Finite Group Databasebeta

← #11808822

Subgroups — #11808822

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63881C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic, complemented
3#10592365C211yesmaximal, characteristic, complemented
4C3×#4675C211yesmaximal, characteristic, complemented
5C3×#4658C211yesmaximal, characteristic, complemented
6#10591368C211yesmaximal, characteristic, complemented
7#10591368C211yesmaximal, characteristic, complemented
8#10591293C211yesmaximal, characteristic, complemented
9#10591292C211yesmaximal, characteristic
10#10591291C211yesmaximal, characteristic
11#10591260C211yesmaximal, characteristic, complemented
12#10591252C211yesmaximal, characteristic, complemented
13#10591205C211yesmaximal, characteristic, complemented
14#10591204C211yesmaximal, characteristic, complemented
15#10591199C211yesmaximal, characteristic, complemented
16#78131—31nomaximal
17#77460—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63881—24no—
42#63838—24no—
43C32×#95C2211yescharacteristic
44#63658C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#893—31no—
56C2×#887—31no—
57C2×#887—31no—
58C2×#67⋊C4—31no—
59C3×#400—31no—
60C3×#397—31no—
61#4992—31no—
62#4991—31no—
63#4985—31no—
64#4959—31no—
65#4959—31no—
66#4947—31no—
67Dic3×C22⋊C4—31no—
68Dic3×C22⋊C4—31no—
69#4675—31no—
70#4675D311yescharacteristic, complemented
71#4673—31no—
72#4673—31no—
73#4673—31no—
74#4672—31no—
75#4666—31no—
76#4666—31no—
77#4666—31no—
78#4666—31no—
79#4666—31no—
80#4666—31no—
81#4666—61no—
82#4658—31no—
83#4658D311yescharacteristic, complemented
84#4648—31no—
85#4648—31no—
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
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—
107C2×#626—22no—
108C2×#626—22no—
109C2×#626—22no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113#3752—22no—
114#3752—22no—
115C4×C3⋊Dic3—22no—
116C4×C3⋊Dic3—22no—
117C3×(C2×D3)⋊C4—22no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×Dic3⋊C4—22no—
122C3×Dic3⋊C4—22no—
123#3724—22no—
124#3722—22no—
125#3722—22no—
126#3722—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129Dic32—22no—
130Dic32—22no—
131Dic32D414yes—
132#2398—91noSylow
133C22×#67—31no—
134C23×Dic3—31no—
135C22×D12—31no—
136C22×C4×D3—31no—
137C22×C4×D3—31no—
138C22×C4×D3—31no—
139C22×C4×D3—61no—
140C22×Dic6—31no—
141C22×Dic6—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—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)⋊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—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—61no—
163C2×(C2×D3)⋊C4—61no—
164C2×(C2×D3)⋊C4C2×D311yescharacteristic
165C2×(C2×D3)⋊C4C2×D311yescharacteristic
166C2×(C2×D3)⋊C4C2×D311yescharacteristic
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×Dic3⋊C4C2×D311yescharacteristic
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—61no—
183C2×C4×Dic3—61no—
184#893—64no—
185#887—64no—
186#887—64no—
187#67⋊C4—64no—
188C3×#95—21no—
189C3×#95—31no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95—31no—
194C3×#95—31no—
195C3×#95C2×D311yescharacteristic
196C3×#95C2×D311yescharacteristic
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—61no—
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32C2411yescharacteristic
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3#4112yes—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D412yes—
244C2×C3⋊Dic3#4112yes—
245C2×C3⋊Dic3#4112yes—
246C2×C3⋊Dic3#4112yes—
247C4×C3⋊D3—44no—
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×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D412yes—
267C2×C3×Dic3C2×D412yes—
268C2×C3×Dic3#4112yes—
269#627—28no—
270#626—28no—
271D3×Dic3—44no—
272C2×C4×Q8—91no—
273C2×C4×D4—91no—
274#400—31no—
275#400—91no—
276#397—31no—
277#397—91no—
278#394—91no—
279#394—91no—
280#393—91no—
281#393—91no—
282C4×C22⋊C4—91no—
283C4×C22⋊C4—91no—
284C4×C22⋊C4—91no—
285C4×C22⋊C4—91no—
286#376—91no—
287C24×C3—31no—
288C23×D3—31no—
289C23×D3—31no—
290C23×D3—61no—
291C23×D3C22×D311yescharacteristic
