Finite Group Databasebeta

← #11806911

Subgroups — #11806911

Order 1152.

1793 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63979C211yesmaximal, characteristic
2C2×Dic3×#67C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic, complemented
4C2×#63902C211yesmaximal, characteristic, complemented
5C2×#63880C211yesmaximal, characteristic, complemented
6#10592656C211yesmaximal, characteristic, complemented
7C3×#4958C211yesmaximal, characteristic, complemented
8C3×#4957C211yesmaximal, characteristic, complemented
9#10591721C211yesmaximal, characteristic, complemented
10#10591386C211yesmaximal, characteristic, complemented
11#10591384C211yesmaximal, characteristic, complemented
12#10591364C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#76306—31nomaximal
17#74679—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41#63979C418yescomplemented
42Dic3×#67—24no—
43C2×#3724C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51#63952—24no—
52#63902—24no—
53#63880—24no—
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C2×#940—31no—
59C2×#940—31no—
60C2×D4×Dic3—31no—
61C2×C4×#67—31no—
62C2×C4×#67—31no—
63C2×#67⋊C4—31no—
64C2×#67⋊C4—31no—
65C2×#67⋊C4—31no—
66C2×#67⋊C4—31no—
67C2×C4×D12—31no—
68C3×#390—31no—
69C3×#386—31no—
70#5220—31no—
71#4988—31no—
72Dic3×C4⋊C4—31no—
73#4958—31no—
74#4958D311yescharacteristic, complemented
75#4957—31no—
76#4957—31no—
77#4957—31no—
78#4957—31no—
79#4957—31no—
80#4957—61no—
81#4957D311yescharacteristic, complemented
82#4956—31no—
83#4956—31no—
84C4×Dic3⋊C4—31no—
85#4665—31no—
86#4665—31no—
87#4649—31no—
88#4649—31no—
89C24×C32C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—22no—
96C2×#638—22no—
97C2×#638C2×C414yescomplemented
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C2×C3×#67—41no—
104C2×C3×#67—41no—
105C2×C3×#67C2×C414yescomplemented
106C2×C3×#67C2×C414yescomplemented
107C22×C3×Dic3—22no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3—41no—
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—41no—
119C2×#626—41no—
120C2×#626C2×C414yescomplemented
121C2×#626C2×C414yescomplemented
122C2×#625—22no—
123C2×#625—22no—
124C2×#625C2×C414yescomplemented
125C2×#624—22no—
126C2×#624—22no—
127C2×#624—41no—
128C2×D3×Dic3—22no—
129C2×D3×Dic3—22no—
130C2×D3×Dic3—22no—
131C2×D3×Dic3—22no—
132C2×D3×Dic3—41no—
133C2×D3×Dic3—41no—
134C32×C22⋊C4—41no—
135#3757—22no—
136#3752—22no—
137#3752—41no—
138#3750—22no—
139C4×C3⋊Dic3—22no—
140C3×#217—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—41no—
145C3×Dic3⋊C4—22no—
146C3×C4×Dic3—22no—
147#3724D414yescomplemented
148Dic3⋊Dic3D414yescomplemented
149#3722—22no—
150(C2×D3)⋊Dic3—22no—
151(C2×D3)⋊Dic3—41no—
152Dic32—22no—
153Dic32—22no—
154Dic32C2×C414yescomplemented
155#2366—91noSylow
156C22×C3×D4—31no—
157C22×C3×D4—31no—
158C23×C3×C4—31no—
159C22×#67—31no—
160C22×#67—31no—
161C22×#67—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—61no—
166C22×#67C2×D311yescharacteristic
167C22×#67C2×D311yescharacteristic
168C23×Dic3—31no—
169C23×Dic3—31no—
170C23×Dic3C2×D311yescharacteristic
171C22×D12—31no—
172C22×D12—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C22⋊C4—21no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4C2×D311yescharacteristic
185C2×C3×C22⋊C4C2×D311yescharacteristic
186C2×C3×C42—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—61no—
192C2×#217C2×D311yescharacteristic
