Finite Group Databasebeta

← #11810269

Subgroups — #11810269

Order 1152.

1389 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2C2×#63896C211yesmaximal, characteristic, complemented
3C2×#63896C211yesmaximal, characteristic, complemented
4C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10592345C211yesmaximal, characteristic, complemented
6C3×#4665C211yesmaximal, characteristic
7C3×#4657C211yesmaximal, characteristic, complemented
8#10591376C211yesmaximal, characteristic
9#10591369C211yesmaximal, characteristic, complemented
10#10591366C211yesmaximal, characteristic, complemented
11#10591348C211yesmaximal, characteristic, complemented
12#10591328C211yesmaximal, characteristic, complemented
13#10591306C211yesmaximal, characteristic, complemented
14#10591306C211yesmaximal, characteristic, complemented
15#10591295C211yesmaximal, characteristic, complemented
16#77742—31nomaximal
17#74693—31nomaximal
18C22×#634C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45#63898—24no—
46#63896—24no—
47#63896—24no—
48D3×Dic3⋊C4—24no—
49C32×#95C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×D4×Dic3—31no—
58C22×Dic3⋊C4—31no—
59C2×#896—31no—
60C2×#896—31no—
61C2×#893—31no—
62C2×D3×C4⋊C4—31no—
63C2×#878—31no—
64C2×#878—31no—
65C3×#398—31no—
66C3×#386—31no—
67#5220—31no—
68#5212—31no—
69#4994—31no—
70#4994—31no—
71#4987—31no—
72#4982—31no—
73#4948—31no—
74#4948—31no—
75#4942—31no—
76#4942—31no—
77#4667—31no—
78#4667—31no—
79#4665—31no—
80#4665D311yescharacteristic
81#4661—31no—
82#4657D311yescharacteristic, complemented
83#4647—31no—
84#4647—31no—
85#4646—31no—
86#4646—31no—
87#4646—61no—
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×#634—22no—
98C2×#634—22no—
99C2×#634—22no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×C3×D12—22no—
107C2×C3×D12—22no—
108C2×C3×D12Q814yescomplemented
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—41no—
112C2×D3×Dic3—22no—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3D414yes—
121#3750—22no—
122C4×C3⋊Dic3—22no—
123C3×(C2×D3)⋊C4—22no—
124C3×(C2×D3)⋊C4—22no—
125C3×(C2×D3)⋊C4—41no—
126C3×C4⋊Dic3—22no—
127C3×Dic3⋊C4—22no—
128C3×Dic3⋊C4—22no—
129C3×Dic3⋊C4—22no—
130#3724—22no—
131#3724D414yescomplemented
132Dic3⋊Dic3—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—41no—
136Dic3⋊Dic3—41no—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—41no—
142#2417—91noSylow
143C22×C3×D4—31no—
144C23×C3×C4—31no—
145C23×Dic3—31no—
146C23×Dic3—31no—
147C23×Dic3—31no—
148C22×D12C2×D311yescharacteristic
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3C2×D311yescharacteristic
153C22×Dic6—31no—
154C22×Dic6—31no—
155C22×Dic6—61no—
156C2×C3×C4⋊C4—31no—
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×#217—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168D4×Dic3—64no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4C2×D311yescharacteristic
175C2×(C2×D3)⋊C4C2×D311yescharacteristic
176C2×(C2×D3)⋊C4C2×D311yescharacteristic
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3C2×D311yescharacteristic
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—61no—
195C2×Dic3⋊C4—64no—
196C2×Dic3⋊C4C2×D311yescharacteristic
197C2×Dic3⋊C4C2×D311yescharacteristic
198C2×Dic3⋊C4C2×D311yescharacteristic
199C2×C4×Dic3—31no—
200C2×C4×Dic3—31no—
201C2×C4×Dic3—61no—
202#896—64no—
203#896—64no—
204#893—64no—
205D3×C4⋊C4—64no—