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—62no—
309C2×#67—62no—
310C2×#67—62no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—62no—
321C22×Dic3—62no—
322C22×Dic3—62no—
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C2×D12—62no—
331C2×D12—62no—
332C2×D12—62no—
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3—62no—
338C2×C4×D3—62no—
339C2×C4×D3—62no—
340C2×C4×D3—62no—
341C2×C4×D3—62no—
342C2×C4×D3—64no—
343C2×C4×D3—122no—
344C2×C4×D3—122no—
345C2×Dic6—62no—
346C2×Dic6—62no—
347C2×Dic6—62no—
348C2×Dic6—62no—
349C2×Dic6—62no—
350C2×Dic6—62no—
351C3×C4⋊C4—62no—
352C3×C4⋊C4—62no—
353C3×C4⋊C4—62no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—62no—
356C3×C22⋊C4—62no—
357#217—62no—
358#217—62no—
359(C2×D3)⋊C4—22no—
360(C2×D3)⋊C4—22no—
361(C2×D3)⋊C4—22no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—62no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—62no—
369(C2×D3)⋊C4—62no—
370(C2×D3)⋊C4—62no—
371(C2×D3)⋊C4—64no—
372(C2×D3)⋊C4—64no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—62no—
376Dic3⋊C4—22no—
377Dic3⋊C4—22no—
378Dic3⋊C4—22no—
379Dic3⋊C4—62no—
380Dic3⋊C4—62no—
381C4×Dic3—34no—
382C4×Dic3—34no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C4×Dic3—62no—
391C4×Dic3—122no—
392C4×Dic3—122no—
393C22×C32C22×D411yescharacteristic
394C22×C32C2×#4111yescharacteristic
395C22×C32C2×#4111yescharacteristic
396C22×C32C2×#4111yescharacteristic
397C22×C32C2×#4111yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C2×C3⋊D3—22no—
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4—41no—
417C3⋊Dic3—22no—
418C3⋊Dic3—41no—
419C3⋊Dic3#12414yes—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×Q8—91no—
428C22×D4—91no—
429C23×C4—91no—
430C23×C4—91no—
431C4×Q8—184no—
432C4×D4—184no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C42—91no—
448C2×C42—91no—
449C2×C42—91no—
450C2×C42—91no—
451C2×C42—91no—
452#95—31no—
453#95—31no—
454#95—31no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463#95D3211yescharacteristic
464C23×C3—21no—
465C23×C3—32no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3C23×D311yescharacteristic
473C23×C3C23×D311yescharacteristic
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—32no—
481C22×D3—32no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3—62no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—121no—
498C22×D3—121no—
499C22×D3—121no—
500C22×D3—121no—
501C22×D3#23712yes—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
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—
550#67—68no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
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—32no—
570C2×Dic3—32no—
571C2×Dic3—32no—
572C2×Dic3—32no—
573C2×Dic3—32no—
574C2×Dic3—32no—
575C2×Dic3—32no—
576C2×Dic3—32no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—62no—
580C2×Dic3—62no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—62no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—124no—
597C2×Dic3D3×D412yes—
598C2×Dic3D3×D412yes—
599C2×Dic3#23912yes—
600D12—68no—
601C4×D3—124no—
602C4×D3—124no—
603C4×D3—124no—
604C4×D3—128no—
605Dic6—68no—
606Dic6—68no—
607C2×C32#52511yescharacteristic
608C2×C32#52511yescharacteristic
609C2×C32C2×#12411yescharacteristic
610C2×C32#52911yescharacteristic
611C2×C32#52911yescharacteristic
612C2×C32#52911yescharacteristic
613C2×C32#52911yescharacteristic
614C3⋊D3—42no—
615C3×D3—42no—
616C24—31no—
617C24—91no—
618C2×Q8—182no—
619C2×Q8—182no—
620C2×Q8—182no—
621C2×D4—182no—
622C2×D4—182no—
623C2×D4—182no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—91no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—182no—
635C22×C4—182no—
636C22×C4—182no—
637C22×C4—182no—
638C22×C4—182no—
639C22×C4—182no—
640C22×C4C2×D3211yescharacteristic
641C22×C4C2×D3211yescharacteristic
642C22×C4C2×D3211yescharacteristic
643C4⋊C4—62no—
644C4⋊C4—62no—
645C4⋊C4—62no—
646C4⋊C4—182no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—62no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—182no—
