Finite Group Databasebeta

← #11808431

Subgroups — #11808431

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×C4×#626C211yesmaximal, characteristic, complemented
4C2×#63855C211yesmaximal, characteristic, complemented
5C3×C4×#217C211yesmaximal, characteristic, complemented
6#10591724C211yesmaximal, characteristic
7#10591712C211yesmaximal, characteristic, complemented
8#10591708C211yesmaximal, characteristic, complemented
9#10591691C211yesmaximal, characteristic, complemented
10#10591347C211yesmaximal, characteristic, complemented
11#10591340C211yesmaximal, characteristic, complemented
12C4×#3724C211yesmaximal, characteristic, complemented
13#10591298C211yesmaximal, characteristic, complemented
14#10591292C211yesmaximal, characteristic, complemented
15C4×#3722C211yesmaximal, characteristic, complemented
16#82345—31nomaximal
17#73581—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C4×#638—24no—
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C3×C4×#67—24no—
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×#3724C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C4×#626—24no—
50#63855—24no—
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×C4×D4—31no—
58C2×C4×#67—31no—
59C2×C4×#67—31no—
60C2×C4×#67—31no—
61C2×C4×#67—61no—
62C2×C4×#67D311yescharacteristic, complemented
63C2×#926—31no—
64C2×C4×D12—31no—
65C2×#872—31no—
66C3×C4×C22⋊C4—31no—
67#5223—31no—
68#5222—31no—
69C4×#217D311yescharacteristic, complemented
70#4994—31no—
71#4982—31no—
72#4961—31no—
73#4960—31no—
74#4959—31no—
75#4959—31no—
76#4959—31no—
77#4952—31no—
78#4948—31no—
79#4948—31no—
80C4×(C2×D3)⋊C4—31no—
81C4×(C2×D3)⋊C4—31no—
82C4×Dic3⋊C4—31no—
83C4×Dic3⋊C4—31no—
84#4676—31no—
85#4675—31no—
86#4672—31no—
87#4657—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—22no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—22no—
97C2×#638—22no—
98C2×#638—22no—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—22no—
104C2×C4×C3⋊D3—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3D414yescomplemented
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—22no—
121#3757—22no—
122#3752—22no—
123#3750—22no—
124C4×C3⋊Dic3D414yescomplemented
125C3×#217—22no—
126C3×#217—22no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×Dic3⋊C4—22no—
130C3×C4×Dic3—22no—
131C3×C4×Dic3—22no—
132C3×C4×Dic3—22no—
133#3724—22no—
134#3724—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138#3722—22no—
139#3722—22no—
140#3722—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144#2392—91noSylow
145C22×C3×D4—31no—
146C23×C3×C4—21no—
147C23×C3×C4—31no—
148C23×C3×C4C2×D311yescharacteristic
149C23×C3×C4C2×D311yescharacteristic
150C22×#67—31no—
151C22×#67—31no—
152C22×#67—31no—
153C22×#67—61no—
154C22×#67C2×D311yescharacteristic
155C22×D12—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—61no—
159C22×C4×D3C2×D311yescharacteristic
160C3×C4×D4—64no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C42—31no—
167C2×C3×C42—31no—
168C2×C3×C42—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—61no—
175C2×#217C2×D311yescharacteristic
176C2×#217C2×D311yescharacteristic
177C2×#217C2×D311yescharacteristic
178C4×#67—24no—
179C4×#67—64no—
180C4×#67—64no—
181C4×#67—64no—
182C4×#67—68no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
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—31no—
194C2×(C2×D3)⋊C4—61no—
195C2×(C2×D3)⋊C4C2×D311yescharacteristic
196#926—64no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—31no—
199C2×C4⋊Dic3—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—61no—
210C2×Dic3⋊C4C2×D311yescharacteristic
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—61no—