193#940—38no—
194#940—38no—
195D4×Dic3—64no—
196C4×#67—64no—
197C4×#67—64no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—61no—
207C2×(C2×D3)⋊C4—61no—
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×(C2×D3)⋊C4C2×D311yescharacteristic
211C2×(C2×D3)⋊C4C2×D311yescharacteristic
212C2×C4⋊Dic3—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—61no—
219C2×Dic3⋊C4C2×D311yescharacteristic
220C2×C4×Dic3—31no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3—31no—
223C2×C4×Dic3—31no—
224C2×C4×Dic3—31no—
225C2×C4×Dic3—31no—
226C2×C4×Dic3—31no—
227C2×C4×Dic3—31no—
228C2×C4×Dic3—61no—
229C2×C4×Dic3C2×D311yescharacteristic
230#67⋊C4—64no—
231#67⋊C4—64no—
232#67⋊C4—64no—
233#67⋊C4—64no—
234C4×D12—64no—
235C3×#95—31no—
236C3×#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95C2×D311yescharacteristic
242C3⋊#95C2×D311yescharacteristic
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32C22×C412yes—
250C23×C32C2411yescharacteristic
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C22×C412yes—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3C22×C412yes—
271C22×C3×D3C22×C412yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278#638—28no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3C22×C412yes—
285C2×C3⋊Dic3C2×D412yes—
286C2×C3⋊Dic3C2×D412yes—
287C2×C3⋊Dic3#4112yes—
288C3×#67—28no—
289C3×#67—44no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—44no—
302C2×C3×Dic3C22×C412yes—
303C2×C3×Dic3C22×C412yes—
304C2×C3×Dic3C2×D412yes—
305C2×C3×Dic3C2×D412yes—
306C2×C3×Dic3C2×D412yes—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3#4112yes—
309#626—28no—
310#626—44no—
311#625—28no—
312#624—44no—
313D3×Dic3—44no—
314D3×Dic3—44no—
315C2×#127—91no—
316C2×C4×D4—91no—
317C2×C4×D4—91no—
318C2×C4×D4—91no—
319C2×C4×D4—91no—
320#390—31no—
321#390—91no—
322#390—91no—
323#390—91no—
324#386—31no—
325#386—91no—
326#386—91no—
327#386—91no—
328C4×C4⋊C4—91no—
329C4×C4⋊C4—91no—
330C24×C3—21no—
331C24×C3—31no—
332C24×C3—31no—
333C24×C3C22×D311yescharacteristic
334C24×C3C22×D311yescharacteristic
335C23×D3—31no—
336C23×D3—31no—
337C23×D3—61no—
338C23×D3C22×D311yescharacteristic
339C23×D3C22×D311yescharacteristic
340C2×C3×D4—34no—
341C2×C3×D4—34no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—121no—
345C2×C3×D4—121no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—62no—
355C22×C3×C4—62no—
356C22×C3×C4—121no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C2×#67—22no—
362C2×#67—22no—
363C2×#67—34no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—34no—
369C2×#67—41no—
370C2×#67—41no—
371C2×#67—64no—
372C2×#67—62no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67—62no—
379C2×#67—62no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—122no—
383C2×#67—122no—
384C2×#67—121no—
385C2×#67—121no—
386C2×#67C4×D314yescomplemented
387C2×#67C4×D314yescomplemented
388C22×Dic3—22no—
389C22×Dic3—22no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—41no—
397C22×Dic3—61no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—62no—
401C22×Dic3—62no—
402C22×Dic3—62no—
403C22×Dic3—62no—
404C22×Dic3—121no—
405C22×Dic3—121no—
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C2×D12—34no—
413C2×D12—34no—
414C2×D12—62no—
415C2×D12—62no—
416C2×D12—121no—
417C2×D12—121no—
418C2×C4×D3—62no—
419C2×C4×D3—62no—
420C2×C4×D3—62no—
421C2×C4×D3—62no—
422C2×C4×D3—62no—
423C2×C4×D3—62no—
424C2×C4×D3—62no—
