Finite Group Databasebeta

← #11808459

Subgroups — #11808459

Order 1152.

1477 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63904C211yesmaximal, characteristic, complemented
2C2×#63880C211yesmaximal, characteristic, complemented
3C2×#63879C211yesmaximal, characteristic, complemented
4C2×#63836C211yesmaximal, characteristic, complemented
5#10592374C211yesmaximal, characteristic, complemented
6C3×#4676C211yesmaximal, characteristic, complemented
7C3×#4666C211yesmaximal, characteristic, complemented
8#10591393C211yesmaximal, characteristic
9#10591390C211yesmaximal, characteristic, complemented
10Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#10591340C211yesmaximal, characteristic, complemented
12#10591312C211yesmaximal, characteristic, complemented
13#10591306C211yesmaximal, characteristic, complemented
14#10591291C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#77281—31nomaximal
17#73581—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×#626C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63904—24no—
48#63880—24no—
49#63879—24no—
50#63836—24no—
51C32×#95C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C4×#67—31no—
58C2×C4×#67—31no—
59C2×#893—31no—
60C2×#892—31no—
61C2×#67⋊C4—31no—
62C2×#67⋊C4—31no—
63C2×C4×D12—31no—
64C2×#872—31no—
65C3×#396—31no—
66C3×C4×C22⋊C4—31no—
67#4994—31no—
68#4991—31no—
69#4982—31no—
70Dic3×C4⋊C4—31no—
71#4961—31no—
72#4961—31no—
73#4960—31no—
74#4960—31no—
75#4959—31no—
76#4959—31no—
77#4948—31no—
78Dic3×C22⋊C4—31no—
79C4×(C2×D3)⋊C4—31no—
80C4×Dic3⋊C4—31no—
81#4676D311yescharacteristic, complemented
82#4675—31no—
83#4675—31no—
84#4675—61no—
85#4672—31no—
86#4666D311yescharacteristic, complemented
87#4657—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×#626—22no—
107C2×#626—22no—
108C2×#626—22no—
109C2×#626—22no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#625—22no—
113C2×#625—22no—
114C2×#625—22no—
115C2×#624—22no—
116C2×#624—22no—
117C2×#624D414yescomplemented
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121#3752—22no—
122#3752—22no—
123#3752—22no—
124#3750—22no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×Dic3⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×C4×Dic3—22no—
134C3×C4×Dic3—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138#3722—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142Dic32—22no—
143Dic32D414yescomplemented
144#2392—91noSylow
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C23×Dic3—31no—
151C22×D12—31no—
152C22×D12—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3C2×D311yescharacteristic
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C42—31no—
166C2×C3×C42—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C4×#67—64no—
171C4×#67—64no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—61no—
184C2×(C2×D3)⋊C4—61no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—61no—
200C2×Dic3⋊C4C2×D311yescharacteristic
201C2×Dic3⋊C4C2×D311yescharacteristic
202C2×Dic3⋊C4C2×D311yescharacteristic
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3C2×D311yescharacteristic
208C2×C4×Dic3C2×D311yescharacteristic
209#893—64no—
210#892—64no—
211#67⋊C4—64no—
212#67⋊C4—64no—
213C4×D12—64no—
214#872—64no—
215C3×#95—21no—
216C3×#95—31no—
217C3×#95C2×D311yescharacteristic
218C3×#95C2×D311yescharacteristic
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—61no—
228C3⋊#95—61no—
229C3⋊#95C2×D311yescharacteristic
230C23×C32C2411yescharacteristic
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3C2×D412yes—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3#4112yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—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⋊Dic3C2×D412yes—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D412yes—
282C2×C3×Dic3C2×D412yes—
283C2×C3×Dic3C2×D412yes—
284C2×C3×Dic3C2×D412yes—
285C2×C3×Dic3#4112yes—
286C2×C3×Dic3#4112yes—
287C2×C3×Dic3#4112yes—
288C3×C4×D3—44no—
289#626—28no—
290#626—28no—
291#625—28no—
292#624—28no—
293D3×Dic3—44no—
294C2×C4×D4—91no—
295C2×C4×D4—91no—
296C2×C4×D4—91no—
297C2×#117—91no—
298#398—91no—
299#397—91no—
300#396—31no—
301#396—91no—
302#394—91no—
303#394—91no—
304#394—91no—
305#392—91no—
306C4×C4⋊C4—91no—
307C4×C22⋊C4—31no—