655C22⋊C4—182no—
656C22⋊C4—182no—
657C42—94no—
658C42—182no—
659C42—182no—
660C42—182no—
661C42—182no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—62no—
670C22×C3—62no—
671C22×C3—62no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C2×D3×D411yescharacteristic
678C22×C3C2×#23711yescharacteristic
679C22×C3C2×#23911yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3D3×#4111yescharacteristic
683C22×C3D3×#4111yescharacteristic
684C22×C3D3×#4111yescharacteristic
685C22×C3D3×#4111yescharacteristic
686C22×C3D3×#4111yescharacteristic
687C22×C3D3×#4111yescharacteristic
688C22×C3D3×#4111yescharacteristic
689C22×C3D3×#4111yescharacteristic
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—64no—
698C2×D3—62no—
699C2×D3—62no—
700C2×D3—62no—
701C2×D3—62no—
702C2×D3—62no—
703C2×D3—62no—
704C2×D3—122no—
705C2×D3—122no—
706C2×D3—122no—
707C2×D3—122no—
708C2×D3—122no—
709C2×D3—122no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—62no—
728C3×C4—62no—
729C3×C4—62no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4—121no—
734Dic3—22no—
735Dic3—22no—
736Dic3—22no—
737Dic3—34no—
738Dic3—34no—
739Dic3—41no—
740Dic3—41no—
741Dic3—41no—
742Dic3—41no—
743Dic3—64no—
744Dic3—62no—
745Dic3—62no—
746Dic3—122no—
747Dic3—122no—
748Dic3—121no—
749Dic3—121no—
750C32#239811yescharacteristic, complemented, Sylow
751C23—32no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—92no—
759C23—181no—
760C23—181no—
761C23—181no—
762C23—181no—
763C23—181no—
764C23—181no—
765C23C22×D3211yescharacteristic
766Q8—188no—
767D4—188no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—92no—
799C2×C4—92no—
800C2×C4—92no—
801C2×C4—92no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—364no—
808C2×C4—364no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—122no—
817C2×C3#560611yescharacteristic
818C2×C3#562711yescharacteristic
819C2×C3#564911yescharacteristic
820C2×C3#564911yescharacteristic
821C2×C3#565611yescharacteristic
822C2×C3#565611yescharacteristic
823C2×C3D3×#12411yescharacteristic
824C2×C3D3×#12411yescharacteristic
825C2×C3#569111yescharacteristic
826C2×C3#569111yescharacteristic
827C2×C3#570611yescharacteristic
828C2×C3#570611yescharacteristic
829C2×C3#570611yescharacteristic
830C2×C3#570611yescharacteristic
831D3—42no—
832D3—124no—
833D3—122no—
834D3—122no—
835C22—62no—
836C22—62no—
837C22—62no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—182no—
843C22—182no—
844C22—182no—
845C22—361no—
846C22—361no—
847C22—361no—
848C22—361no—
849C22#6430611yescharacteristic
850C22#6430611yescharacteristic
851C22#6430611yescharacteristic
852C22D32×D411yescharacteristic
853C22D3×#23711yescharacteristic
854C22#6431211yescharacteristic
855C22D3×#23911yescharacteristic
856C4—41no—
857C4—41no—
858C4—41no—
859C4—62no—
860C4—62no—
861C4—62no—
862C4—94no—
863C4—121no—
864C4—121no—
865C4—121no—
866C4—121no—
867C4—182no—
868C4—361no—
869C3—21no—
870C3#7746011yescharacteristic, complemented
871C3#7813111yescharacteristic, complemented
872C2—122no—
873C2—362no—
874C2#1059397911yescharacteristic
875C2#1059413011yescharacteristic
876C2#1059426711yescharacteristic
877C2#1059428811yescharacteristic
878C2#1059444111yescharacteristic
879C2#1059446511yescharacteristic
880C2#1059461511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63838C2semidirect
3. #10592365C2semidirect
4. C3×#4675C2semidirect
5. C3×#4658C2semidirect
6. #10591368C2semidirect
7. #10591368C2semidirect
8. #10591293C2semidirect
11. #10591260C2semidirect
12. #10591252C2semidirect
13. #10591205C2semidirect
14. #10591204C2semidirect
15. #10591199C2semidirect
70. #4675D3semidirect
83. #4658D3semidirect
750. C32#2398semidirect
870. C3#77460semidirect
871. C3#78131semidirect

Maximal subgroups

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

subgroupindex
C2×#638812
C2×#638382
#105923652
C3×#46752
C3×#46582
#105913682
#105912932
#105912922
#105912912
#105912602
#105912522
#105912052
#105912042
#105911992
#781313
#774603