425C2×C4×D3—62no—
426C2×C4×D3—121no—
427C2×C4×D3—121no—
428C2×C4×D3—121no—
429C2×C4×D3—121no—
430C3×C4⋊C4—62no—
431C3×C22⋊C4—41no—
432C3×C22⋊C4—41no—
433C3×C22⋊C4—42no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—62no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—62no—
438C3×C22⋊C4—121no—
439C3×C42—62no—
440#217—22no—
441#217—62no—
442#217—62no—
443#217—62no—
444#217—122no—
445#217—121no—
446(C2×D3)⋊C4—22no—
447(C2×D3)⋊C4—22no—
448(C2×D3)⋊C4—22no—
449(C2×D3)⋊C4—41no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—122no—
456(C2×D3)⋊C4—121no—
457(C2×D3)⋊C4—121no—
458(C2×D3)⋊C4—121no—
459(C2×D3)⋊C4—122no—
460C4⋊Dic3—34no—
461Dic3⋊C4—22no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—62no—
466Dic3⋊C4—62no—
467Dic3⋊C4—122no—
468C4×Dic3—22no—
469C4×Dic3—34no—
470C4×Dic3—34no—
471C4×Dic3—62no—
472C4×Dic3—62no—
473C4×Dic3—62no—
474C4×Dic3—62no—
475C4×Dic3—62no—
476C4×Dic3—62no—
477C4×Dic3—122no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32C23×C411yescharacteristic
486C22×C32C22×D411yescharacteristic
487C22×C32C22×D411yescharacteristic
488C22×C32C2×#4111yescharacteristic
489C22×C32C2×#4111yescharacteristic
490C22×C32H(5,𝔽2)11yescharacteristic
491C22×C32H(5,𝔽2)11yescharacteristic
492C2×C3⋊D3—22no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—41no—
498C2×C3⋊D3—41no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3—41no—
508C2×C3×D3—41no—
509C2×C3×D3—41no—
510C2×C3×D3—41no—
511C2×C3×D3—41no—
512C2×C3×D3—41no—
513C32×C4—41no—
514C32×C4—41no—
515C3⋊Dic3—22no—
516C3⋊Dic3—41no—
517C3⋊Dic3C4×D414yescomplemented
518C3×Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3—22no—
521C3×Dic3—22no—
522C3×Dic3—41no—
523C3×Dic3C4×D414yescomplemented
524C22×D4—31no—
525C22×D4—31no—
526C22×D4—91no—
527C22×D4—91no—
528C22×D4—91no—
529C22×D4—91no—
530C23×C4—31no—
531C23×C4—91no—
532C23×C4—91no—
533C23×C4—91no—
534#127—98no—
535C4×D4—184no—
536C4×D4—184no—
537C4×D4—184no—
538C4×D4—184no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—91no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4D3211yescharacteristic
555C2×C42—31no—
556C2×C42—91no—
557C2×C42—91no—
558C2×C42—91no—
559C2×C42—91no—
560#95—31no—
561#95—31no—
562#95—91no—
563#95—91no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—22no—
578C23×C3—32no—
579C23×C3—32no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3C2×C4×D312yes—
599C23×C3C2×C4×D312yes—
600C23×C3C23×D311yescharacteristic
601C23×C3C23×D311yescharacteristic
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—32no—
615C22×D3—32no—
616C22×D3—62no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3—121no—
632C22×D3—121no—
633C22×D3—121no—
634C22×D3—121no—
635C22×D3C2×C4×D312yes—
636C22×D3C2×C4×D312yes—
637C3×D4—68no—
638C3×D4—124no—
639C2×C3×C4—22no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—124no—
676#67—28no—
677#67—44no—
678#67—68no—
679#67—68no—
680#67—68no—
681#67—68no—
682#67—68no—
683#67—128no—
684#67—124no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—32no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—32no—
704C2×Dic3—44no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—62no—
708C2×Dic3—62no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—121no—
720C2×Dic3—121no—
721C2×Dic3—121no—
722C2×Dic3—121no—
723C2×Dic3—121no—
724C2×Dic3—124no—
725C2×Dic3—124no—
726C2×Dic3C2×C4×D312yes—
727C2×Dic3C2×C4×D312yes—
