42—121no—
623C42—182no—
624C42—182no—
625C42—182no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C22×C4×D311yescharacteristic
641C22×C3C22×C4×D311yescharacteristic
642C22×C3C22×D1211yescharacteristic
643C22×C3C2×#23511yescharacteristic
644C22×C3C2×D3×D411yescharacteristic
645C22×C3#100411yescharacteristic
646C22×C3#100411yescharacteristic
647C22×C3#100711yescharacteristic
648C22×C3D3×#4111yescharacteristic
649C22×C3#101011yescharacteristic
650C22×C3#101011yescharacteristic
651C22×C3#101011yescharacteristic
652C22×C3#101011yescharacteristic
653C22×C3#101011yescharacteristic
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C3×C4—24no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—34no—
667C3×C4—42no—
668C3×C4—42no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—62no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677Dic3—22no—
678Dic3—22no—
679Dic3—22no—
680Dic3—41no—
681Dic3—41no—
682Dic3—41no—
683Dic3—62no—
684Dic3—62no—
685Dic3—62no—
686Dic3—62no—
687Dic3—122no—
688Dic3—122no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694Dic3—241no—
695Dic3C4×D1214yes—
696C32#232311yescharacteristic, complemented, Sylow
697C23—32no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23C22×D3211yescharacteristic
705Q8—188no—
706C2×C4—21no—
707C2×C4—21no—
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—32no—
717C2×C4—32no—
718C2×C4—32no—
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—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—92no—
735C2×C4—92no—
736C2×C4—188no—
737C2×C4—181no—
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×C4C4×D3212yes—
748C2×C4D3×D1212yes—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—122no—
757C2×C3C2×C4×D1211yescharacteristic
758C2×C3#551011yescharacteristic
759C2×C3#551611yescharacteristic
760C2×C3#552611yescharacteristic
761C2×C3C4×D3×D411yescharacteristic
762C2×C3#554611yescharacteristic
763C2×C3#554611yescharacteristic
764C2×C3#556111yescharacteristic
765C2×C3#557211yescharacteristic
766C2×C3#558311yescharacteristic
767C2×C3#559711yescharacteristic
768C2×C3#566211yescharacteristic
769C2×C3#567511yescharacteristic
770C2×C3#570111yescharacteristic
771D3—42no—
772C22—62no—
773C22—62no—
774C22—62no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22#6429711yescharacteristic
780C22#6429811yescharacteristic
781C22#6429811yescharacteristic
782C22C2×C4×D3211yescharacteristic
783C22C2×D3×D1211yescharacteristic
784C22D3×#23511yescharacteristic
785C22#6433011yescharacteristic
786C4—22no—
787C4—22no—
788C4—34no—
789C4—41no—
790C4—62no—
791C4—62no—
792C4—62no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—182no—
797C4—182no—
798C4—361no—
799C4—361no—
800C3—21no—
801C3#7376211yescharacteristic, complemented
802C3#7545911yescharacteristic, complemented
803C2—122no—
804C2#1059388511yescharacteristic
805C2#1059389411yescharacteristic
806C2#1059392811yescharacteristic
807C2C4×D3×D1211yescharacteristic
808C2#1059487611yescharacteristic
809C2#1059491111yescharacteristic
810C2#1059502411yescharacteristic
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
3. C2×#63837C2semidirect
4. #10592627C2semidirect
6. C3×C4×Dic3⋊C4C2semidirect
8. #10591330C2semidirect
12. #10591271C2semidirect
13. #10591268C2semidirect
14. #10591250C2semidirect
15. #10591235C2semidirect
43. #63893C4semidirect
74. C4×Dic3⋊C4D3semidirect
696. C32#2323semidirect
801. C3#73762semidirect
802. C3#75459semidirect

Maximal subgroups

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

subgroupindex
C2×#638932
C2×#638772
C2×#638372
#105926272
C3×#49402
C3×C4×Dic3⋊C42
#105913662
#105913302
#105913162
#105912842
#105912802
#105912712
#105912682
#105912502
#105912352
#754593
#737623