308C4×C22⋊C4—91no—
309C24×C3—31no—
310C24×C3—31no—
311C23×D3—31no—
312C23×D3—31no—
313C23×D3—61no—
314C23×D3C22×D311yescharacteristic
315C23×D3C22×D311yescharacteristic
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—62no—
326C22×C3×C4—62no—
327C22×C3×C4—62no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C2×#67—62no—
335C2×#67—62no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—62no—
356C22×Dic3—62no—
357C22×Dic3—62no—
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—62no—
369C2×D12—62no—
370C2×C4×D3—22no—
371C2×C4×D3—22no—
372C2×C4×D3—22no—
373C2×C4×D3—34no—
374C2×C4×D3—34no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C3×C4⋊C4—62no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—62no—
385C3×C22⋊C4—62no—
386C3×C22⋊C4—62no—
387C3×C22⋊C4—62no—
388C3×C22⋊C4—62no—
389C3×C22⋊C4—62no—
390C3×C42—62no—
391C3×C42—62no—
392#217—62no—
393#217—62no—
394#217—62no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—22no—
398(C2×D3)⋊C4—22no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—122no—
412(C2×D3)⋊C4—122no—
413(C2×D3)⋊C4—122no—
414C4⋊Dic3—62no—
415C4⋊Dic3—62no—
416C4⋊Dic3—62no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—62no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—122no—
426C4×Dic3—22no—
427C4×Dic3—22no—
428C4×Dic3—34no—
429C4×Dic3—34no—
430C4×Dic3—62no—
431C4×Dic3—62no—
432C22×C32C22×D411yescharacteristic
433C22×C32C22×D411yescharacteristic
434C22×C32C2×#4111yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32C2×#4111yescharacteristic
438C22×C32C2×#4111yescharacteristic
439C2×C3⋊D3—22no—
440C2×C3⋊D3—22no—
441C2×C3⋊D3—22no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C32×C4—41no—
461C32×C4—41no—
462C32×C4—41no—
463C3⋊Dic3—22no—
464C3⋊Dic3—41no—
465C3⋊Dic3—41no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3#12114yes—
472C22×D4—91no—
473C22×D4—91no—
474C22×D4—91no—
475C23×C4—31no—
476C23×C4—91no—
477C23×C4—91no—
478C4×D4—184no—
479C4×D4—184no—
480C4×D4—184no—
481#117—184no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C42—31no—
502C2×C42—31no—
503C2×C42—91no—
504C2×C42—91no—
505#95—31no—
506#95—91no—
507#95—91no—
508#95—91no—
509#95—91no—
510#95D3211yescharacteristic
511C23×C3—21no—
512C23×C3—32no—
513C23×C3—32no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3C23×D311yescharacteristic
527C23×C3C23×D311yescharacteristic
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—32no—
541C22×D3—32no—
542C22×D3—62no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—121no—
556C22×D3—121no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3#23512yes—
562C22×D3#23912yes—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—124no—
609#67—68no—
610#67—68no—
611#67—68no—
612#67—68no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—62no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—124no—
652C2×Dic3#23512yes—
653C2×Dic3#23512yes—
654C2×Dic3D3×D412yes—
655C2×Dic3D3×D412yes—
656C2×Dic3D3×D412yes—
657C2×Dic3D3×D412yes—
658C2×Dic3#23712yes—
659D12—68no—
660D12—68no—
661C4×D3—44no—
662C4×D3—68no—
663C4×D3—68no—
664C4×D3—124no—
665C2×C32C2×#12111yescharacteristic
666C2×C32#52511yescharacteristic
667C2×C32#52511yescharacteristic
668C2×C32#52511yescharacteristic
669C2×C32#52911yescharacteristic
670C2×C32#52911yescharacteristic
671C2×C32#53211yescharacteristic
672C3⋊D3—42no—
673C3×D3—42no—
674C3×D3—42no—
675C24—31no—
676C24—31no—
677C24—91no—
678C2×D4—182no—
679C2×D4—182no—
680C2×D4—182no—
681C2×D4—182no—
682C2×D4—182no—
683C2×D4—182no—
684C2×D4—182no—
685C2×D4—182no—
686C2×D4—182no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—62no—
694C22×C4—62no—
695C22×C4—62no—
696C22×C4—94no—
697C22×C4—91no—
698C22×C4—91no—
699C22×C4—91no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4C2×D3211yescharacteristic
706C22×C4C2×D3211yescharacteristic
707C22×C4C2×D3211yescharacteristic
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—182no—
712C4⋊C4—182no—
713C4⋊C4—182no—
714C4⋊C4—182no—
715C22⋊C4—62no—
716C22⋊C4—62no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—182no—
721C22⋊C4—182no—
722C22⋊C4—182no—
723C22⋊C4—182no—
724C22⋊C4—182no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C42—62no—
728C42—62no—
729C42—94no—