728C2×Dic3D3×D412yes—
729C2×Dic3D3×D412yes—
730C2×Dic3D3×D412yes—
731C2×Dic3D3×D412yes—
732C2×Dic3#23712yes—
733D12—68no—
734D12—124no—
735C4×D3—124no—
736C4×D3—124no—
737C4×D3—124no—
738C4×D3—124no—
739C2×C32—42no—
740C2×C32C2×C4×D411yescharacteristic
741C2×C32C2×C4×D411yescharacteristic
742C2×C32#51811yescharacteristic
743C2×C32D4211yescharacteristic
744C2×C32#55011yescharacteristic
745C2×C32#55011yescharacteristic
746C2×C32#55911yescharacteristic
747C3⋊D3—42no—
748C3×D3—42no—
749C3×D3—42no—
750C24—31no—
751C24—31no—
752C24—91no—
753C24C2×D3211yescharacteristic
754C2×D4—34no—
755C2×D4—34no—
756C2×D4—62no—
757C2×D4—62no—
758C2×D4—94no—
759C2×D4—94no—
760C2×D4—94no—
761C2×D4—94no—
762C2×D4—121no—
763C2×D4—121no—
764C2×D4—182no—
765C2×D4—182no—
766C2×D4—182no—
767C2×D4—182no—
768C2×D4—182no—
769C2×D4—182no—
770C2×D4—361no—
771C2×D4—361no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—31no—
777C22×C4—31no—
778C22×C4—62no—
779C22×C4—62no—
780C22×C4—91no—
781C22×C4—91no—
782C22×C4—91no—
783C22×C4—121no—
784C22×C4—182no—
785C22×C4—182no—
786C22×C4—182no—
787C22×C4—182no—
788C22×C4—182no—
789C22×C4—182no—
790C22×C4—361no—
791C22×C4—361no—
792C22×C4—361no—
793C22×C4C2×D3211yescharacteristic
794C22×C4C2×D3211yescharacteristic
795C4⋊C4—62no—
796C4⋊C4—94no—
797C4⋊C4—94no—
798C4⋊C4—182no—
799C22⋊C4—41no—
800C22⋊C4—62no—
801C22⋊C4—62no—
802C22⋊C4—62no—
803C22⋊C4—62no—
804C22⋊C4—121no—
805C22⋊C4—182no—
806C22⋊C4—182no—
807C22⋊C4—182no—
808C22⋊C4—182no—
809C22⋊C4—361no—
810C22⋊C4—361no—
811C42—62no—
812C42—94no—
813C42—182no—
814C42—182no—
815C42—182no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—81no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3C22×C4×D311yescharacteristic
859C22×C3C22×C4×D311yescharacteristic
860C22×C3C2×D3×D411yescharacteristic
861C22×C3C2×D3×D411yescharacteristic
862C22×C3C2×D3×D411yescharacteristic
863C22×C3C2×D3×D411yescharacteristic
864C22×C3C2×#23711yescharacteristic
865C22×C3#100411yescharacteristic
866C22×C3#100411yescharacteristic
867C22×C3#100411yescharacteristic
868C22×C3D3×#4111yescharacteristic
869C22×C3D3×#4111yescharacteristic
870C22×C3D3×#4111yescharacteristic
871C22×C3#100911yescharacteristic
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—41no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—122no—
893C2×D3—122no—
894C2×D3—122no—
895C2×D3—121no—
896C2×D3—121no—
897C2×D3—121no—
898C2×D3—121no—
899C2×D3—121no—
900C2×D3—121no—
901C2×D3—121no—
902C2×D3—121no—
903C2×D3—241no—
904C2×D3—241no—
905C2×D3—241no—
906C2×D3—241no—
907C3×C4—34no—
908C3×C4—42no—
909C3×C4—41no—
910C3×C4—41no—
911C3×C4—41no—
912C3×C4—41no—
913C3×C4—62no—
914C3×C4—62no—
915C3×C4—62no—
916C3×C4—62no—
917C3×C4—81no—
918C3×C4—121no—
919Dic3—22no—
920Dic3—22no—
921Dic3—22no—
922Dic3—22no—
923Dic3—34no—
924Dic3—34no—
925Dic3—41no—
926Dic3—64no—
927Dic3—62no—
928Dic3—62no—
929Dic3—122no—
930Dic3—121no—
931Dic3—121no—
932Dic3—241no—
933Dic3#67⋊C414yescomplemented
934C32#236611yescharacteristic, complemented, Sylow
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—32no—
942C23—32no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—92no—
956C23—181no—
957C23—181no—
958C23—181no—
959C23—181no—
960C23—181no—
961C23—181no—
962C23C4×D3212yes—
963C23C22×D3211yescharacteristic
964D4—68no—
965D4—124no—
966D4—188no—
967D4—188no—
968D4—188no—
969D4—364no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—32no—
