Finite Group Databasebeta

← #11801698

Subgroups — #11801698

Order 1152.

1399 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63880C211yesmaximal, characteristic
2C2×#63877C211yesmaximal, characteristic, complemented
3C2×#63836C211yesmaximal, characteristic, complemented
4#10592368C211yesmaximal, characteristic, complemented
5C3×#4669C211yesmaximal, characteristic, complemented
6C3×#4649C211yesmaximal, characteristic, complemented
7#10591384C211yesmaximal, characteristic
8#10591384C211yesmaximal, characteristic
9Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#10591286C211yesmaximal, characteristic, complemented
11#10591246C211yesmaximal, characteristic, complemented
12C4×Dic32C211yesmaximal, characteristic, complemented
13#10591234C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#75450—31nomaximal
17#73617—31nomaximal
18C22×#626C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3750C2211yescharacteristic
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×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63880C418yescomplemented
48#63877—24no—
49#63836—24no—
50C32×#95C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#892—31no—
57C2×#67⋊C4—31no—
58C2×#877—31no—
59C2×C4×D12—31no—
60C2×#872—31no—
61C2×#872—31no—
62C3×#388—31no—
63C3×C4×C4⋊C4—31no—
64#4988—31no—
65#4988—31no—
66#4976—31no—
67#4972—31no—
68#4972—31no—
69#4957—31no—
70#4957—31no—
71#4951—31no—
72Dic3×C22⋊C4—31no—
73#4940—31no—
74C4×(C2×D3)⋊C4—31no—
75C4×(C2×D3)⋊C4—31no—
76C42×Dic3—31no—
77C42×Dic3—31no—
78#4669—31no—
79#4669—31no—
80#4669—31no—
81#4669—31no—
82#4669—61no—
83#4669D311yescharacteristic, complemented
84#4666—31no—
85#4649D311yescharacteristic, complemented
86#4647—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
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×#626—22no—
103C2×#626—22no—
104C2×#626C2×C414yes—
105C2×#624—22no—
106C2×#624—22no—
107C2×#624C2×C414yes—
108C2×D3×Dic3—22no—
109C2×D3×Dic3—22no—
110C2×D3×Dic3C2×C414yes—
111#3752—22no—
112#3752—22no—
113#3752C2×C414yes—
114#3750—22no—
115C4×C3⋊Dic3—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—22no—
118C3×(C2×D3)⋊C4C2×C414yes—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×Dic3⋊C4—22no—
122C3×C4×Dic3—22no—
123C3×C4×Dic3—22no—
124C3×C4×Dic3—22no—
125C3×C4×Dic3C2×C414yes—
126#3724—22no—
127Dic3⋊Dic3—22no—
128Dic3⋊Dic3C2×C414yes—
129#3722—22no—
130#3722—22no—
131(C2×D3)⋊Dic3—22no—
132(C2×D3)⋊Dic3—22no—
133Dic32—22no—
134Dic32—22no—
135Dic32—22no—
136Dic32D414yescomplemented
137#2293—91noSylow
138C22×#67—31no—
139C23×Dic3—31no—
140C22×D12—31no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C42—31no—
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×C3×C42—31no—
154C2×#217—31no—
155C2×#217—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—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×(C2×D3)⋊C4C2×D311yescharacteristic
172C2×(C2×D3)⋊C4C2×D311yescharacteristic
173C2×(C2×D3)⋊C4C2×D311yescharacteristic
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—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⋊C4—61no—
183C2×Dic3⋊C4C2×D311yescharacteristic
184C2×Dic3⋊C4C2×D311yescharacteristic
185C2×Dic3⋊C4C2×D311yescharacteristic
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—61no—
197C2×C4×Dic3C2×D311yescharacteristic
198C2×C4×Dic3C2×D311yescharacteristic
199C2×C4×Dic3C2×D311yescharacteristic
200C2×C4×Dic3C2×D311yescharacteristic
201#892—64no—
202#67⋊C4—38no—
203#877—64no—
204C4×D12—38no—
