Finite Group Databasebeta

← #11801832

Subgroups — #11801832

Order 1152.

1397 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63877C211yesmaximal, characteristic
2C2×#63877C211yesmaximal, characteristic
3C2×C4×D3×Dic3C211yesmaximal, characteristic
4#10592346C211yesmaximal, characteristic, complemented
5C3×#4668C211yesmaximal, characteristic
6C3×#4649C211yesmaximal, characteristic, complemented
7#10591379C211yesmaximal, characteristic
8#10591372C211yesmaximal, characteristic
9#10591337C211yesmaximal, characteristic, complemented
10#10591277C211yesmaximal, characteristic
11Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#10591264C211yesmaximal, characteristic, complemented
13#10591256C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#74378—31nomaximal
17#73755—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
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×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63877—24no—
46#63877C418yescomplemented
47C4×D3×Dic3—24no—
48C32×#95C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C22×C4×Dic3—31no—
57C2×#877—31no—
58C2×#877—31no—
59C2×#872—31no—
60C2×#872—31no—
61C2×C42×D3—31no—
62C3×#385—31no—
63C3×C4×C4⋊C4—31no—
64#5210—31no—
65#4989—31no—
66#4989—31no—
67#4976—31no—
68#4976—31no—
69#4976—31no—
70#4976—31no—
71Dic3×C4⋊C4—31no—
72Dic3×C4⋊C4—31no—
73#4950—31no—
74#4946—31no—
75C4×C4⋊Dic3—31no—
76C4×Dic3⋊C4—31no—
77C4×Dic3⋊C4—31no—
78#4668—31no—
79#4668D311yescharacteristic
80#4649—31no—
81#4649D311yescharacteristic, complemented
82#4647—31no—
83#4647—31no—
84#4647—31no—
85#4647—31no—
86#4647—61no—
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×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×D3×Dic3—22no—
106C2×D3×Dic3—22no—
107C2×D3×Dic3—22no—
108C2×D3×Dic3C2×C414yes—
109C2×D3×Dic3D414yes—
110C2×D3×Dic3Q814yes—
111C4⋊(C3⋊Dic3)—22no—
112#3750—22no—
113#3750—22no—
114#3750C2×C414yescomplemented
115C4×C3⋊Dic3—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4C2×C414yes—
118C3×C4⋊Dic3—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×Dic3⋊C4—22no—
122C3×C4×Dic3—22no—
123C3×C4×Dic3—22no—
124C3×C4×Dic3C2×C414yescomplemented
125#3724—22no—
126#3724—22no—
127#3724C2×C414yescomplemented
128Dic3⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3C2×C414yes—
131Dic32—22no—
132Dic32—22no—
133Dic32—22no—
134Dic32C2×C414yescomplemented
135#2296—91noSylow
136C23×C3×C4—31no—
137C23×Dic3—31no—
138C23×Dic3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C22×C4×D3C2×D311yescharacteristic
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C42—31no—
149C2×C3×C42—31no—
150C2×C3×C42—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4C2×D311yescharacteristic
156C2×(C2×D3)⋊C4C2×D311yescharacteristic
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—61no—
161C2×C4⋊Dic3C2×D311yescharacteristic
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
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—31no—
175C2×Dic3⋊C4—61no—
176C2×Dic3⋊C4—61no—
177C2×Dic3⋊C4—61no—
178C2×Dic3⋊C4C2×D311yescharacteristic
179C2×Dic3⋊C4C2×D311yescharacteristic
180C2×Dic3⋊C4C2×D311yescharacteristic
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
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—61no—
192C2×C4×Dic3—64no—
193C2×C4×Dic3C2×D311yescharacteristic
194C2×C4×Dic3C2×D311yescharacteristic
195C2×C4×Dic3C2×D311yescharacteristic
196#877—38no—
197#877—64no—
198#872—38no—
199#872—64no—
200C42×D3—64no—
201C3×#95—21no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95C2×D311yescharacteristic
205C3×#95C2×D311yescharacteristic
206C3⋊#95—31no—
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—61no—
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C23×C32C2411yescharacteristic
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3C22×C412yes—
225C22×C3×D3C2×D412yes—
226C22×C3×D3C2×Q812yes—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4C22×C412yes—
235C2×C32×C4#4112yes—
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⋊Dic3—21no—
243C2×C3⋊Dic3C22×C412yes—
244C2×C3⋊Dic3C22×C412yes—
245C2×C3⋊Dic3C2×D412yes—
246C2×C3⋊Dic3C2×Q812yes—
247C2×C3⋊Dic3#4112yes—
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×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3C2×D412yes—
266C2×C3×Dic3C2×Q812yes—
267C2×C3×Dic3#4112yes—
268C2×C3×Dic3#4112yes—