206#878—64no—
207#878—64no—
208C3×#95—21no—
209C3×#95—31no—
210C3×#95—31no—
211C3×#95—31no—
212C3×#95C2×D311yescharacteristic
213C3×#95C2×D311yescharacteristic
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—61no—
223C3⋊#95—61no—
224C3⋊#95—61no—
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
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×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D412yes—
240C22×C3×D3C2×Q812yes—
241C22×C3×D3C2×Q812yes—
242C22×C3×D3#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×Q812yes—
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⋊Dic3C2×D412yes—
262C2×C3⋊Dic3C2×D412yes—
263C2×C3⋊Dic3#4112yes—
264#634—44no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
281C2×C3×Dic3C2×D412yes—
282C2×C3×Dic3C2×D412yes—
283C3×D12—28no—
284C3×C4×D3—44no—
285D3×Dic3—28no—
286D3×Dic3—44no—
287D3×Dic3—44no—
288C2×C22⋊Q8—91no—
289C2×C22⋊Q8—91no—
290C2×C4×D4—91no—
291C22×C4⋊C4—91no—
292#398—31no—
293#398—91no—
294#396—91no—
295#396—91no—
296#391—91no—
297#389—91no—
298#386—31no—
299#386—91no—
300#380—91no—
301#380—91no—
302#380—91no—
303C24×C3—31no—
304C24×C3—31no—
305C23×D3C22×D311yescharacteristic
306C23×D3C22×D311yescharacteristic
307C2×C3×D4—34no—
308C2×C3×D4—62no—
309C2×C3×D4—62no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—62no—
320C22×C3×C4—62no—
321C22×C3×C4—121no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—34no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—62no—
342C22×Dic3—62no—
343C22×Dic3—62no—
344C22×Dic3—62no—
345C22×Dic3—62no—
346C22×Dic3—62no—
347C22×Dic3—62no—
348C22×Dic3—121no—
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C2×D12—22no—
356C2×D12—22no—
357C2×D12Dic614yescomplemented
358C2×C4×D3—22no—
359C2×C4×D3—22no—
360C2×C4×D3—34no—
361C2×C4×D3—41no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—62no—
366C2×C4×D3—62no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—121no—
370C2×Dic6—62no—
371C2×Dic6—62no—
372C2×Dic6—62no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—64no—
377C2×Dic6—122no—
378C2×Dic6—122no—
379C3×C4⋊C4—62no—
380C3×C4⋊C4—62no—
381C3×C4⋊C4—62no—
382C3×C4⋊C4—62no—
383C3×C22⋊C4—62no—
384C3×C22⋊C4—62no—
385C3×C22⋊C4—121no—
386#217—62no—
387#217—62no—
388#217—62no—
389#217—62no—
390#217—121no—
391(C2×D3)⋊C4—22no—
392(C2×D3)⋊C4—22no—
393(C2×D3)⋊C4—41no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—121no—
399C4⋊Dic3—22no—
400C4⋊Dic3—62no—
401C4⋊Dic3—62no—
402C4⋊Dic3—62no—
403C4⋊Dic3—121no—
404C4⋊Dic3—121no—
405Dic3⋊C4—22no—
406Dic3⋊C4—22no—
407Dic3⋊C4—22no—
408Dic3⋊C4—34no—
409Dic3⋊C4—34no—
410Dic3⋊C4—62no—
411Dic3⋊C4—62no—
412Dic3⋊C4—62no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—122no—
418Dic3⋊C4—121no—
419Dic3⋊C4—121no—
420C4×Dic3—62no—
421C4×Dic3—62no—
422C4×Dic3—122no—
423C22×C32C22×D411yescharacteristic
424C22×C32C22×D411yescharacteristic
425C22×C32C22×Q811yescharacteristic
426C22×C32C2×#4111yescharacteristic
427C22×C32C2×#4111yescharacteristic
428C22×C32H(5,𝔽2)11yescharacteristic
429C22×C322−1+411yescharacteristic
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3C22⋊Q814yescomplemented
444C32×C4—22no—
445C32×C4—41no—
446C32×C4—41no—
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3⋊Dic3—41no—
450C3⋊Dic3#12114yes—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C22×Q8—91no—
458C22×D4—31no—
459C23×C4—31no—
460C23×C4—91no—
