Finite Group Databasebeta

← #11804851

Subgroups — #11804851

Order 1152.

1949 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C2×C4×#625C211yesmaximal, characteristic, complemented
3C2×#63879C211yesmaximal, characteristic, complemented
4#10592345C211yesmaximal, characteristic, complemented
5C3×#4665C211yesmaximal, characteristic, complemented
6C3×D3×#95C211yesmaximal, characteristic, complemented
7#10591381C211yesmaximal, characteristic, complemented
8#10591381C211yesmaximal, characteristic, complemented
9#10591376C211yesmaximal, characteristic, complemented
10#10591369C211yesmaximal, characteristic, complemented
11#10591368C211yesmaximal, characteristic, complemented
12#10591362C211yesmaximal, characteristic, complemented
13D3×C3⋊#95C211yesmaximal, characteristic, complemented
14#10591294C211yesmaximal, characteristic, complemented
15#10591273C211yesmaximal, characteristic, complemented
16#74672—31nomaximal
17#73368—31nomaximal
18C22×#634C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×#3795—24no—
30C2×#3795—24no—
31C2×#3795C418yescomplemented
32C2×#3750C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C4×#625—24no—
45#63879—24no—
46C32×#95C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C22×#237—31no—
59C22×#235—31no—
60C2×C4×#67—31no—
61C2×C4×#67—31no—
62C2×C4×#67—31no—
63C2×#67⋊C4—31no—
64C3×#386—31no—
65C2×C3×#95—31no—
66#5220—31no—
67#5213—31no—
68#5213—31no—
69#5211—31no—
70C2×C3⋊#95—31no—
71#4956—31no—
72#4956—31no—
73#4943—31no—
74#4942—31no—
75Dic3×C22⋊C4—31no—
76#4667—31no—
77#4666—31no—
78#4665—31no—
79#4665D311yescharacteristic, complemented
80#4664—31no—
81#4664—31no—
82D3×#95—31no—
83D3×#95D311yescharacteristic, complemented
84#4646—31no—
85#4646—31no—
86#4646—31no—
87#4646—31no—
88#4646—61no—
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C2×#634—22no—
100C2×#634—22no—
101C2×#634C2×C414yescomplemented
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×D12—22no—
108C2×C3×D12—22no—
109C2×C3×D12C2×C414yescomplemented
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—41no—
119C2×C3×C4×D3—41no—
120C2×C3×C4×D3—41no—
121C2×C3×C4×D3C2×C414yescomplemented
122C2×#625—22no—
123C2×#625—22no—
124C2×#625C2×C414yes—
125C2×#625C2×C414yescomplemented
126C2×#625D414yes—
127C2×#625D414yes—
128C2×D3×Dic3—22no—
129C2×D3×Dic3—22no—
130C2×D3×Dic3—22no—
131C2×D3×Dic3—22no—
132C2×D3×Dic3—22no—
133C2×D3×Dic3—22no—
134C2×D3×Dic3—41no—
135C2×D3×Dic3C2×C414yescomplemented
136C2×D3×Dic3C2×C414yescomplemented
137#3795—232no—
138#3750—22no—
139C4×C3⋊Dic3—22no—
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—41no—
143#3724—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—41no—
149Dic32—22no—
150#2339—91noSylow
151C22×C3×D4—31no—
152C23×C3×C4—31no—
153C23×C3×C4—31no—
154C23×C3×C4—31no—
155C23×C3×C4—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—31no—
160C23×Dic3—31no—
161C23×Dic3—31no—
162C23×Dic3—31no—
163C2×#237—38no—
164C2×#237—64no—
165C2×#237—64no—
166C2×#235—38no—
167C2×#235—64no—
168C2×#235—64no—
169C22×D12C2×D311yescharacteristic
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3C2×D311yescharacteristic
174C22×C4×D3C2×D311yescharacteristic
175C22×C4×D3C2×D311yescharacteristic
176C22×C4×D3C2×D311yescharacteristic