269C3×C4×D3—28no—
270D3×Dic3—28no—
271D3×Dic3C4⋊C4116yescomplemented
272C2×#117—91no—
273C2×#117—91no—
274C22×C42—91no—
275#389—91no—
276#389—91no—
277#389—91no—
278#389—91no—
279#385—31no—
280#385—91no—
281#385—91no—
282#385—91no—
283C4×C4⋊C4—31no—
284C4×C4⋊C4—91no—
285C4×C4⋊C4—91no—
286C4×C4⋊C4—91no—
287C24×C3—31no—
288C23×D3C22×D311yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—62no—
300C22×C3×C4—62no—
301C22×C3×C4—62no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—34no—
311C22×Dic3—34no—
312C22×Dic3—34no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—62no—
324C22×Dic3—62no—
325C22×Dic3—62no—
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C2×C4×D3—22no—
334C2×C4×D3—22no—
335C2×C4×D3—22no—
336C2×C4×D3—34no—
337C2×C4×D3—34no—
338C2×C4×D3—34no—
339C2×C4×D3—62no—
340C2×C4×D3—62no—
341C2×C4×D3—62no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—62no—
345C3×C4⋊C4—62no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—62no—
348C3×C42—34no—
349C3×C42—62no—
350C3×C42—62no—
351#217—34no—
352#217—62no—
353(C2×D3)⋊C4—22no—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4C4×D314yes—
357C4⋊Dic3—22no—
358C4⋊Dic3—62no—
359C4⋊Dic3—62no—
360C4⋊Dic3—62no—
361C4⋊Dic3—122no—
362Dic3⋊C4—22no—
363Dic3⋊C4—22no—
364Dic3⋊C4—22no—
365Dic3⋊C4—34no—
366Dic3⋊C4—34no—
367Dic3⋊C4—34no—
368Dic3⋊C4—34no—
369Dic3⋊C4—64no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377Dic3⋊C4—62no—
378Dic3⋊C4—62no—
379Dic3⋊C4—122no—
380Dic3⋊C4—122no—
381C4×Dic3—22no—
382C4×Dic3—22no—
383C4×Dic3—34no—
384C4×Dic3—34no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C4×Dic3—62no—
391C4×Dic3—62no—
392C4×Dic3—62no—
393C4×Dic3—122no—
394C4×Dic3C4×D314yescomplemented
395C22×C32C23×C411yescharacteristic
396C22×C32C22×D411yescharacteristic
397C22×C32C22×Q811yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3C2×C4⋊C414yes—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—41no—
412C3⋊Dic3—22no—
413C3⋊Dic3—22no—
414C3⋊Dic3—41no—
415C3⋊Dic3C2×C4⋊C414yes—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3C2×C4⋊C414yes—
423C23×C4—31no—
424C23×C4—91no—
425C23×C4—91no—
426#117—98no—
427#117—184no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4—91no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C42—31no—
445C2×C42—31no—
446C2×C42—31no—
447C2×C42—91no—
448C2×C42—91no—
449C2×C42—91no—
450C2×C42—91no—
451C2×C42—91no—
452C2×C42—184no—
453#95—31no—
454#95—31no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95D3211yescharacteristic
461C23×C3—21no—
462C23×C3—32no—
463C23×C3—32no—
464C23×C3—32no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3C23×D311yescharacteristic
470C23×C3C23×D311yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3C2×C4×D312yes—
476C22×D3D3×D412yes—
477C22×D3D3×Q812yes—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
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—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—32no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—68no—
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×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4C2×C4×D312yes—
524C2×C3×C4C2×C4×D312yes—
525C2×C3×C4#23512yes—
526C2×C3×C4#23712yes—
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—21no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—316no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—62no—
556C2×Dic3—62no—
557C2×Dic3—68no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—121no—
573C2×Dic3—121no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3C2×C4×D312yes—
580C2×Dic3C2×C4×D312yes—
581C2×Dic3C2×C4×D312yes—
582C2×Dic3#23512yes—
583C2×Dic3D3×D412yes—
584C2×Dic3#23712yes—
585C2×Dic3D3×Q812yes—
586C4×D3—28no—
587C4×D3—316no—
588C4×D3—68no—
589C2×C32C22×C4⋊C411yescharacteristic
590C2×C32C4×#4111yescharacteristic
591C2×C32C4×#4111yescharacteristic
592C2×C32#52511yescharacteristic
593C2×C32#52511yescharacteristic
594C2×C32#53311yescharacteristic
595C2×C32#53311yescharacteristic
596C3×D3—24no—
597C24—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—94no—
609C22×C4—94no—
610C22×C4—94no—
611C22×C4—91no—
612C22×C4—91no—
613C22×C4—91no—
614C22×C4—91no—
615C22×C4—182no—
616C22×C4—182no—
617C22×C4—182no—
618C22×C4C2×D3211yescharacteristic
619C22×C4C2×D3211yescharacteristic
620C22×C4C2×D3211yescharacteristic
621C4⋊C4—62no—