205#872—64no—
206#872—64no—
207C3×#95—21no—
208C3×#95—31no—
209C3×#95—31no—
210C3×#95C2×D311yescharacteristic
211C3×#95C2×D311yescharacteristic
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—61no—
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32C2411yescharacteristic
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⋊D3C22×C412yes—
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—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C22×C412yes—
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⋊Dic3C22×C412yes—
252C2×C3⋊Dic3C2×D412yes—
253C2×C3⋊Dic3#4112yes—
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×Dic3C22×C412yes—
267C2×C3×Dic3C22×C412yes—
268C2×C3×Dic3C22×C412yes—
269C2×C3×Dic3C2×D412yes—
270C2×C3×Dic3C2×D412yes—
271C2×C3×Dic3#4112yes—
272C2×C3×Dic3#4112yes—
273C2×C3×Dic3#4112yes—
274C2×C3×Dic3#4112yes—
275#626—28no—
276#624—28no—
277D3×Dic3—28no—
278C2×C4×D4—91no—
279C2×#117—91no—
280C2×#117—91no—
281#390—91no—
282#390—91no—
283#389—91no—
284#389—91no—
285#388—31no—
286#388—91no—
287#388—91no—
288#388—91no—
289C4×C4⋊C4—31no—
290C4×C22⋊C4—91no—
291C4×C22⋊C4—91no—
292C43—91no—
293C24×C3—31no—
294C23×D3—31no—
295C23×D3—31no—
296C23×D3—61no—
297C23×D3C22×D311yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C2×#67—34no—
315C2×#67—62no—
316C2×#67—62no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—34no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—62no—
328C22×Dic3—62no—
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C2×D12—34no—
337C2×D12—62no—
338C2×D12—62no—
339C2×C4×D3—34no—
340C2×C4×D3—34no—
341C2×C4×D3—34no—
342C2×C4×D3—62no—
343C2×C4×D3—62no—
344C2×C4×D3—62no—
345C2×C4×D3—62no—
346C2×C4×D3—62no—
347C2×C4×D3—62no—
348C3×C4⋊C4—62no—
349C3×C4⋊C4—62no—
350C3×C4⋊C4—62no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4—62no—
353C3×C22⋊C4—62no—
354C3×C42—34no—
355C3×C42—62no—
356C3×C42—62no—
357C3×C42—62no—
358#217—62no—
359#217—62no—
360(C2×D3)⋊C4—22no—
361(C2×D3)⋊C4—22no—
362(C2×D3)⋊C4—34no—
363(C2×D3)⋊C4—34no—
364(C2×D3)⋊C4—64no—
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—62no—
372(C2×D3)⋊C4—62no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—122no—
376(C2×D3)⋊C4—122no—
377(C2×D3)⋊C4C4×D314yes—
378C4⋊Dic3—34no—
379C4⋊Dic3—62no—
380Dic3⋊C4—22no—
381Dic3⋊C4—22no—
382Dic3⋊C4—22no—
383Dic3⋊C4—34no—
384Dic3⋊C4—62no—
385Dic3⋊C4—62no—
386Dic3⋊C4—62no—
387Dic3⋊C4—62no—
388Dic3⋊C4—62no—
389Dic3⋊C4—122no—
390C4×Dic3—22no—
391C4×Dic3—22no—
392C4×Dic3—22no—
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—122no—
404C4×Dic3C4×D314yes—
405C22×C32C23×C411yescharacteristic
406C22×C32C22×D411yescharacteristic
407C22×C32C2×#4111yescharacteristic
408C22×C32C2×#4111yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C22×C32C2×#4111yescharacteristic
411C22×C32C2×#4111yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—22no—
414C2×C3⋊D3—22no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C32×C4—22no—
427C32×C4—41no—
428C32×C4—41no—
429C3⋊Dic3—22no—
430C3⋊Dic3—22no—
431C3⋊Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3#11714yescomplemented
438C3×Dic3C4×D414yes—
439C22×D4—91no—
440C23×C4—91no—
441C23×C4—91no—
442C4×D4—98no—
443#117—184no—
444#117—184no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—91no—
451C2×C4⋊C4—91no—
452C2×C22⋊C4—31no—
453C2×C22⋊C4—31no—
454C2×C22⋊C4—31no—
455C2×C22⋊C4—91no—
456C2×C22⋊C4—91no—
457C2×C22⋊C4—91no—
458C2×C22⋊C4—91no—
459C2×C22⋊C4—91no—
460C2×C22⋊C4—91no—
