Finite Group Databasebeta

← #11801696

Subgroups — #11801696

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67⋊Dic3C211yesmaximal, characteristic
2C2×#63957C211yesmaximal, characteristic, complemented
3C2×#63878C211yesmaximal, characteristic, complemented
4C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#4957C211yesmaximal, characteristic
6C3×#4944C211yesmaximal, characteristic, complemented
7#10591707C211yesmaximal, characteristic
8#10591702C211yesmaximal, characteristic, complemented
9#10591368C211yesmaximal, characteristic, complemented
10#10591327C211yesmaximal, characteristic, complemented
11#10591282C211yesmaximal, characteristic, complemented
12#10591279C211yesmaximal, characteristic, complemented
13#10591246C211yesmaximal, characteristic, complemented
14#10591241C211yesmaximal, characteristic, complemented
15C4×Dic32C211yesmaximal, characteristic, complemented
16#76289—31nomaximal
17#75450—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34#67⋊Dic3C418yescomplemented
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43#63957—24no—
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49#63878—24no—
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×D4×Dic3—31no—
57C2×#892—31no—
58C2×#67⋊C4—31no—
59C2×#877—31no—
60C2×#877—31no—
61C2×#877—31no—
62C3×#390—31no—
63C3×#388—31no—
64#5221—31no—
65#4976—31no—
66Dic3×C4⋊C4—31no—
67#4972—31no—
68#4957—31no—
69#4957D311yescharacteristic
70#4951—31no—
71#4945—31no—
72#4945—31no—
73#4944—31no—
74#4944D311yescharacteristic, complemented
75Dic3×C22⋊C4—31no—
76Dic3×C22⋊C4—31no—
77Dic3×C22⋊C4—31no—
78Dic3×C22⋊C4—61no—
79#4940—31no—
80C42×Dic3—31no—
81C42×Dic3—31no—
82#4928—31no—
83#4669—31no—
84#4666—31no—
85#4649—31no—
86#4647—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3—22no—
92C22×C3⋊Dic3—22no—
93C22×C3⋊Dic3C2×C414yes—
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67C2×C414yes—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×D3×Dic3—22no—
109C2×D3×Dic3—22no—
110C2×D3×Dic3C2×C414yes—
111C32×C22⋊C4—22no—
112#3757—22no—
113C4×C3⋊Dic3—22no—
114C4×C3⋊Dic3—22no—
115C3×#217—22no—
116C3×#217—22no—
117C3×#217C2×C414yes—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×Dic3⋊C4—22no—
122C3×C4×Dic3—22no—
123C3×C4×Dic3—22no—
124#3724—22no—
125#3724—22no—
126Dic3⋊Dic3—22no—
127Dic3⋊Dic3—22no—
128Dic3⋊Dic3C2×C414yes—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3—22no—
131(C2×D3)⋊Dic3C2×C414yes—
132Dic32—22no—
133Dic32—22no—
134Dic32—22no—
135Dic32C2×C414yes—
136Dic32D414yescomplemented
137#2293—91noSylow
138C22×C3×D4—31no—
139C22×#67C2×D311yescharacteristic
140C23×Dic3—31no—
141C23×Dic3—31no—
142C23×Dic3—31no—
143C23×Dic3—61no—
144C22×C4×D3—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4C2×D311yescharacteristic
154C2×C3×C22⋊C4C2×D311yescharacteristic
155C2×C3×C42—31no—
156C2×C3×C42—31no—
157C2×#217—31no—
158C2×#217—31no—
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—61no—
163C2×#217C2×D311yescharacteristic
164C2×#217C2×D311yescharacteristic
165C2×#217C2×D311yescharacteristic
166D4×Dic3—38no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4C2×D311yescharacteristic
171C2×(C2×D3)⋊C4C2×D311yescharacteristic
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4C2×D311yescharacteristic
183C2×Dic3⋊C4C2×D311yescharacteristic
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—31no—
197C2×C4×Dic3—31no—
198C2×C4×Dic3—61no—
199C2×C4×Dic3—61no—
200C2×C4×Dic3C2×D311yescharacteristic