622C4⋊C4—62no—
623C4⋊C4—62no—
624C4⋊C4—62no—
625C4⋊C4—94no—
626C4⋊C4—94no—
627C4⋊C4—182no—
628C4⋊C4—182no—
629C4⋊C4—182no—
630C4⋊C4—182no—
631C4⋊C4—182no—
632C4⋊C4—182no—
633C22⋊C4—34no—
634C22⋊C4—62no—
635C22⋊C4—94no—
636C22⋊C4—182no—
637C42—34no—
638C42—62no—
639C42—62no—
640C42—94no—
641C42—182no—
642C42—182no—
643C42—182no—
644C42—182no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—34no—
653C22×C3—62no—
654C22×C3—62no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3C22×C4×D311yescharacteristic
660C22×C3C22×C4×D311yescharacteristic
661C22×C3C2×#23511yescharacteristic
662C22×C3C2×#23511yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C2×#23711yescharacteristic
666C22×C3C2×#23711yescharacteristic
667C22×C3C2×D3×Q811yescharacteristic
668C22×C3C2×D3×Q811yescharacteristic
669C22×C3D3×#4111yescharacteristic
670C22×C3D3×#4111yescharacteristic
671C22×C3D3×#4111yescharacteristic
672C22×C3D3×#4111yescharacteristic
673C2×D3—22no—
674C2×D3—22no—
675C2×D3—22no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—22no—
679C2×D3D3×C4⋊C414yes—
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—22no—
684C3×C4—34no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—62no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—62no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4—121no—
696Dic3—22no—
697Dic3—22no—
698Dic3—22no—
699Dic3—22no—
700Dic3—34no—
701Dic3—34no—
702Dic3—41no—
703Dic3—41no—
704Dic3—64no—
705Dic3—62no—
706Dic3—62no—
707Dic3—62no—
708Dic3—62no—
709Dic3—122no—
710Dic3—122no—
711Dic3—121no—
712Dic3—121no—
713Dic3—241no—
714Dic3D3×C4⋊C414yes—
715C32#229611yescharacteristic, complemented, Sylow
716C23—32no—
717C23—32no—
718C23—32no—
719C23—61no—
720C23—61no—
721C23—61no—
722C23—61no—
723C23C22×D3211yescharacteristic
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—68no—
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—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—916no—
754C2×C4—92no—
755C2×C4—92no—
756C2×C4—92no—
757C2×C4—92no—
758C2×C4—92no—
759C2×C4—188no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4#379512yes—
768C2×C4C4×D3212yes—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—64no—
777C2×C3C4×#23511yescharacteristic
778C2×C3C2×D3×C4⋊C411yescharacteristic
779C2×C3C2×D3×C4⋊C411yescharacteristic
780C2×C3#552211yescharacteristic
781C2×C3C4×#23711yescharacteristic
782C2×C3C4×#23711yescharacteristic
783C2×C3#554711yescharacteristic
784C2×C3#554711yescharacteristic
785C2×C3#557811yescharacteristic
786C2×C3#557811yescharacteristic
787C2×C3#558611yescharacteristic
788C2×C3#562211yescharacteristic
789C2×C3#562211yescharacteristic
790C2×C3#565611yescharacteristic
791D3—24no—
792C22—34no—
793C22—62no—
794C22—62no—
795C22—62no—
796C22—62no—
797C22—62no—
798C22—62no—
799C22C2×#379511yescharacteristic
800C22C2×C4×D3211yescharacteristic
801C22D3×#23511yescharacteristic
802C22D32×D411yescharacteristic
803C22D3×#23711yescharacteristic
804C22#6431211yescharacteristic
805C22D32×Q811yescharacteristic
806C4—22no—
807C4—22no—
808C4—34no—
809C4—41no—
810C4—62no—
811C4—62no—
812C4—62no—
813C4—62no—
814C4—94no—
815C4—121no—
816C4—121no—
817C4—182no—
818C4—182no—
819C4—361no—
820C3—21no—
821C3#7375511yescharacteristic, complemented
822C3#7437811yescharacteristic, complemented
823C2—64no—
824C2C4×#379511yescharacteristic
825C2#1059404811yescharacteristic
826C2#1059405411yescharacteristic
827C2#1059426611yescharacteristic
828C2#1059438511yescharacteristic
829C2#1059438611yescharacteristic
830C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #10592346C2semidirect
6. C3×#4649C2semidirect
9. #10591337C2semidirect
11. Dic3×C4⋊Dic3C2semidirect
12. #10591264C2semidirect
13. #10591256C2semidirect
14. #10591243C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
46. #63877C4semidirect
81. #4649D3semidirect
114. #3750C2×C4semidirect
124. C3×C4×Dic3C2×C4semidirect
127. #3724C2×C4semidirect
134. Dic32C2×C4semidirect
271. D3×Dic3C4⋊C4semidirect
394. C4×Dic3C4×D3semidirect
715. C32#2296semidirect
821. C3#73755semidirect
822. C3#74378semidirect

Maximal subgroups

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

subgroupindex
C2×#638772
C2×C4×D3×Dic32
#105923462
C3×#46682
C3×#46492
#105913792
#105913722
#105913372
#105912772
Dic3×C4⋊Dic32
#105912642
#105912562
#105912432
Dic3×Dic3⋊C42
#743783
#737553