Finite Group Databasebeta

← #11812899

Subgroups — #11812899

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C2×C3×#929C211yesmaximal, characteristic, complemented
3C2×#63958C211yesmaximal, characteristic
4C2×#63883C211yesmaximal, characteristic, complemented
5C3×#5210C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic, complemented
7#10591717C211yesmaximal, characteristic, complemented
8#10591709C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591374C211yesmaximal, characteristic, complemented
11#10591340C211yesmaximal, characteristic, complemented
12#10591303C211yesmaximal, characteristic, complemented
13#10591283C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#82897—31nomaximal
17#74608—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C4×#638—24no—
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C3×#929—24no—
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47#63958—24no—
48#63883—24no—
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×#123—31no—
58C2×#938—31no—
59C2×#929D311yescharacteristic, complemented
60C2×C4×#67—31no—
61C2×C4×#67—31no—
62C2×C4×#67—61no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C2×#884—31no—
66C3×#385—31no—
67#5222—31no—
68#5210D311yescharacteristic, complemented
69#4993—31no—
70#4990—31no—
71#4989—31no—
72#4989—31no—
73#4982—31no—
74#4980—31no—
75#4961—31no—
76#4956—31no—
77#4956—31no—
78#4956—31no—
79#4956—31no—
80#4953—31no—
81#4952—31no—
82#4949—31no—
83#4945—31no—
84#4665—31no—
85#4665—31no—
86#4657—31no—
87#4652—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—22no—
97C2×#638—22no—
98C2×#638D414yes—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—22no—
104C2×C4×C3⋊D3—41no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#624—22no—
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—22no—
123C2×#624—41no—
124#3757—22no—
125#3752—22no—
126#3750—22no—
127C4×C3⋊Dic3—22no—
128C3×#217—22no—
129C3×#217—22no—
130C3×#217—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4—41no—
136C3×Dic3⋊C4D414yescomplemented
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140#3722—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—41no—
144#2443—91noSylow
145C22×C3×D4—31no—
146C23×C3×C4—21no—
147C23×C3×C4C2×D311yescharacteristic
148C23×C3×C4C2×D311yescharacteristic
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—31no—
152C22×#67—61no—
153C22×#67C2×D311yescharacteristic
154C22×D12—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—61no—
162C3×#123—64no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—61no—
178C2×#217C2×D311yescharacteristic
179C2×#217C2×D311yescharacteristic
180C2×#217C2×D311yescharacteristic
181#938—64no—
182#929—24no—
183C4×#67—64no—
184C4×#67—64no—
185C4×#67—68no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—61no—
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×(C2×D3)⋊C4C2×D311yescharacteristic
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—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⋊C4C2×D311yescharacteristic
206C2×Dic3⋊C4C2×D311yescharacteristic
207C2×Dic3⋊C4C2×D311yescharacteristic
208C2×Dic3⋊C4C2×D311yescharacteristic
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—61no—
212D3×C4⋊C4—64no—
213D3×C4⋊C4—64no—
214#884—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⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32C2×D412yes—
238C23×C32C2411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3C2×D412yes—
244C22×C3⋊D3#4112yes—
245C22×C3⋊D3#4112yes—
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—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—44no—
259C2×C32×C4C2×D412yes—
260#638—28no—
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—
270C4×C3⋊D3—44no—
271C3×#67—44no—
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×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×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3#4112yes—
293#626—44no—
294#624—28no—
295#624—44no—
296C2×#123—31no—
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—91no—
305#387—91no—
306#386—91no—
307#386—91no—
308#386—91no—
309#385—31no—
310#385—91no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C23×D3—31no—
316C23×D3—31no—
317C23×D3—61no—
318C23×D3C22×D311yescharacteristic
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—121no—
322C22×C3×C4—24no—
323C22×C3×C4—22no—
324C22×C3×C4—22no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—42no—
337C22×C3×C4—41no—
338C22×C3×C4—41no—
339C22×C3×C4—42no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—22no—
345C2×#67—22no—
346C2×#67—34no—
347C2×#67—34no—
348C2×#67—41no—
349C2×#67—64no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—62no—