201C2×C4×Dic3C2×D311yescharacteristic
202#892—64no—
203#67⋊C4—38no—
204#877—64no—
205#877—64no—
206#877—64no—
207C3×#95—31no—
208C3×#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—61no—
218C3⋊#95—61no—
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32C22×C412yes—
228C23×C32C2411yescharacteristic
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3C22×C412yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4#4112yes—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—28no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C22×C412yes—
251C2×C3⋊Dic3C22×C412yes—
252C2×C3⋊Dic3C2×D412yes—
253C2×C3⋊Dic3#4112yes—
254C2×C3⋊Dic3#4112yes—
255C3×#67—28no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3C22×C412yes—
271C2×C3×Dic3C22×C412yes—
272C2×C3×Dic3C22×C412yes—
273C2×C3×Dic3C2×D412yes—
274C2×C3×Dic3C2×D412yes—
275C2×C3×Dic3#4112yes—
276C2×C3×Dic3#4112yes—
277D3×Dic3—28no—
278C2×C4×D4—91no—
279C2×#117—91no—
280C2×#117—91no—
281#390—31no—
282#390—91no—
283#389—91no—
284#389—91no—
285#388—31no—
286#388—91no—
287#388—91no—
288#388—91no—
289C4×C4⋊C4—91no—
290C4×C22⋊C4—91no—
291C4×C22⋊C4—91no—
292C43—91no—
293C24×C3—21no—
294C24×C3—31no—
295C24×C3C22×D311yescharacteristic
296C24×C3C22×D311yescharacteristic
297C23×D3C22×D311yescharacteristic
298C2×C3×D4—34no—
299C2×C3×D4—62no—
300C2×C3×D4—62no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C2×#67—22no—
315C2×#67—22no—
316C2×#67C4×D314yes—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—34no—
320C22×Dic3—34no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—34no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—64no—
333C22×Dic3—62no—
334C22×Dic3—62no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337C22×Dic3—62no—
338C22×Dic3—62no—
339C22×Dic3—122no—
340C22×Dic3—122no—
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C2×C4×D3—34no—
349C2×C4×D3—62no—
350C2×C4×D3—62no—
351C3×C4⋊C4—62no—
352C3×C4⋊C4—62no—
353C3×C22⋊C4—24no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—34no—
357C3×C22⋊C4—62no—
358C3×C22⋊C4—62no—
359C3×C22⋊C4—62no—
360C3×C22⋊C4—62no—
361C3×C42—62no—
362C3×C42—62no—
363#217—22no—
364#217—22no—
365#217—34no—
366#217—62no—
367#217—62no—
368#217—62no—
369#217—64no—
370#217—62no—
371#217C4×D314yes—
372(C2×D3)⋊C4—22no—
373(C2×D3)⋊C4—22no—
374(C2×D3)⋊C4—34no—
375(C2×D3)⋊C4—62no—
376(C2×D3)⋊C4—62no—
377C4⋊Dic3—34no—
378C4⋊Dic3—62no—
379C4⋊Dic3—62no—
380Dic3⋊C4—22no—
381Dic3⋊C4—22no—
382Dic3⋊C4—34no—
383Dic3⋊C4—62no—
384Dic3⋊C4—62no—
385Dic3⋊C4—62no—
386Dic3⋊C4—62no—
387Dic3⋊C4—62no—
388Dic3⋊C4—62no—
389C4×Dic3—22no—
390C4×Dic3—22no—
391C4×Dic3—34no—
392C4×Dic3—34no—
393C4×Dic3—34no—
394C4×Dic3—34no—
395C4×Dic3—62no—
396C4×Dic3—62no—
397C4×Dic3—62no—
398C4×Dic3—62no—
399C4×Dic3—62no—
400C4×Dic3—62no—
401C4×Dic3—62no—
402C4×Dic3—62no—
403C4×Dic3—62no—
404C4×Dic3—62no—
405C4×Dic3—122no—
406C4×Dic3—122no—
407C22×C32—22no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C23×C411yescharacteristic
415C22×C32C22×D411yescharacteristic
416C22×C32C2×#4111yescharacteristic
417C22×C32C2×#4111yescharacteristic
418C22×C32C2×#4111yescharacteristic
419C22×C32C2×#4111yescharacteristic
420C22×C32C2×#4111yescharacteristic
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C32×C4—22no—
429C32×C4—41no—
430C3⋊Dic3—22no—
431C3⋊Dic3—22no—
432C3⋊Dic3—41no—
433C3⋊Dic3C4×D414yes—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3#11714yescomplemented
441C22×D4—31no—
442C23×C4—91no—
443C23×C4—91no—
444C4×D4—98no—