977C2×C4—32no—
978C2×C4—32no—
979C2×C4—32no—
980C2×C4—32no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—92no—
995C2×C4—92no—
996C2×C4—92no—
997C2×C4—92no—
998C2×C4—124no—
999C2×C4—181no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4—181no—
1004C2×C4—364no—
1005C2×C4—364no—
1006C2×C4—364no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—42no—
1015C2×C3—42no—
1016C2×C3—82no—
1017C2×C3—122no—
1018C2×C3—122no—
1019C2×C3C2×#67⋊C411yescharacteristic
1020C2×C3#548611yescharacteristic
1021C2×C3C4×D3×D411yescharacteristic
1022C2×C3C4×D3×D411yescharacteristic
1023C2×C3C4×D3×D411yescharacteristic
1024C2×C3#554511yescharacteristic
1025C2×C3#559011yescharacteristic
1026C2×C3#559911yescharacteristic
1027C2×C3#559911yescharacteristic
1028C2×C3#559911yescharacteristic
1029C2×C3#560911yescharacteristic
1030C2×C3#566411yescharacteristic
1031C2×C3#568111yescharacteristic
1032C2×C3#571811yescharacteristic
1033D3—42no—
1034D3—42no—
1035D3—122no—
1036D3—122no—
1037D3—242no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—121no—
1052C22—121no—
1053C22—121no—
1054C22—121no—
1055C22—121no—
1056C22—121no—
1057C22—121no—
1058C22—121no—
1059C22—182no—
1060C22—182no—
1061C22—182no—
1062C22—361no—
1063C22—361no—
1064C22—361no—
1065C22—361no—
1066C22C2×C4×D3211yescharacteristic
1067C22#6430711yescharacteristic
1068C22D32×D411yescharacteristic
1069C22D32×D411yescharacteristic
1070C22D3×#23711yescharacteristic
1071C22#6431211yescharacteristic
1072C22#6433011yescharacteristic
1073C4—34no—
1074C4—41no—
1075C4—41no—
1076C4—62no—
1077C4—62no—
1078C4—62no—
1079C4—62no—
1080C4—94no—
1081C4—121no—
1082C4—182no—
1083C4—361no—
1084C3—21no—
1085C3#7467911yescharacteristic, complemented
1086C3#7630611yescharacteristic, complemented
1087C2—42no—
1088C2—122no—
1089C2—122no—
1090C2—362no—
1091C2#1059414311yescharacteristic
1092C2D3×#67⋊C411yescharacteristic
1093C2#1059425511yescharacteristic
1094C2#1059427511yescharacteristic
1095C2#1059505611yescharacteristic
1096C2#1059522711yescharacteristic
1097C2#1059526911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63979C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2366
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×#67C2semidirect
3. C2×#63952C2semidirect
4. C2×#63902C2semidirect
5. C2×#63880C2semidirect
6. #10592656C2semidirect
7. C3×#4958C2semidirect
8. C3×#4957C2semidirect
9. #10591721C2semidirect
10. #10591386C2semidirect
11. #10591384C2semidirect
12. #10591364C2semidirect
13. #10591275C2semidirect
14. #10591243C2semidirect
15. #10591241C2semidirect
41. #63979C4semidirect
74. #4958D3semidirect
81. #4957D3semidirect
97. C2×#638C2×C4semidirect
105. C2×C3×#67C2×C4semidirect
106. C2×C3×#67C2×C4semidirect
120. C2×#626C2×C4semidirect
121. C2×#626C2×C4semidirect
124. C2×#625C2×C4semidirect
147. #3724D4semidirect
148. Dic3⋊Dic3D4semidirect
154. Dic32C2×C4semidirect
386. C2×#67C4×D3semidirect
387. C2×#67C4×D3semidirect
517. C3⋊Dic3C4×D4semidirect
523. C3×Dic3C4×D4semidirect
933. Dic3#67⋊C4semidirect
934. C32#2366semidirect
1085. C3#74679semidirect
1086. C3#76306semidirect

Maximal subgroups

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

subgroupindex
C2×#639792
C2×Dic3×#672
C2×#639522
C2×#639022
C2×#638802
#105926562
C3×#49582
C3×#49572
#105917212
#105913862
#105913842
#105913642
#105912752
#105912432
#105912412
#763063
#746793