214C2×C4×Dic3C2×D311yescharacteristic
215C2×C4×Dic3C2×D311yescharacteristic
216C2×C4×Dic3C2×D311yescharacteristic
217C4×D12—64no—
218#872—64no—
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×C32#4112yes—
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#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×D3C2×D412yes—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—44no—
257C2×C32×C4C2×D412yes—
258C2×C32×C4C2×D412yes—
259C2×C32×C4#4112yes—
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⋊Dic3C2×D412yes—
269C2×C3⋊Dic3C2×D412yes—
270C4×C3⋊D3—44no—
271C3×#67—28no—
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×Dic3#4112yes—
292C2×C3×Dic3#4112yes—
293C3×C4×D3—28no—
294#626—28no—
295C2×C4×D4—31no—
296C2×C4×D4—91no—
297C2×C4×D4—91no—
298C2×#117—91no—
299#398—91no—
300#397—91no—
301#396—91no—
302#396—91no—
303#394—91no—
304#394—91no—
305#394—91no—
306#392—91no—
307C4×C4⋊C4—91no—
308C4×C22⋊C4—31no—
309C4×C22⋊C4—91no—
310C24×C3—21no—
311C24×C3—31no—
312C24×C3C22×D311yescharacteristic
313C24×C3C22×D311yescharacteristic
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—61no—
317C23×D3C22×D311yescharacteristic
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C22×C3×C4—24no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—22no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—22no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—34no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—42no—
339C22×C3×C4—42no—
340C22×C3×C4—62no—
341C22×C3×C4—62no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C2×#67—22no—
347C2×#67—22no—
348C2×#67—22no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—62no—
354C2×#67—62no—
355C2×#67—64no—
356C2×#67—64no—
357C2×#67—64no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—62no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C2×D12—62no—
378C2×D12—62no—
379C2×D12—62no—
380C2×C4×D3—22no—
381C2×C4×D3—22no—
382C2×C4×D3—64no—
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—122no—
390C2×C4×D3—122no—
391C2×C4×D3#6714yescomplemented
392C3×C4⋊C4—62no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—62no—
397C3×C42—62no—
398C3×C42—62no—
399C3×C42—62no—
400#217—22no—
401#217—22no—
402#217—22no—
403#217—62no—
404#217—62no—
405#217—62no—
406#217—62no—
407#217—62no—
408#217—64no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—64no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—62no—
422C4⋊Dic3—62no—
423C4⋊Dic3—62no—
424C4⋊Dic3—62no—
425Dic3⋊C4—22no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—64no—
434Dic3⋊C4—62no—
435Dic3⋊C4—62no—
436C4×Dic3—22no—
437C4×Dic3—22no—
438C4×Dic3—22no—
439C4×Dic3—34no—
440C4×Dic3—34no—
441C4×Dic3—64no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32C22×D411yescharacteristic
450C22×C32C22×D411yescharacteristic
451C22×C32C2×#4111yescharacteristic
452C22×C32C2×#4111yescharacteristic
453C22×C32C2×#4111yescharacteristic
454C22×C32C2×#4111yescharacteristic
455C22×C32C2×#4111yescharacteristic
456C2×C3⋊D3—22no—
457C2×C3⋊D3—22no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C32×C4—41no—
471C32×C4#12114yes—
472C3⋊Dic3—22no—
473C3⋊Dic3—22no—
474C3⋊Dic3—41no—
475C3×Dic3—22no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C22×D4—31no—
483C22×D4—91no—
484C22×D4—91no—
485C23×C4—31no—
486C23×C4—91no—
487C23×C4D3211yescharacteristic
488C4×D4—64no—
489C4×D4—184no—
490C4×D4—184no—
491#117—184no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C42—31no—
512C2×C42—31no—
513C2×C42—31no—
514C2×C42—91no—
515#95—31no—
516#95—31no—
517#95—91no—
518#95—91no—
519#95—91no—
520#95—91no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—21no—