445#117—184no—
446#117—184no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—91no—
451C2×C4⋊C4—91no—
452C2×C4⋊C4—91no—
453C2×C4⋊C4—91no—
454C2×C22⋊C4—31no—
455C2×C22⋊C4—31no—
456C2×C22⋊C4—31no—
457C2×C22⋊C4—31no—
458C2×C22⋊C4—31no—
459C2×C22⋊C4—91no—
460C2×C22⋊C4—91no—
461C2×C22⋊C4—91no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4D3211yescharacteristic
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—91no—
467C2×C42—91no—
468C2×C42—91no—
469C2×C42—91no—
470C2×C42—91no—
471C2×C42—91no—
472C2×C42—91no—
473#95—31no—
474#95—31no—
475#95—91no—
476#95—91no—
477#95—91no—
478#95—91no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—22no—
495C23×C3—32no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3C2×C4×D312yes—
507C23×C3C2×C4×D312yes—
508C23×C3C23×D311yescharacteristic
509C23×C3C23×D311yescharacteristic
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3C2×C4×D312yes—
517C3×D4—68no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—22no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—22no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4#23712yes—
556C2×C3×C4#23712yes—
557#67—28no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—32no—
573C2×Dic3—32no—
574C2×Dic3—32no—
575C2×Dic3—32no—
576C2×Dic3—32no—
577C2×Dic3—32no—
578C2×Dic3—32no—
579C2×Dic3—32no—
580C2×Dic3—32no—
581C2×Dic3—32no—
582C2×Dic3—62no—
583C2×Dic3—62no—
584C2×Dic3—62no—
585C2×Dic3—62no—
586C2×Dic3—62no—
587C2×Dic3—68no—
588C2×Dic3—68no—
589C2×Dic3—68no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—62no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—128no—
606C2×Dic3—121no—
607C2×Dic3—121no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3C2×C4×D312yes—
613C2×Dic3C2×C4×D312yes—
614C2×Dic3C2×C4×D312yes—
615C2×Dic3D3×D412yes—
616C2×Dic3D3×D412yes—
617C2×Dic3#23712yes—
618C2×Dic3#23712yes—
619C4×D3—68no—
620C2×C32—42no—
621C2×C32C2×#11711yescharacteristic
622C2×C32C2×C4×D411yescharacteristic
623C2×C32C4×#4111yescharacteristic
624C2×C32#52911yescharacteristic
625C2×C32#52911yescharacteristic
626C2×C32#53211yescharacteristic
627C2×C32#53211yescharacteristic
628C3×D3—42no—
629C24—31no—
630C24C2×D3211yescharacteristic
631C2×D4—34no—
632C2×D4—62no—
633C2×D4—62no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—94no—
642C22×C4—91no—
643C22×C4—91no—
644C22×C4—91no—
645C22×C4—94no—
646C22×C4—91no—
647C22×C4—182no—
648C22×C4—182no—
649C22×C4—182no—
650C22×C4—182no—
651C22×C4C2×D3211yescharacteristic
652C22×C4C2×D3211yescharacteristic
653C4⋊C4—62no—
654C4⋊C4—62no—
655C4⋊C4—94no—
656C4⋊C4—182no—
657C4⋊C4—182no—
658C4⋊C4—182no—
659C4⋊C4—182no—
660C22⋊C4—22no—
661C22⋊C4—34no—
662C22⋊C4—62no—
663C22⋊C4—62no—
664C22⋊C4—62no—
665C22⋊C4—62no—
666C22⋊C4—94no—
667C22⋊C4—182no—
668C22⋊C4—182no—
669C22⋊C4—182no—
670C42—62no—
671C42—62no—
672C42—94no—
673C42—94no—
674C42—182no—
675C42—182no—
676C42—182no—
677C42—182no—
678C42—182no—
679C22×C3—24no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3C22×C4×D311yescharacteristic
715C22×C3C22×C4×D311yescharacteristic
716C22×C3C2×D3×D411yescharacteristic
717C22×C3C2×D3×D411yescharacteristic
718C22×C3C2×#23711yescharacteristic
719C22×C3C2×#23711yescharacteristic
720C22×C3C2×#23711yescharacteristic
721C22×C3C2×#23711yescharacteristic
722C22×C3D3×#4111yescharacteristic
723C22×C3D3×#4111yescharacteristic
724C22×C3D3×#4111yescharacteristic
725C22×C3D3×#4111yescharacteristic
726C22×C3D3×#4111yescharacteristic
727C22×C3D3×#4111yescharacteristic