177C22×Dic6—31no—
178C22×Dic6—31no—
179C22×Dic6—61no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C4×#67—64no—
189C4×#67—64no—
190C4×#67—64no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4C2×D311yescharacteristic
197C2×(C2×D3)⋊C4C2×D311yescharacteristic
198C2×(C2×D3)⋊C4C2×D311yescharacteristic
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—61no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—61no—
209#67⋊C4—64no—
210C3×#95—21no—
211C3×#95—31no—
212C3×#95—31no—
213C3×#95—31no—
214C3×#95—31no—
215C3×#95C2×D311yescharacteristic
216C3×#95C2×D311yescharacteristic
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⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—61no—
232C3⋊#95—61no—
233C3⋊#95—61no—
234C3⋊#95C2×D311yescharacteristic
235C3⋊#95C2×D311yescharacteristic
236C3⋊#95C2×D311yescharacteristic
237C3⋊#95C2×D311yescharacteristic
238C23×C32C2411yescharacteristic
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×D3—21no—
253C22×C3×D3C22×C412yes—
254C22×C3×D3C22×C412yes—
255C22×C3×D3C22×C412yes—
256C22×C3×D3C2×D412yes—
257C22×C3×D3C2×D412yes—
258C22×C3×D3C2×D412yes—
259C22×C3×D3C2×D412yes—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C22×C412yes—
268C2×C32×C4#4112yescomplemented
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⋊Dic3C22×C412yes—
278C2×C3⋊Dic3C22×C412yes—
279C2×C3⋊Dic3C2×D412yes—
280C2×C3⋊Dic3C2×D412yes—
281#634—28no—
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×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3C22×C412yes—
296C2×C3×Dic3#4112yescomplemented
297C3×D12—28no—
298C3×C4×D3—28no—
299C3×C4×D3—44no—
300C3×C4×D3—44no—
301C3×C4×D3—44no—
302#625—28no—
303#625C22⋊C4116yescomplemented
304D3×Dic3—28no—
305D3×Dic3—28no—
306D3×Dic3—44no—
307C22×#41—91no—
308C2×C4×D4—91no—
309C2×C4×D4—91no—
310#391—91no—
311#391—91no—
312#386—31no—
313#386—91no—
314#386—91no—
315#386—91no—
316#381—91no—
317#381—91no—
318#380—91no—
319C4×C22⋊C4—91no—
320C2×#95—31no—
321C2×#95—91no—
322C24×C3—31no—
323C24×C3—31no—
324C24×C3—31no—
325C23×D3C22×D311yescharacteristic
326C23×D3C22×D311yescharacteristic
327C23×D3C22×D311yescharacteristic
328C2×C3×D4—34no—
329C2×C3×D4—62no—
330C2×C3×D4—62no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—34no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—62no—
341C22×C3×C4—62no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—62no—
348C22×C3×C4—121no—
349C22×C3×C4—121no—
350C22×C3×C4—121no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—34no—
364C2×#67—34no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—34no—
374C22×Dic3—34no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—62no—
384C22×Dic3—62no—
385C22×Dic3—62no—
386C22×Dic3—62no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—121no—
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395#237—632no—
396#235—632no—
397C2×D12—22no—
398C2×D12—22no—
399C2×D12C4×D314yescomplemented
400C2×C4×D3—22no—
401C2×C4×D3—22no—
402C2×C4×D3—22no—
403C2×C4×D3—22no—
404C2×C4×D3—22no—
405C2×C4×D3—22no—
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—41no—
411C2×C4×D3—41no—
412C2×C4×D3—41no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C2×C4×D3—62no—
417C2×C4×D3—62no—
418C2×C4×D3—62no—
419C2×C4×D3—121no—
