Finite Group Databasebeta

← #11812923

Subgroups — #11812923

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 995 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63912C211yesmaximal, characteristic
3C2×#63905C211yesmaximal, characteristic, complemented
4C2×C4×#626C211yesmaximal, characteristic, complemented
5C3×#4990C211yesmaximal, characteristic, complemented
6C3×#4989C211yesmaximal, characteristic, complemented
7#10591394C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591387C211yesmaximal, characteristic, complemented
11#10591351C211yesmaximal, characteristic, complemented
12#10591303C211yesmaximal, characteristic, complemented
13#10591298C211yesmaximal, characteristic, complemented
14#10591290C211yesmaximal, characteristic, complemented
15#10591197C211yesmaximal, characteristic, complemented
16#75848—31nomaximal
17#74608—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C4⋊C4×C3⋊D3—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46#63912—24no—
47#63905—24no—
48C4×#626—24no—
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#929—31no—
58C2×C4×#67—31no—
59C2×D3×C4⋊C4—31no—
60C2×D3×C4⋊C4—31no—
61C2×D3×C4⋊C4—61no—
62C2×#884—31no—
63C2×#884—31no—
64C2×#883—31no—
65C2×C4×D12—31no—
66C3×#388—31no—
67C3×#385—31no—
68#4993—31no—
69#4990D311yescharacteristic, complemented
70#4989—31no—
71#4989D311yescharacteristic, complemented
72#4961—31no—
73#4961—31no—
74#4956—31no—
75#4956—31no—
76#4956—31no—
77#4952—31no—
78#4949—31no—
79#4933—31no—
80#4675—31no—
81#4668—31no—
82#4665—31no—
83#4665—31no—
84#4665—31no—
85#4661—31no—
86#4657—31no—
87#4652—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
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—22no—
104C2×C4×C3⋊D3—41no—
105C2×C4×C3⋊D3—41no—
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—41no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626D414yes—
121C2×#625—22no—
122C2×#625—22no—
123C2×#625—41no—
124C32×C4⋊C4—22no—
125C4⋊(C3⋊Dic3)—22no—
126#3750—22no—
127#3750D414yescomplemented
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×Dic3⋊C4—41no—
134C3×C4×Dic3—22no—
135#3724—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138#3722—22no—
139#3722—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—41no—
144#2443—91noSylow
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—61no—
159C22×C4×D3—61no—
160C22×C4×D3—61no—
161C22×C4×D3C2×D311yescharacteristic
162C2×C3×C4⋊C4—21no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4C2×D311yescharacteristic
165C2×C3×C4⋊C4C2×D311yescharacteristic
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C42—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176#929—64no—
177C4×#67—64no—
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—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
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×C4⋊Dic3—31no—
195C2×C4⋊Dic3—61no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—61no—
205C2×Dic3⋊C4—61no—
206C2×Dic3⋊C4C2×D311yescharacteristic
207C2×C4×Dic3C2×D311yescharacteristic
208D3×C4⋊C4—64no—
209D3×C4⋊C4—64no—
210D3×C4⋊C4—68no—
211#884—64no—
212#884—64no—
213#883—64no—
214C4×D12—64no—
215C3×#95—31no—
216C3×#95—31no—
217C3×#95—31no—
218C3×#95—31no—
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⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C23×C32C2411yescharacteristic
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3C2×D412yes—
237C22×C3⋊D3#4112yes—
238C22×C3⋊D3#4112yes—
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—21no—
251C22×C3×D3—21no—
252C22×C3×D3C2×D412yes—
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×C4C2×D412yes—
261C2×C32×C4#4112yes—
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⋊Dic3C2×D412yes—
271C4×C3⋊D3—28no—
272C4×C3⋊D3—44no—
273C4×C3⋊D3—44no—
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×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3C2×D412yes—
292C3×C4×D3—44no—
293#626—28no—
294#626—44no—
295#625—44no—
296C2×#123—91no—
297C2×#121—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300#399—91no—
301#398—91no—
302#397—91no—
303#394—91no—
304#388—31no—
305#387—91no—
306#386—91no—
307#386—91no—
308#386—91no—
309#385—31no—
310#385—91no—
311C24×C3—31no—
312C24×C3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—61no—
316C23×D3C22×D311yescharacteristic
317C23×D3C22×D311yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—121no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—34no—
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—
346C2×#67—121no—