730C42—182no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3C2×#23511yescharacteristic
753C22×C3C2×#23511yescharacteristic
754C22×C3C2×#23511yescharacteristic
755C22×C3C2×D3×D411yescharacteristic
756C22×C3C2×D3×D411yescharacteristic
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×#23711yescharacteristic
760C22×C3C2×#23911yescharacteristic
761C22×C3D3×#4111yescharacteristic
762C22×C3D3×#4111yescharacteristic
763C22×C3D3×#4111yescharacteristic
764C22×C3D3×#4111yescharacteristic
765C22×C3D3×#4111yescharacteristic
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—62no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—122no—
787C2×D3—122no—
788C2×D3—122no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—241no—
798C2×D3—241no—
799C2×D3—241no—
800C2×D3—241no—
801C3×C4—34no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—41no—
807C3×C4—41no—
808C3×C4—62no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—81no—
813C3×C4—81no—
814C3×C4—81no—
815C3×C4—121no—
816Dic3—22no—
817Dic3—22no—
818Dic3—22no—
819Dic3—22no—
820Dic3—41no—
821Dic3—62no—
822Dic3—62no—
823Dic3—122no—
824Dic3—121no—
825Dic3—121no—
826Dic3—121no—
827Dic3—121no—
828Dic3—241no—
829Dic3—241no—
830Dic3#88414yes—
831C32#239211yescharacteristic, complemented, Sylow
832C23—32no—
833C23—32no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—92no—
847C23—181no—
848C23—181no—
849C23—181no—
850C23—181no—
851C23—181no—
852C23—181no—
853C23C22×D3211yescharacteristic
854D4—188no—
855D4—188no—
856D4—188no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—32no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—92no—
885C2×C4—124no—
886C2×C4—188no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—364no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—122no—
904C2×C3—122no—
905C2×C3#547911yescharacteristic
906C2×C3C2×#88411yescharacteristic
907C2×C3#552811yescharacteristic
908C2×C3#554711yescharacteristic
909C2×C3#554711yescharacteristic
910C2×C3#554711yescharacteristic
911C2×C3#554811yescharacteristic
912C2×C3#559611yescharacteristic
913C2×C3D3×#12111yescharacteristic
914C2×C3#560611yescharacteristic
915C2×C3#562411yescharacteristic
916C2×C3#562711yescharacteristic
917C2×C3#562711yescharacteristic
918C2×C3#570611yescharacteristic
919D3—42no—
920D3—42no—
921D3—122no—
922D3—122no—
923D3—242no—
924C22—62no—
925C22—62no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22—62no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22—121no—
938C22—182no—
939C22—182no—
940C22—182no—
941C22—361no—
942C22—361no—
943C22—361no—
944C22—361no—
945C22D3×#23511yescharacteristic
946C22D3×#23511yescharacteristic
947C22D3×#23511yescharacteristic
948C22D32×D411yescharacteristic
949C22D32×D411yescharacteristic
950C22D3×#23711yescharacteristic
951C22D3×#23911yescharacteristic
952C4—34no—
953C4—41no—
954C4—41no—
955C4—41no—
956C4—62no—
957C4—62no—
958C4—62no—
959C4—62no—
960C4—121no—
961C4—182no—
962C4—361no—
963C4—361no—
964C3—21no—
965C3#7358111yescharacteristic, complemented
966C3#7728111yescharacteristic, complemented
967C2—122no—
968C2—122no—
969C2—362no—
970C2#1059397511yescharacteristic
971C2#1059405811yescharacteristic
972C2D3×#88411yescharacteristic
973C2#1059428611yescharacteristic
974C2#1059440211yescharacteristic
975C2#1059462311yescharacteristic
976C2#1059462311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radical#10591393C2
hypercenter#95D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63904C2semidirect
2. C2×#63880C2semidirect
3. C2×#63879C2semidirect
4. C2×#63836C2semidirect
5. #10592374C2semidirect
6. C3×#4676C2semidirect
7. C3×#4666C2semidirect
9. #10591390C2semidirect
10. Dic3×(C2×D3)⋊C4C2semidirect
11. #10591340C2semidirect
12. #10591312C2semidirect
13. #10591306C2semidirect
14. #10591291C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
81. #4676D3semidirect
86. #4666D3semidirect
117. C2×#624D4semidirect
143. Dic32D4semidirect
831. C32#2392semidirect
965. C3#73581semidirect
966. C3#77281semidirect

Maximal subgroups

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

subgroupindex
C2×#639042
C2×#638802
C2×#638792
C2×#638362
#105923742
C3×#46762
C3×#46662
#105913932
#105913902
Dic3×(C2×D3)⋊C42
#105913402
#105913122
#105913062
#105912912
Dic3×Dic3⋊C42
#772813
#735813