420C2×C4×D3C4×D314yescomplemented
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—64no—
424C2×Dic6—62no—
425C2×Dic6—62no—
426C2×Dic6—62no—
427C2×Dic6—62no—
428C2×Dic6—122no—
429C2×Dic6—122no—
430C3×C22⋊C4—62no—
431C3×C22⋊C4—62no—
432C3×C22⋊C4—121no—
433#217—62no—
434#217—62no—
435#217—62no—
436#217—62no—
437#217—121no—
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—41no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—121no—
446Dic3⋊C4—62no—
447Dic3⋊C4—62no—
448Dic3⋊C4—62no—
449Dic3⋊C4—62no—
450Dic3⋊C4—122no—
451C4×Dic3—62no—
452C4×Dic3—62no—
453C4×Dic3—62no—
454C4×Dic3—62no—
455C4×Dic3—122no—
456C22×C32C23×C411yescharacteristic
457C22×C32C22×D411yescharacteristic
458C22×C32C22×D411yescharacteristic
459C22×C32C2×#4111yescharacteristic
460C22×C32C2×#4111yescharacteristic
461C22×C32H(5,𝔽2)11yescharacteristic
462C22×C322−1+411yescharacteristic
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3C2×C22⋊C414yes—
483C2×C3×D3C2×C22⋊C414yes—
484C32×C4—22no—
485C32×C4—22no—
486C32×C4—41no—
487C3⋊Dic3—22no—
488C3⋊Dic3—41no—
489C3⋊Dic3—41no—
490C3⋊Dic3C2×C22⋊C414yes—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—41no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—98no—
497C2×#41—184no—
498C2×#41—184no—
499C22×Q8—91no—
500C22×D4—31no—
501C22×D4—91no—
502C22×D4—91no—
503C23×C4—31no—
504C23×C4—31no—
505C23×C4—31no—
506C23×C4—31no—
507C23×C4—91no—
508C23×C4—91no—
509C23×C4—91no—
510C4×D4—184no—
511C4×D4—184no—
512C2×C4⋊C4—91no—
513C2×C4⋊C4—91no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—31no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522C2×C42—91no—
523C2×C42—91no—
524#95—31no—
525#95—31no—
526#95—31no—
527#95—31no—
528#95—91no—
529#95—91no—
530#95—91no—
531#95—91no—
532#95—91no—
533#95—91no—
534#95—91no—
535#95D3211yescharacteristic
536C23×C3—21no—
537C23×C3—32no—
538C23×C3—32no—
539C23×C3—32no—
540C23×C3—32no—
541C23×C3—32no—
542C23×C3—32no—
543C23×C3—32no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3C23×D311yescharacteristic
559C23×C3C23×D311yescharacteristic
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3C2×C4×D312yes—
575C22×D3C2×C4×D312yes—
576C22×D3C2×C4×D312yes—
577C22×D3D3×D412yes—
578C22×D3D3×D412yes—
579C22×D3D3×D412yes—
580C22×D3D3×D412yes—
581C3×D4—68no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
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—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—68no—
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—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—124no—
622C2×C3×C4—124no—
623C2×C3×C4—124no—
624C2×C3×C4C2×C4×D312yes—
625C2×C3×C4C2×C4×D312yes—
626C2×C3×C4#23512yescomplemented
627C2×C3×C4#23712yescomplemented
628#67—316no—
629#67—316no—
630#67—68no—
631#67—68no—
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—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—68no—
658C2×Dic3—68no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—62no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—121no—
677C2×Dic3—121no—
678C2×Dic3—121no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681C2×Dic3—121no—
682C2×Dic3—121no—
683C2×Dic3—124no—
684C2×Dic3C2×C4×D312yes—
685C2×Dic3#23512yescomplemented
686D12—28no—