347C2×#67—121no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C2×D12—34no—
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—62no—
369C2×C4×D3—22no—
370C2×C4×D3—22no—
371C2×C4×D3—41no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—64no—
377C2×C4×D3—64no—
378C2×C4×D3—64no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—64no—
388C2×C4×D3—64no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—122no—
392C2×C4×D3—122no—
393C2×C4×D3—121no—
394C2×C4×D3—121no—
395C2×C4×D3—121no—
396C2×C4×D3—121no—
397C2×C4×D3—122no—
398C2×C4×D3—122no—
399C3×C4⋊C4—24no—
400C3×C4⋊C4—22no—
401C3×C4⋊C4—22no—
402C3×C4⋊C4—121no—
403C3×C22⋊C4—62no—
404C3×C22⋊C4—62no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—62no—
408C3×C42—62no—
409#217—62no—
410#217—62no—
411#217—62no—
412#217—121no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—22no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—62no—
422(C2×D3)⋊C4—62no—
423(C2×D3)⋊C4—62no—
424(C2×D3)⋊C4—62no—
425(C2×D3)⋊C4—121no—
426C4⋊Dic3—62no—
427C4⋊Dic3—62no—
428C4⋊Dic3—62no—
429C4⋊Dic3—62no—
430C4⋊Dic3—64no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—41no—
434Dic3⋊C4—64no—
435Dic3⋊C4—62no—
436Dic3⋊C4—62no—
437Dic3⋊C4—62no—
438Dic3⋊C4—62no—
439Dic3⋊C4—64no—
440Dic3⋊C4—62no—
441Dic3⋊C4—62no—
442C4×Dic3—22no—
443C22×C32C22×D411yescharacteristic
444C22×C32C22×D411yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32H(5,𝔽2)11yescharacteristic
449C22×C322−1+411yescharacteristic
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3#12314yescomplemented
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C32×C4—22no—
472C32×C4—22no—
473C32×C4—41no—
474C3⋊Dic3—22no—
475C3⋊Dic3—22no—
476C3⋊Dic3—41no—
477C3×Dic3—22no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C22×D4—91no—
484C22×D4—91no—
485C22×D4—91no—
486C23×C4—31no—
487C23×C4—91no—
488C23×C4—91no—
489C23×C4—91no—
490#123—184no—
491#121—184no—
492C4×D4—184no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—184no—
501C2×C4⋊C4D3211yescharacteristic
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C42—31no—
514#95—31no—
515#95—31no—
516#95—31no—
517#95—31no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95—91no—
522C23×C3—21no—
523C23×C3—32no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3C23×D311yescharacteristic
538C23×C3C23×D311yescharacteristic
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—32no—
553C22×D3—32no—
554C22×D3—32no—
555C22×D3—32no—
556C22×D3—32no—
557C22×D3—32no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3D3×D412yes—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—22no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—32no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
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—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—124no—
616C2×C3×C4#23512yes—
617C2×C3×C4#23512yes—
618C2×C3×C4D3×D412yes—
619C2×C3×C4D3×D412yes—
620#67—68no—
621#67—124no—
622#67—124no—
623#67—124no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—62no—
646C2×Dic3—62no—
647C2×Dic3—62no—
648C2×Dic3—62no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—62no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3D3×D412yes—
669D12—68no—
670D12—124no—
671C4×D3—44no—
672C4×D3—616no—
673C4×D3—68no—
674C4×D3—68no—
675C4×D3—124no—
676C4×D3—124no—
677C4×D3—124no—
678C4×D3—124no—
679C4×D3—128no—
680C4×D3—128no—
681C2×C32C2×#12311yescharacteristic
682C2×C32#52511yescharacteristic
683C2×C32#53911yescharacteristic
684C2×C32D4211yescharacteristic
685C2×C32#54711yescharacteristic
686C2×C32#54811yescharacteristic
687C2×C32#55311yescharacteristic
688C3⋊D3—24no—
689C3×D3—42no—
690C3×D3—81no—
691C24—31no—
692C24—31no—
693C24—91no—
694C2×D4—94no—
695C2×D4—182no—
696C2×D4—182no—
697C2×D4—182no—
698C2×D4—182no—
699C2×D4—182no—
700C2×D4—182no—
701C2×D4—182no—
702C2×D4—361no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—62no—
710C22×C4—62no—
711C22×C4—91no—
712C22×C4—91no—
713C22×C4—91no—
714C22×C4—121no—
715C22×C4—182no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—182no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—361no—
723C22×C4—361no—
724C22×C4C2×D3211yescharacteristic
725C22×C4C2×D3211yescharacteristic
726C22×C4C2×D3211yescharacteristic
727C4⋊C4—22no—
728C4⋊C4—94no—
729C4⋊C4—121no—
730C4⋊C4—182no—
731C4⋊C4—182no—
732C4⋊C4—182no—
733C4⋊C4—182no—
734C4⋊C4—182no—
735C22⋊C4—62no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—62no—
739C22⋊C4—62no—
740C22⋊C4—182no—
741C22⋊C4—182no—
742C22⋊C4—182no—