461C2×C22⋊C4—91no—
462C2×C42—31no—
463C2×C42—31no—
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—91no—
467C2×C42—91no—
468C2×C42—91no—
469C2×C42—91no—
470C2×C42—91no—
471#95—31no—
472#95—31no—
473#95—91no—
474#95—91no—
475#95—91no—
476#95D3211yescharacteristic
477C23×C3—21no—
478C23×C3—32no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3C23×D311yescharacteristic
486C23×C3C23×D311yescharacteristic
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—32no—
494C22×D3—32no—
495C22×D3—62no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—121no—
509C22×D3—121no—
510C22×D3—121no—
511C22×D3—121no—
512C22×D3—121no—
513C22×D3—121no—
514C22×D3C2×C4×D312yes—
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—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—22no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
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—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4C2×C4×D312yes—
562C2×C3×C4C2×C4×D312yes—
563#67—68no—
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—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
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—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—68no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3C2×C4×D312yes—
605C2×Dic3C2×C4×D312yes—
606C2×Dic3C2×C4×D312yes—
607C2×Dic3#23512yes—
608C2×Dic3#23512yes—
609C2×Dic3D3×D412yes—
610C2×Dic3D3×D412yes—
611C2×Dic3#23712yes—
612C2×Dic3#23912yes—
613D12—68no—
614C4×D3—68no—
615C4×D3—68no—
616C4×D3—68no—
617C2×C32C2×#11711yescharacteristic
618C2×C32C2×C4×D411yescharacteristic
619C2×C32C4×#4111yescharacteristic
620C2×C32#52911yescharacteristic
621C2×C32#52911yescharacteristic
622C2×C32#53211yescharacteristic
623C2×C32#53211yescharacteristic
624C3⋊D3—42no—
625C3×D3—42no—
626C24—31no—
627C24—91no—
628C2×D4—94no—
629C2×D4—182no—
630C2×D4—182no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—94no—
639C22×C4—94no—
640C22×C4—91no—
641C22×C4—91no—
642C22×C4—91no—
643C22×C4—182no—
644C22×C4—182no—
645C22×C4—182no—
646C22×C4—182no—
647C22×C4C2×D3211yescharacteristic
648C22×C4C2×D3211yescharacteristic
649C22×C4C2×D3211yescharacteristic
650C4⋊C4—62no—
651C4⋊C4—62no—
652C4⋊C4—62no—
653C4⋊C4—94no—
654C4⋊C4—182no—
655C4⋊C4—182no—
656C4⋊C4—182no—
657C22⋊C4—34no—
658C22⋊C4—62no—
659C22⋊C4—62no—
660C22⋊C4—94no—
661C22⋊C4—182no—
662C22⋊C4—182no—
663C22⋊C4—182no—
664C22⋊C4—182no—
665C22⋊C4—182no—
666C22⋊C4—182no—
667C42—34no—
668C42—62no—
669C42—62no—
670C42—62no—
671C42—94no—
672C42—182no—
673C42—182no—
674C42—182no—
675C42—182no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—62no—
684C22×C3—62no—
685C22×C3—62no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3C22×C4×D311yescharacteristic
691C22×C3C22×C4×D311yescharacteristic
692C22×C3C2×#23511yescharacteristic
693C22×C3C2×#23511yescharacteristic
694C22×C3C2×D3×D411yescharacteristic
695C22×C3C2×D3×D411yescharacteristic
696C22×C3C2×#23711yescharacteristic
697C22×C3C2×#23911yescharacteristic
698C22×C3D3×#4111yescharacteristic
699C22×C3D3×#4111yescharacteristic
700C22×C3D3×#4111yescharacteristic
701C22×C3D3×#4111yescharacteristic
702C22×C3D3×#4111yescharacteristic
703C22×C3D3×#4111yescharacteristic
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—62no—
712C2×D3—62no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—122no—
718C2×D3—122no—
719C2×D3—122no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—241no—
729C2×D3—241no—
730C2×D3—241no—