687C4×D3—28no—
688C4×D3—44no—
689C4×D3—44no—
690C4×D3—44no—
691C4×D3—68no—
692C4×D3—68no—
693C4×D3—124no—
694Dic6—68no—
695Dic6—68no—
696Dic6—128no—
697C2×C32C22×C22⋊C411yescharacteristic
698C2×C32C4×#4111yescharacteristic
699C2×C32#52011yescharacteristic
700C2×C32#54611yescharacteristic
701C2×C32#54611yescharacteristic
702C2×C32#54711yescharacteristic
703C2×C32#54711yescharacteristic
704C3×D3—24no—
705C3×D3—24no—
706C3×D3—42no—
707C24—31no—
708C24—31no—
709C24—31no—
710#41—1832no—
711C2×Q8—94no—
712C2×Q8—182no—
713C2×Q8—182no—
714C2×D4—34no—
715C2×D4—62no—
716C2×D4—62no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—94no—
720C2×D4—94no—
721C2×D4—182no—
722C2×D4—182no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—34no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—62no—
730C22×C4—62no—
731C22×C4—62no—
732C22×C4—62no—
733C22×C4—62no—
734C22×C4—62no—
735C22×C4—62no—
736C22×C4—62no—
737C22×C4—94no—
738C22×C4—94no—
739C22×C4—91no—
740C22×C4—91no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—121no—
744C22×C4—121no—
745C22×C4—121no—
746C22×C4—182no—
747C22×C4—182no—
748C22×C4—182no—
749C22×C4—182no—
750C22×C4—182no—
751C22×C4—182no—
752C22×C4—361no—
753C22×C4C2×D3211yescharacteristic
754C22×C4C2×D3211yescharacteristic
755C22×C4C2×D3211yescharacteristic
756C4⋊C4—182no—
757C4⋊C4—182no—
758C22⋊C4—62no—
759C22⋊C4—62no—
760C22⋊C4—121no—
761C22⋊C4—182no—
762C22⋊C4—182no—
763C22⋊C4—182no—
764C22⋊C4—182no—
765C22⋊C4—361no—
766C42—182no—
767C42—182no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—34no—
776C22×C3—34no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3C22×C4×D311yescharacteristic
797C22×C3C22×C4×D311yescharacteristic
798C22×C3C2×#23511yescharacteristic
799C22×C3C2×#23511yescharacteristic
800C22×C3C2×D3×D411yescharacteristic
801C22×C3C2×D3×D411yescharacteristic
802C22×C3C2×D3×D411yescharacteristic
803C22×C3C2×D3×D411yescharacteristic
804C22×C3C2×#23711yescharacteristic
805C22×C3#100411yescharacteristic
806C22×C3#100411yescharacteristic
807C22×C3#100711yescharacteristic
808C22×C3D3×#4111yescharacteristic
809C22×C3#101011yescharacteristic
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—41no—
826C2×D3—41no—
827C2×D3—41no—
828C2×D3—41no—
829C2×D3D3×C22⋊C414yes—
830C2×D3D3×C22⋊C414yes—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—22no—
834C3×C4—22no—
835C3×C4—42no—
836C3×C4—42no—
837C3×C4—41no—
838C3×C4—41no—
839C3×C4—62no—
840C3×C4—62no—
841C3×C4—81no—
842C3×C4—121no—
843C3×C4—121no—
844C3×C4—121no—
845Dic3—22no—
846Dic3—22no—
847Dic3—34no—
848Dic3—34no—
849Dic3—41no—
850Dic3—41no—
851Dic3—41no—
852Dic3—64no—
853Dic3—62no—
854Dic3—62no—
855Dic3—122no—
856Dic3—122no—
857Dic3—121no—
858Dic3—121no—
859Dic3—121no—
860Dic3—121no—
861Dic3—241no—
862C32#233911yescharacteristic, complemented, Sylow
863C23—32no—
864C23—32no—
865C23—32no—
866C23—32no—
867C23—32no—
868C23—32no—
869C23—32no—
870C23—61no—
871C23—61no—
872C23—61no—
873C23—61no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23—61no—
880C23—61no—
881C23—61no—
882C23—61no—
883C23—61no—
884C23C22×D3211yescharacteristic
885Q8—188no—
886D4—68no—
887D4—916no—
888D4—188no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—32no—
897C2×C4—32no—