743C22⋊C4—182no—
744C22⋊C4—182no—
745C22⋊C4—361no—
746C42—62no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—62no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3C2×#23511yescharacteristic
769C22×C3C2×#23511yescharacteristic
770C22×C3C2×D3×D411yescharacteristic
771C22×C3C2×D3×D411yescharacteristic
772C22×C3C2×D3×D411yescharacteristic
773C22×C3C2×D3×D411yescharacteristic
774C22×C3#100411yescharacteristic
775C22×C3#100711yescharacteristic
776C22×C3D3×#4111yescharacteristic
777C22×C3D3×#4111yescharacteristic
778C22×C3D3×#4111yescharacteristic
779C22×C3D3×#4111yescharacteristic
780C22×C3#100911yescharacteristic
781C22×C3#101011yescharacteristic
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—34no—
786C2×D3—34no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—41no—
794C2×D3—41no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—64no—
799C2×D3—64no—
800C2×D3—64no—
801C2×D3—64no—
802C2×D3—64no—
803C2×D3—64no—
804C2×D3—64no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—62no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—62no—
817C3×C4—24no—
818C3×C4—22no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—42no—
823C3×C4—42no—
824C3×C4—41no—
825C3×C4—41no—
826C3×C4—62no—
827C3×C4—121no—
828C3×C4—121no—
829C3×C4—121no—
830C3×C4—121no—
831C3×C4—121no—
832Dic3—22no—
833Dic3—41no—
834Dic3—41no—
835Dic3—41no—
836Dic3—41no—
837Dic3—41no—
838Dic3—64no—
839Dic3—62no—
840Dic3—62no—
841Dic3—62no—
842Dic3—62no—
843Dic3—122no—
844Dic3—122no—
845Dic3—121no—
846Dic3—121no—
847C32#244311yescharacteristic, complemented, Sylow
848C23—32no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—92no—
863C23—92no—
864C23—92no—
865C23—181no—
866C23—181no—
867C23—181no—
868C23—181no—
869C23C22×D3211yescharacteristic
870D4—188no—
871D4—364no—
872D4—364no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—32no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—92no—
899C2×C4—92no—
900C2×C4—124no—
901C2×C4—188no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—364no—
910C2×C4—364no—
911C2×C4#379812yes—
912C2×C4#381112yes—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—122no—
921C2×C3—241no—
922C2×C3#550711yescharacteristic
923C2×C3#553011yescharacteristic
924C2×C3#554711yescharacteristic
925C2×C3#554711yescharacteristic
926C2×C3#555111yescharacteristic
927C2×C3#555811yescharacteristic
928C2×C3#559011yescharacteristic
929C2×C3#560911yescharacteristic
930C2×C3#563311yescharacteristic
931C2×C3#563811yescharacteristic
932C2×C3D3×#12311yescharacteristic
933C2×C3D3×#12311yescharacteristic
934C2×C3#567711yescharacteristic
935C2×C3#570711yescharacteristic
936D3—42no—
937D3—68no—
938D3—64no—
939D3—64no—
940D3—81no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—94no—
945C22—121no—
946C22—121no—
947C22—121no—
948C22—121no—
949C22—121no—
950C22—121no—
951C22—121no—
952C22—121no—
953C22—121no—
954C22—121no—
955C22—121no—
956C22—182no—
957C22—182no—
958C22—182no—
959C22—182no—
960C22—182no—
961C22—182no—
962C22C2×#379811yescharacteristic
963C22#6430611yescharacteristic
964C22D32×D411yescharacteristic
965C22#6431411yescharacteristic
966C22#6431511yescharacteristic
967C22#6431911yescharacteristic
968C22C2×#381111yescharacteristic
969C4—22no—
970C4—22no—
971C4—41no—
972C4—62no—
973C4—121no—
974C4—121no—
975C4—121no—
976C4—121no—
977C4—121no—
978C4—182no—
979C4—182no—
980C4—361no—
981C3—21no—
982C3#7460811yescharacteristic, complemented
983C3#7584811yescharacteristic, complemented
984C2—122no—
985C2—184no—
986C2—241no—
987C2#1059451511yescharacteristic
988C2#1059457311yescharacteristic
989C2#1059458311yescharacteristic
990C2#1059460811yescharacteristic
991C2#1059501611yescharacteristic
992C2#1059529211yescharacteristic
993C2#1059536211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63912C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×#63905C2semidirect
4. C2×C4×#626C2semidirect
5. C3×#4990C2semidirect
6. C3×#4989C2semidirect
7. #10591394C2semidirect
8. #10591387C2semidirect
9. #10591387C2semidirect
10. #10591387C2semidirect
11. #10591351C2semidirect
12. #10591303C2semidirect
13. #10591298C2semidirect
14. #10591290C2semidirect
15. #10591197C2semidirect
69. #4990D3semidirect
71. #4989D3semidirect
127. #3750D4semidirect
456. C2×C3⋊D3#123semidirect
847. C32#2443semidirect
982. C3#74608semidirect
983. C3#75848semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#639122
C2×#639052
C2×C4×#6262
C3×#49902
C3×#49892
#105913942
#105913872
#105913512
#105913032
#105912982
#105912902
#105911972
#758483
#746083