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—22no—
537C23×C3—32no—
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#23512yes—
549C23×C3#23512yes—
550C23×C3C23×D311yescharacteristic
551C23×C3C23×D311yescharacteristic
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—32no—
559C22×D3—32no—
560C22×D3—62no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—61no—
564C22×D3—61no—
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×D3—61no—
574C22×D3—61no—
575C22×D3—121no—
576C22×D3—121no—
577C22×D3—121no—
578C22×D3—121no—
579C22×D3C2×#6712yes—
580C3×D4—68no—
581C2×C3×C4—22no—
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—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—48no—
597C2×C3×C4—44no—
598C2×C3×C4—44no—
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—68no—
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#23512yes—
619C2×C3×C4D3×D412yes—
620C2×C3×C4D3×D412yes—
621C2×C3×C4D3×D412yes—
622C2×C3×C4#23712yes—
623C2×C3×C4C2×#6712yes—
624#67—28no—
625#67—68no—
626#67—616no—
627#67—68no—
628#67—68no—
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—32no—
650C2×Dic3—32no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
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—121no—
671C2×Dic3—121no—
672C2×Dic3—121no—
673C2×Dic3—121no—
674C2×Dic3#23512yes—
675C2×Dic3#23512yes—
676C2×Dic3C2×#6712yes—
677D12—68no—
678C4×D3—28no—
679C4×D3—128no—
680C4×D3—124no—
681C4×D3—124no—
682C2×C32—42no—
683C2×C32C2×#12111yescharacteristic
684C2×C32#52511yescharacteristic
685C2×C32#52511yescharacteristic
686C2×C32#52511yescharacteristic
687C2×C32#52911yescharacteristic
688C2×C32#52911yescharacteristic
689C2×C32#53211yescharacteristic
690C3⋊D3—42no—
691C3×D3—42no—
692C24—31no—
693C24—91no—
694C24C2×D3211yescharacteristic
695C2×D4—62no—
696C2×D4—62no—
697C2×D4—62no—
698C2×D4—182no—
699C2×D4—182no—
700C2×D4—182no—
701C2×D4—182no—
702C2×D4—182no—
703C2×D4—182no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—34no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—62no—
716C22×C4—62no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—182no—
723C22×C4C2×D3211yescharacteristic
724C22×C4C2×D3211yescharacteristic
725C4⋊C4—62no—
726C4⋊C4—182no—
727C4⋊C4—182no—
728C4⋊C4—182no—
729C4⋊C4—182no—
730C4⋊C4—182no—
731C4⋊C4—182no—
732C22⋊C4—62no—
733C22⋊C4—62no—
734C22⋊C4—62no—
735C22⋊C4—62no—
736C22⋊C4—182no—
737C22⋊C4—182no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—182no—
742C22⋊C4—182no—
743C22⋊C4—182no—
744C42—62no—
745C42—62no—
746C42—62no—
747C42—94no—
748C22×C3—24no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—121no—
783C22×C3C2×#23511yescharacteristic
784C22×C3C2×#23511yescharacteristic
785C22×C3C2×#23511yescharacteristic
786C22×C3C2×#23511yescharacteristic
787C22×C3C2×#23511yescharacteristic
788C22×C3C2×D3×D411yescharacteristic
789C22×C3C2×D3×D411yescharacteristic
790C22×C3C2×D3×D411yescharacteristic
791C22×C3C2×#23711yescharacteristic
792C22×C3D3×#4111yescharacteristic
793C22×C3D3×#4111yescharacteristic
794C22×C3D3×#4111yescharacteristic
795C22×C3D3×#4111yescharacteristic
796C22×C3C22×#6711yescharacteristic
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—22no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—41no—
803C2×D3—41no—
804C2×D3—64no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—122no—
812C2×D3—122no—
813C2×D3—122no—
814C2×D3—122no—
815C2×D3—122no—
816C2×D3—122no—
817C2×D3—121no—
818C2×D3—121no—
819C2×D3—121no—
820C2×D3—121no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—121no—
824C2×D3—121no—
825C3×C4—24no—
826C3×C4—42no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—62no—