728C2×D3—22no—
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—34no—
738C3×C4—42no—
739C3×C4—42no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—62no—
743C3×C4—62no—
744C3×C4—62no—
745C3×C4—62no—
746C3×C4—121no—
747C3×C4—121no—
748Dic3—22no—
749Dic3—22no—
750Dic3—22no—
751Dic3—22no—
752Dic3—34no—
753Dic3—34no—
754Dic3—41no—
755Dic3—41no—
756Dic3—64no—
757Dic3—62no—
758Dic3—62no—
759Dic3—62no—
760Dic3—62no—
761Dic3—122no—
762Dic3—122no—
763Dic3—122no—
764Dic3—121no—
765Dic3—121no—
766Dic3#87714yescomplemented
767C32#229311yescharacteristic, complemented, Sylow
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—32no—
775C23—61no—
776C23—61no—
777C23—61no—
778C23—61no—
779C23—61no—
780C23—61no—
781C23C4×D3212yes—
782C23C22×D3211yescharacteristic
783D4—68no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—32no—
790C2×C4—32no—
791C2×C4—32no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—32no—
795C2×C4—32no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—92no—
811C2×C4—92no—
812C2×C4—92no—
813C2×C4—92no—
814C2×C4—92no—
815C2×C4—188no—
816C2×C4—188no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—181no—
823C2×C4—181no—
824C2×C4#380512yes—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—44no—
833C2×C3—42no—
834C2×C3—42no—
835C2×C3—122no—
836C2×C3C2×#87711yescharacteristic
837C2×C3D3×#11711yescharacteristic
838C2×C3C4×#23711yescharacteristic
839C2×C3C4×#23711yescharacteristic
840C2×C3C4×D3×D411yescharacteristic
841C2×C3C4×D3×D411yescharacteristic
842C2×C3#559611yescharacteristic
843C2×C3#559611yescharacteristic
844C2×C3#560011yescharacteristic
845C2×C3#564911yescharacteristic
846C2×C3#566811yescharacteristic
847C2×C3#568011yescharacteristic
848C2×C3#570611yescharacteristic
849C2×C3#571611yescharacteristic
850D3—42no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—121no—
865C22C2×C4×D3211yescharacteristic
866C22#6430611yescharacteristic
867C22D32×D411yescharacteristic
868C22D3×#23711yescharacteristic
869C22D3×#23711yescharacteristic
870C22#6431211yescharacteristic
871C22C2×#380511yescharacteristic
872C4—22no—
873C4—34no—
874C4—41no—
875C4—62no—
876C4—62no—
877C4—62no—
878C4—62no—
879C4—94no—
880C4—121no—
881C4—121no—
882C4—182no—
883C4—182no—
884C4—361no—
885C3—21no—
886C3#7545011yescharacteristic, complemented
887C3#7628911yescharacteristic, complemented
888C2—42no—
889C2—122no—
890C2D3×#87711yescharacteristic
891C2#1059406111yescharacteristic
892C2#1059413711yescharacteristic
893C2#1059425511yescharacteristic
894C2C4×#380511yescharacteristic
895C2#1059513311yescharacteristic
896C2#1059520211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2293
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63957C2semidirect
3. C2×#63878C2semidirect
4. C22⋊C4×C3⋊Dic3C2semidirect
6. C3×#4944C2semidirect
8. #10591702C2semidirect
9. #10591368C2semidirect
10. #10591327C2semidirect
11. #10591282C2semidirect
12. #10591279C2semidirect
13. #10591246C2semidirect
14. #10591241C2semidirect
15. C4×Dic32C2semidirect
34. #67⋊Dic3C4semidirect
74. #4944D3semidirect
136. Dic32D4semidirect
440. C3×Dic3#117semidirect
766. Dic3#877semidirect
767. C32#2293semidirect
886. C3#75450semidirect
887. C3#76289semidirect

Maximal subgroups

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

subgroupindex
C2×#67⋊Dic32
C2×#639572
C2×#638782
C22⋊C4×C3⋊Dic32
C3×#49572
C3×#49442
#105917072
#105917022
#105913682
#105913272
#105912822
#105912792
#105912462
#105912412
C4×Dic322
#762893
#754503