354C2×#67—62no—
355C2×#67—62no—
356C2×#67—62no—
357C2×#67—64no—
358C2×#67—64no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C2×D12—62no—
376C2×D12—62no—
377C2×D12—62no—
378C2×C4×D3—62no—
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—62no—
388C2×C4×D3—62no—
389C2×C4×D3—64no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—122no—
394C2×C4×D3—121no—
395C2×C4×D3—121no—
396C2×C4×D3—121no—
397C2×C4×D3—121no—
398C2×C4×D3—122no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—62no—
401C3×C4⋊C4—62no—
402C3×C4⋊C4—121no—
403C3×C22⋊C4—62no—
404C3×C22⋊C4—62no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—62no—
408#217—22no—
409#217—22no—
410#217—22no—
411#217—62no—
412#217—64no—
413#217—62no—
414#217—62no—
415#217—62no—
416#217—121no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—22no—
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—64no—
425(C2×D3)⋊C4—62no—
426(C2×D3)⋊C4—121no—
427C4⋊Dic3—62no—
428C4⋊Dic3—62no—
429C4⋊Dic3—62no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432Dic3⋊C4—41no—
433Dic3⋊C4—62no—
434Dic3⋊C4—62no—
435Dic3⋊C4—62no—
436Dic3⋊C4—62no—
437Dic3⋊C4—64no—
438Dic3⋊C4—62no—
439Dic3⋊C4#6714yescomplemented
440C4×Dic3—62no—
441C4×Dic3—62no—
442C4×Dic3—64no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32C22×D411yescharacteristic
451C22×C32C22×D411yescharacteristic
452C22×C32C2×#4111yescharacteristic
453C22×C32C2×#4111yescharacteristic
454C22×C32C2×#4111yescharacteristic
455C22×C32H(5,𝔽2)11yescharacteristic
456C22×C322−1+411yescharacteristic
457C2×C3⋊D3—22no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—22no—
460C2×C3⋊D3—22no—
461C2×C3⋊D3—22no—
462C2×C3⋊D3—22no—
463C2×C3⋊D3#12314yescomplemented
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—41no—
473C3⋊Dic3—22no—
474C3⋊Dic3—41no—
475C3⋊Dic3—41no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C3×Dic3—22no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C22×D4—31no—
484C22×D4—91no—
485C22×D4—91no—
486C23×C4—91no—
487C23×C4—91no—
488C23×C4—91no—
489C23×C4D3211yescharacteristic
490#123—64no—
491#121—184no—
492C4×D4—184no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—184no—
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—91no—
514#95—31no—
515#95—31no—
516#95—91no—
517#95—91no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95—91no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—22no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3D3×D412yes—
550C23×C3D3×D412yes—
551C23×C3C23×D311yescharacteristic
552C23×C3C23×D311yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—32no—
561C22×D3—32no—
562C22×D3—32no—
563C22×D3—32no—
564C22×D3—32no—
565C22×D3—32no—
566C22×D3—62no—
567C22×D3—62no—
568C22×D3—62no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—121no—
578C22×D3—121no—
579C22×D3—121no—
580C22×D3—121no—
581C3×D4—124no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
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—22no—
596C2×C3×C4—32no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—44no—
602C2×C3×C4—44no—
603C2×C3×C4—48no—
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—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4D3×D412yes—
623C2×C3×C4C2×#6712yes—
624#67—44no—
625#67—68no—
626#67—68no—
627#67—616no—
628#67—124no—
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—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—62no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—121no—
673C2×Dic3—121no—
674C2×Dic3#23512yes—
675C2×Dic3C2×#6712yes—
676C2×Dic3C2×#6712yes—
677D12—124no—
678C4×D3—68no—
679C4×D3—68no—
680C4×D3—124no—
681C4×D3—124no—
682C4×D3—124no—
683C4×D3—124no—
684C4×D3—128no—
685C2×C32—42no—
686C2×C32C2×#12311yescharacteristic
687C2×C32#52511yescharacteristic
688C2×C32#53911yescharacteristic
689C2×C32D4211yescharacteristic
690C2×C32#54711yescharacteristic
691C2×C32#54811yescharacteristic
692C2×C32#55311yescharacteristic
693C3⋊D3—24no—
694C3×D3—81no—
695C24—31no—
696C24—91no—
697C24C2×D3211yescharacteristic
698C2×D4—62no—
699C2×D4—62no—
700C2×D4—94no—
701C2×D4—121no—
702C2×D4—182no—
703C2×D4—182no—
704C2×D4—182no—
705C2×D4—182no—
706C2×D4—182no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—41no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—182no—
723C22×C4—182no—
724C22×C4—182no—
725C22×C4—182no—
726C22×C4—182no—
727C22×C4—361no—
728C22×C4—361no—
729C22×C4C2×D3211yescharacteristic
730C22×C4C2×D3211yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—62no—
733C4⋊C4—62no—
734C4⋊C4—121no—
735C4⋊C4—182no—
736C4⋊C4—182no—
737C4⋊C4—182no—
738C4⋊C4—182no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—182no—
745C22⋊C4—182no—
746C22⋊C4—182no—