731C2×D3—241no—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—34no—
735C3×C4—34no—
736C3×C4—42no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—62no—
742C3×C4—62no—
743C3×C4—62no—
744C3×C4—81no—
745C3×C4—81no—
746C3×C4—121no—
747C3×C4—121no—
748Dic3—22no—
749Dic3—22no—
750Dic3—22no—
751Dic3—41no—
752Dic3—41no—
753Dic3—62no—
754Dic3—62no—
755Dic3—62no—
756Dic3—62no—
757Dic3—62no—
758Dic3—62no—
759Dic3—122no—
760Dic3—122no—
761Dic3—122no—
762Dic3#87214yescomplemented
763Dic3#89314yes—
764C32#229311yescharacteristic, complemented, Sylow
765C23—32no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23—61no—
771C23—61no—
772C23—92no—
773C23—181no—
774C23—181no—
775C23—181no—
776C23—181no—
777C23—181no—
778C23—181no—
779C23C22×D3211yescharacteristic
780D4—188no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
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—32no—
797C2×C4—32no—
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—188no—
814C2×C4—188no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4C4×D3212yes—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—122no—
830C2×C3C2×#87211yescharacteristic
831C2×C3C2×#89311yescharacteristic
832C2×C3D3×#11711yescharacteristic
833C2×C3#552211yescharacteristic
834C2×C3C4×#23711yescharacteristic
835C2×C3C4×D3×D411yescharacteristic
836C2×C3#554811yescharacteristic
837C2×C3#554811yescharacteristic
838C2×C3#558011yescharacteristic
839C2×C3#558011yescharacteristic
840C2×C3#559611yescharacteristic
841C2×C3#564911yescharacteristic
842C2×C3#566811yescharacteristic
843C2×C3#570611yescharacteristic
844D3—42no—
845D3—122no—
846D3—122no—
847D3—242no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—121no—
852C22—121no—
853C22—121no—
854C22—121no—
855C22—182no—
856C22—182no—
857C22—182no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22C2×C4×D3211yescharacteristic
863C22D3×#23511yescharacteristic
864C22D3×#23511yescharacteristic
865C22D32×D411yescharacteristic
866C22D3×#23711yescharacteristic
867C22#6431211yescharacteristic
868C22D3×#23911yescharacteristic
869C4—22no—
870C4—34no—
871C4—34no—
872C4—41no—
873C4—41no—
874C4—62no—
875C4—62no—
876C4—62no—
877C4—121no—
878C4—121no—
879C4—182no—
880C4—182no—
881C4—182no—
882C3—21no—
883C3#7361711yescharacteristic, complemented
884C3#7545011yescharacteristic, complemented
885C2—122no—
886C2—362no—
887C2D3×#87211yescharacteristic
888C2#1059404811yescharacteristic
889C2#1059405811yescharacteristic
890C2#1059406811yescharacteristic
891C2#1059441611yescharacteristic
892C2#1059442311yescharacteristic
893C2D3×#89311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2293
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63877C2semidirect
3. C2×#63836C2semidirect
4. #10592368C2semidirect
5. C3×#4669C2semidirect
6. C3×#4649C2semidirect
9. Dic3×(C2×D3)⋊C4C2semidirect
10. #10591286C2semidirect
11. #10591246C2semidirect
12. C4×Dic32C2semidirect
13. #10591234C2semidirect
14. #10591233C2semidirect
15. #10591202C2semidirect
47. #63880C4semidirect
83. #4669D3semidirect
85. #4649D3semidirect
136. Dic32D4semidirect
437. C3×Dic3#117semidirect
762. Dic3#872semidirect
764. C32#2293semidirect
883. C3#73617semidirect
884. C3#75450semidirect

Maximal subgroups

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

subgroupindex
C2×#638802
C2×#638772
C2×#638362
#105923682
C3×#46692
C3×#46492
#105913842
Dic3×(C2×D3)⋊C42
#105912862
#105912462
C4×Dic322
#105912342
#105912332
#105912022
#754503
#736173