461C23×C4—91no—
462C23×C4—91no—
463C22⋊Q8—184no—
464C22⋊Q8—184no—
465C4×D4—184no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—91no—
471C2×C4⋊C4—91no—
472C2×C4⋊C4—91no—
473C2×C4⋊C4—91no—
474C2×C4⋊C4—91no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C4⋊C4—184no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—91no—
483C2×C22⋊C4—91no—
484C2×C22⋊C4—91no—
485C2×C22⋊C4—91no—
486C2×C22⋊C4—91no—
487C2×C42—91no—
488#95—31no—
489#95—31no—
490#95—31no—
491#95—91no—
492#95—91no—
493#95—91no—
494#95—91no—
495#95D3211yescharacteristic
496C23×C3—21no—
497C23×C3—32no—
498C23×C3—32no—
499C23×C3—32no—
500C23×C3—32no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3—61no—
511C23×C3C23×D311yescharacteristic
512C23×C3C23×D311yescharacteristic
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3C2×Dic612yes—
524C22×D3C2×Dic612yes—
525C22×D3D3×D412yes—
526C22×D3#23712yes—
527C3×D4—68no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—22no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—22no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—124no—
572C2×C3×C4C2×Dic612yes—
573C2×C3×C4D3×Q812yes—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—68no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—121no—
620C2×Dic3—121no—
621C2×Dic3—121no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—124no—
627C2×Dic3—124no—
628C2×Dic3D3×D412yes—
629C2×Dic3D3×D412yes—
630C2×Dic3D3×D412yes—
631D12—28no—
632C4×D3—44no—
633C4×D3—68no—
634C4×D3—124no—
635C4×D3—124no—
636Dic6—124no—
637Dic6—124no—
638Dic6—128no—
639C2×C32C2×#12111yescharacteristic
640C2×C32C2×C22⋊Q811yescharacteristic
641C2×C32#53711yescharacteristic
642C2×C32#54611yescharacteristic
643C2×C32D4×Q811yescharacteristic
644C2×C32#55211yescharacteristic
645C2×C32#55411yescharacteristic
646C3×D3—24no—
647C3×D3—42no—
648C24—31no—
649C24—31no—
650C2×Q8—182no—
651C2×Q8—182no—
652C2×Q8—182no—
653C2×D4—34no—
654C2×D4—62no—
655C2×D4—62no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—94no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—91no—
668C22×C4—91no—
669C22×C4—121no—
670C22×C4—182no—
671C22×C4—182no—
672C22×C4—182no—
673C22×C4—182no—
674C22×C4—182no—
675C22×C4—182no—
676C22×C4—182no—
677C22×C4—361no—
678C22×C4C2×D3211yescharacteristic
679C22×C4C2×D3211yescharacteristic
680C22×C4C2×D3211yescharacteristic
681C4⋊C4—62no—
682C4⋊C4—62no—
683C4⋊C4—62no—
684C4⋊C4—62no—
685C4⋊C4—94no—
686C4⋊C4—182no—
687C4⋊C4—182no—
688C4⋊C4—182no—
689C4⋊C4—182no—
690C4⋊C4—182no—
691C4⋊C4—361no—
692C4⋊C4—361no—
693C22⋊C4—62no—
694C22⋊C4—62no—
695C22⋊C4—121no—
696C22⋊C4—182no—
697C22⋊C4—182no—
698C22⋊C4—182no—
699C22⋊C4—182no—
700C22⋊C4—361no—
701C42—182no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—34no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3C22×Dic611yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C2×D3×D411yescharacteristic
727C22×C3C2×D3×D411yescharacteristic
728C22×C3C2×#23711yescharacteristic
729C22×C3#100411yescharacteristic
730C22×C3C2×D3×Q811yescharacteristic
731C22×C3#100711yescharacteristic
732C22×C3D3×#4111yescharacteristic
733C22×C3D3×#4111yescharacteristic
734C22×C3D3×#4111yescharacteristic
735C22×C3#100911yescharacteristic
736C22×C3#101011yescharacteristic
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3#87814yescomplemented
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—42no—