830C3×C4—62no—
831C3×C4—62no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4—121no—
835C3×C4—121no—
836C3×C4#88414yes—
837C3×C4#93914yes—
838Dic3—22no—
839Dic3—22no—
840Dic3—22no—
841Dic3—41no—
842Dic3—41no—
843Dic3—41no—
844Dic3—41no—
845Dic3—64no—
846Dic3—62no—
847Dic3—62no—
848Dic3—62no—
849Dic3—62no—
850Dic3—122no—
851Dic3—122no—
852Dic3—121no—
853Dic3—121no—
854C32#239211yescharacteristic, complemented, Sylow
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—32no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—92no—
869C23—181no—
870C23—181no—
871C23—181no—
872C23—181no—
873C23—181no—
874C23—181no—
875C23#379812yes—
876C23C22×D3211yescharacteristic
877D4—68no—
878D4—188no—
879D4—188no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—32no—
884C2×C4—32no—
885C2×C4—32no—
886C2×C4—44no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—68no—
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—92no—
907C2×C4—92no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—181no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—364no—
916C2×C4#380412yes—
917C2×C4D3×#6712yes—
918C2×C4#381112yes—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—44no—
927C2×C3—42no—
928C2×C3—42no—
929C2×C3—122no—
930C2×C3#547911yescharacteristic
931C2×C3C2×#88411yescharacteristic
932C2×C3#552811yescharacteristic
933C2×C3#553811yescharacteristic
934C2×C3#554711yescharacteristic
935C2×C3#554711yescharacteristic
936C2×C3#554711yescharacteristic
937C2×C3#554711yescharacteristic
938C2×C3#554811yescharacteristic
939C2×C3#554811yescharacteristic
940C2×C3#555711yescharacteristic
941C2×C3#579111yescharacteristic
942C2×C3C2×#93911yescharacteristic
943C2×C3#582811yescharacteristic
944D3—42no—
945D3—124no—
946D3—122no—
947D3—122no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—121no—
959C22—121no—
960C22—121no—
961C22—121no—
962C22—182no—
963C22—182no—
964C22—182no—
965C22—361no—
966C22—361no—
967C22—361no—
968C22—361no—
969C22C2×#379811yescharacteristic
970C22D3×#23511yescharacteristic
971C22D3×#23511yescharacteristic
972C22#6430611yescharacteristic
973C22C2×#380411yescharacteristic
974C22C2×D3×#6711yescharacteristic
975C22C2×#381111yescharacteristic
976C4—41no—
977C4—62no—
978C4—62no—
979C4—62no—
980C4—121no—
981C4—121no—
982C4—121no—
983C4—121no—
984C4—182no—
985C4—182no—
986C4—361no—
987C4#6397114yes—
988C3—21no—
989C3#7358111yescharacteristic, complemented
990C3#8234511yescharacteristic, complemented
991C2—42no—
992C2—122no—
993C2—362no—
994C2#1059483611yescharacteristic
995C2#1059483911yescharacteristic
996C2#1059500211yescharacteristic
997C2#1059501611yescharacteristic
998C2#1059501711yescharacteristic
999C2#1059506011yescharacteristic
1000C2C2×#6397111yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
prime radical#10591724C2
hypercenterC23×C4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×C4×#626C2semidirect
4. C2×#63855C2semidirect
5. C3×C4×#217C2semidirect
7. #10591712C2semidirect
8. #10591708C2semidirect
9. #10591691C2semidirect
10. #10591347C2semidirect
11. #10591340C2semidirect
12. C4×#3724C2semidirect
13. #10591298C2semidirect
14. #10591292C2semidirect
15. C4×#3722C2semidirect
62. C2×C4×#67D3semidirect
69. C4×#217D3semidirect
117. C2×C3×C4×D3D4semidirect
124. C4×C3⋊Dic3D4semidirect
391. C2×C4×D3#67semidirect
854. C32#2392semidirect
989. C3#73581semidirect
990. C3#82345semidirect

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×C4×#672
C2×C4×#6262
C2×#638552
C3×C4×#2172
#105917242
#105917122
#105917082
#105916912
#105913472
#105913402
C4×#37242
#105912982
#105912922
C4×#37222
#823453
#735813