747C22⋊C4—182no—
748C22⋊C4—182no—
749C22⋊C4—361no—
750C42—182no—
751C22×C3—24no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—121no—
783C22×C3—121no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3C2×#23511yescharacteristic
787C22×C3C2×D3×D411yescharacteristic
788C22×C3C2×D3×D411yescharacteristic
789C22×C3C2×D3×D411yescharacteristic
790C22×C3#100411yescharacteristic
791C22×C3#100411yescharacteristic
792C22×C3#100711yescharacteristic
793C22×C3D3×#4111yescharacteristic
794C22×C3D3×#4111yescharacteristic
795C22×C3D3×#4111yescharacteristic
796C22×C3D3×#4111yescharacteristic
797C22×C3D3×#4111yescharacteristic
798C22×C3#101011yescharacteristic
799C22×C3C22×#6711yescharacteristic
800C2×D3—34no—
801C2×D3—34no—
802C2×D3—41no—
803C2×D3—41no—
804C2×D3—41no—
805C2×D3—41no—
806C2×D3—41no—
807C2×D3—41no—
808C2×D3—41no—
809C2×D3—64no—
810C2×D3—62no—
811C2×D3—62no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—122no—
823C2×D3—122no—
824C2×D3—122no—
825C2×D3—122no—
826C2×D3—122no—
827C2×D3—122no—
828C3×C4—24no—
829C3×C4—22no—
830C3×C4—22no—
831C3×C4—42no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—62no—
835C3×C4—62no—
836C3×C4—62no—
837C3×C4—121no—
838C3×C4—121no—
839C3×C4—121no—
840C3×C4—121no—
841Dic3—22no—
842Dic3—22no—
843Dic3—22no—
844Dic3—41no—
845Dic3—41no—
846Dic3—41no—
847Dic3—41no—
848Dic3—64no—
849Dic3—62no—
850Dic3—62no—
851Dic3—122no—
852Dic3—122no—
853Dic3—121no—
854Dic3—121no—
855Dic3—121no—
856Dic3—121no—
857C32#244311yescharacteristic, complemented, Sylow
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—61no—
869C23—61no—
870C23—61no—
871C23—92no—
872C23—92no—
873C23—92no—
874C23—181no—
875C23—181no—
876C23—181no—
877C23—181no—
878C23#381112yes—
879C23C22×D3211yescharacteristic
880D4—124no—
881D4—188no—
882D4—364no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—32no—
889C2×C4—32no—
890C2×C4—32no—
891C2×C4—44no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
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—92no—
911C2×C4—188no—
912C2×C4—181no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—181no—
919C2×C4—181no—
920C2×C4—364no—
921C2×C4—364no—
922C2×C4D3×#6712yes—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—44no—
931C2×C3—42no—
932C2×C3—42no—
933C2×C3—241no—
934C2×C3#550711yescharacteristic
935C2×C3#554711yescharacteristic
936C2×C3#555811yescharacteristic
937C2×C3#559011yescharacteristic
938C2×C3#563311yescharacteristic
939C2×C3#563811yescharacteristic
940C2×C3D3×#12311yescharacteristic
941C2×C3D3×#12311yescharacteristic
942C2×C3#565511yescharacteristic
943C2×C3#566011yescharacteristic
944C2×C3#566111yescharacteristic
945C2×C3D4×#6711yescharacteristic
946C2×C3#582811yescharacteristic
947C2×C3#583111yescharacteristic
948D3—64no—
949D3—64no—
950D3—81no—
951D3—124no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—94no—
960C22—121no—
961C22—121no—
962C22—121no—
963C22—121no—
964C22—121no—
965C22—121no—
966C22—121no—
967C22—182no—
968C22—182no—
969C22—182no—
970C22—182no—
971C22—182no—
972C22—182no—
973C22#6429711yescharacteristic
974C22D3×#23511yescharacteristic
975C22#6430611yescharacteristic
976C22#6430611yescharacteristic
977C22C2×D3×#6711yescharacteristic
978C22C2×#381111yescharacteristic
979C22#6433011yescharacteristic
980C4—22no—
981C4—41no—
982C4—62no—
983C4—62no—
984C4—62no—
985C4—121no—
986C4—121no—
987C4—121no—
988C4—121no—
989C4—182no—
990C4—361no—
991C4—361no—
992C3—21no—
993C3#7460811yescharacteristic, complemented
994C3#8289711yescharacteristic, complemented
995C2—42no—
996C2—184no—
997C2—241no—
998C2#1059483011yescharacteristic
999C2#1059491711yescharacteristic
1000C2#1059496811yescharacteristic
1001C2#1059502511yescharacteristic
1002C2#1059506011yescharacteristic
1003C2#1059507911yescharacteristic
1004C2#1059552611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC2×#63958C2
hypercenterC23×C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C2×C3×#929C2semidirect
4. C2×#63883C2semidirect
5. C3×#5210C2semidirect
6. #10591722C2semidirect
7. #10591717C2semidirect
8. #10591709C2semidirect
9. #10591387C2semidirect
10. #10591374C2semidirect
11. #10591340C2semidirect
12. #10591303C2semidirect
13. #10591283C2semidirect
14. #10591275C2semidirect
15. #10591192C2semidirect
59. C2×#929D3semidirect
68. #5210D3semidirect
136. C3×Dic3⋊C4D4semidirect
439. Dic3⋊C4#67semidirect
463. C2×C3⋊D3#123semidirect
857. C32#2443semidirect
993. C3#74608semidirect
994. C3#82897semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×#9292
C2×#639582
C2×#638832
C3×#52102
#105917222
#105917172
#105917092
#105913872
#105913742
#105913402
#105913032
#105912832
#105912752
#105911922
#828973
#746083