898C2×C4—68no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—92no—
913C2×C4—92no—
914C2×C4—92no—
915C2×C4—92no—
916C2×C4—124no—
917C2×C4—124no—
918C2×C4—124no—
919C2×C4—188no—
920C2×C4—188no—
921C2×C4—181no—
922C2×C4—181no—
923C2×C4—181no—
924C2×C4—181no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—181no—
928C2×C4—181no—
929C2×C4—364no—
930C2×C4#379512yescomplemented
931C2×C4C4×D3212yes—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—64no—
940C2×C3—64no—
941C2×C3—122no—
942C2×C3C4×#23511yescharacteristic
943C2×C3C2×D3×C22⋊C411yescharacteristic
944C2×C3C2×D3×C22⋊C411yescharacteristic
945C2×C3#549011yescharacteristic
946C2×C3#549011yescharacteristic
947C2×C3#550411yescharacteristic
948C2×C3#550711yescharacteristic
949C2×C3#550711yescharacteristic
950C2×C3C4×#23711yescharacteristic
951C2×C3#554611yescharacteristic
952C2×C3#559111yescharacteristic
953C2×C3#561011yescharacteristic
954C2×C3#561111yescharacteristic
955C2×C3#565511yescharacteristic
956D3—24no—
957D3—24no—
958D3—42no—
959C22—34no—
960C22—34no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—62no—
970C22—62no—
971C22—62no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22C2×#379511yescharacteristic
981C22C2×C4×D3211yescharacteristic
982C22D3×#23511yescharacteristic
983C22D32×D411yescharacteristic
984C22D32×D411yescharacteristic
985C22#6431311yescharacteristic
986C22#6431511yescharacteristic
987C4—22no—
988C4—22no—
989C4—41no—
990C4—62no—
991C4—62no—
992C4—94no—
993C4—121no—
994C4—121no—
995C4—121no—
996C4—182no—
997C4—361no—
998C4—361no—
999C3—21no—
1000C3#7336811yescharacteristic, complemented
1001C3#7467211yescharacteristic, complemented
1002C2—64no—
1003C2—64no—
1004C2—122no—
1005C2C4×#379511yescharacteristic
1006C2#1059418411yescharacteristic
1007C2D32×C22⋊C411yescharacteristic
1008C2#1059427311yescharacteristic
1009C2#1059435911yescharacteristic
1010C2#1059437011yescharacteristic
1011C2#1059451311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#3795C2
hypercenter#95D32
hypocenterC32#2339
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#625C2semidirect
3. C2×#63879C2semidirect
4. #10592345C2semidirect
5. C3×#4665C2semidirect
6. C3×D3×#95C2semidirect
7. #10591381C2semidirect
8. #10591381C2semidirect
9. #10591376C2semidirect
10. #10591369C2semidirect
11. #10591368C2semidirect
12. #10591362C2semidirect
13. D3×C3⋊#95C2semidirect
14. #10591294C2semidirect
15. #10591273C2semidirect
31. C2×#3795C4semidirect
79. #4665D3semidirect
83. D3×#95D3semidirect
101. C2×#634C2×C4semidirect
109. C2×C3×D12C2×C4semidirect
121. C2×C3×C4×D3C2×C4semidirect
125. C2×#625C2×C4semidirect
135. C2×D3×Dic3C2×C4semidirect
136. C2×D3×Dic3C2×C4semidirect
268. C2×C32×C4#41semidirect
296. C2×C3×Dic3#41semidirect
303. #625C22⋊C4semidirect
399. C2×D12C4×D3semidirect
420. C2×C4×D3C4×D3semidirect
626. C2×C3×C4#235semidirect
627. C2×C3×C4#237semidirect
685. C2×Dic3#235semidirect
862. C32#2339semidirect
930. C2×C4#3795semidirect
1000. C3#73368semidirect
1001. C3#74672semidirect

Maximal subgroups

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

subgroupindex
C22×#37952
C2×C4×#6252
C2×#638792
#105923452
C3×#46652
C3×D3×#952
#105913812
#105913762
#105913692
#105913682
#105913622
D3×C3⋊#952
#105912942
#105912732
#746723
#733683