754C3×C4—42no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—62no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—81no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4—121no—
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—34no—
770Dic3—34no—
771Dic3—41no—
772Dic3—41no—
773Dic3—41no—
774Dic3—64no—
775Dic3—122no—
776Dic3—122no—
777Dic3—121no—
778Dic3—121no—
779Dic3—121no—
780Dic3—121no—
781Dic3—121no—
782Dic3—121no—
783Dic3—241no—
784C32#241711yescharacteristic, complemented, Sylow
785C23—32no—
786C23—32no—
787C23—32no—
788C23—32no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23—61no—
793C23—61no—
794C23—61no—
795C23—61no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23C22×D3211yescharacteristic
800Q8—364no—
801D4—68no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—92no—
829C2×C4—92no—
830C2×C4—92no—
831C2×C4—124no—
832C2×C4—188no—
833C2×C4—181no—
834C2×C4—181no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—364no—
843C2×C4—364no—
844C2×C4D3×Dic612yes—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—64no—
853C2×C3—122no—
854C2×C3C2×#87811yescharacteristic
855C2×C3D4×Dic611yescharacteristic
856C2×C3#553911yescharacteristic
857C2×C3#559111yescharacteristic
858C2×C3#559711yescharacteristic
859C2×C3D3×#12111yescharacteristic
860C2×C3D3×#12111yescharacteristic
861C2×C3D3×C22⋊Q811yescharacteristic
862C2×C3#562911yescharacteristic
863C2×C3#565011yescharacteristic
864C2×C3#565411yescharacteristic
865C2×C3#569011yescharacteristic
866C2×C3#569311yescharacteristic
867C2×C3#572711yescharacteristic
868D3—24no—
869D3—42no—
870C22—34no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—62no—
879C22—62no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22C2×D3×Dic611yescharacteristic
885C22#6430611yescharacteristic
886C22#6430711yescharacteristic
887C22D32×D411yescharacteristic
888C22D32×D411yescharacteristic
889C22D3×#23711yescharacteristic
890C22#6431511yescharacteristic
891C4—22no—
892C4—41no—
893C4—41no—
894C4—62no—
895C4—62no—
896C4—62no—
897C4—94no—
898C4—121no—
899C4—121no—
900C4—121no—
901C4—361no—
902C4—361no—
903C4—361no—
904C3—21no—
905C3#7469311yescharacteristic, complemented
906C3#7774211yescharacteristic, complemented
907C2—64no—
908C2—122no—
909C2#1059394111yescharacteristic
910C2D3×#87811yescharacteristic
911C2#1059426511yescharacteristic
912C2#1059427411yescharacteristic
913C2#1059436811yescharacteristic
914C2#1059437611yescharacteristic
915C2#1059443011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×C3×D12C22
hypercenter#95D32
hypocenterC32#2417
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63896C2semidirect
3. C2×#63896C2semidirect
4. C2×D3×Dic3⋊C4C2semidirect
5. #10592345C2semidirect
7. C3×#4657C2semidirect
9. #10591369C2semidirect
10. #10591366C2semidirect
11. #10591348C2semidirect
12. #10591328C2semidirect
13. #10591306C2semidirect
14. #10591306C2semidirect
15. #10591295C2semidirect
82. #4657D3semidirect
108. C2×C3×D12Q8semidirect
131. #3724D4semidirect
357. C2×D12Dic6semidirect
443. C2×C3×D3C22⋊Q8semidirect
750. C2×D3#878semidirect
784. C32#2417semidirect
905. C3#74693semidirect
906. C3#77742semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
C2×#638962
C2×D3×Dic3⋊C42
#105923452
C3×#46652
C3×#46572
#105913762
#105913692
#105913662
#105913482
#105913282
#105913062
#105912952
#777423
#746933