Finite Group Databasebeta

← #11808236

Subgroups — #11808236

Order 1152.

2017 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3798C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×C4×#626C211yesmaximal, characteristic, complemented
4C2×C4×#625C211yesmaximal, characteristic, complemented
5C4×#3752C211yesmaximal, characteristic, complemented
6C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#10591393C211yesmaximal, characteristic, complemented
8#10591392C211yesmaximal, characteristic, complemented
9#10591391C211yesmaximal, characteristic, complemented
10#10591390C211yesmaximal, characteristic, complemented
11#10591389C211yesmaximal, characteristic, complemented
12#10591338C211yesmaximal, characteristic, complemented
13#10591293C211yesmaximal, characteristic, complemented
14#10591292C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#82400—31nomaximal
17#73580—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C2×#3798—24no—
30C2×#3798—24no—
31C2×#3798—24no—
32C2×C32×C42C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×C4×D12—24no—
43C2×#3724C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C4×#626—24no—
52C4×#625—24no—
53#63658C2211yescharacteristic
54#63658C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57#63579C2211yescharacteristic
58#63579C2211yescharacteristic
59C22×#235—31no—
60C22×#235—31no—
61C2×C3×C4×D4—31no—
62C2×C4×#67—31no—
63C2×C4×#67—31no—
64C2×C4×#67—31no—
65C2×C4×D12—31no—
66C2×C4×D12D311yescharacteristic, complemented
67C3×C4×C22⋊C4—31no—
68#5223—31no—
69#5223—31no—
70C4×#217—31no—
71#4991—31no—
72#4979—31no—
73#4961—31no—
74#4961—31no—
75#4960—31no—
76#4960—31no—
77#4960—31no—
78#4959—31no—
79#4959—31no—
80#4947—31no—
81C4×(C2×D3)⋊C4—31no—
82C4×(C2×D3)⋊C4—31no—
83C4×(C2×D3)⋊C4—31no—
84C4×(C2×D3)⋊C4—61no—
85C4×(C2×D3)⋊C4D311yescharacteristic, complemented
86#4673—31no—
87#4672—31no—
88#4671—31no—
89#4656—31no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C23×C3×D3C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3D414yescomplemented
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×C3×D12—22no—
109C2×C3×D12—22no—
110C2×C3×D12—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×D3D414yescomplemented
119C2×C3×C4×D3D414yescomplemented
120C2×#627—22no—
121C2×#627—22no—
122C2×#627—22no—
123C2×#626—22no—
124C2×#626—22no—
125C2×#626—22no—
126C2×#626—22no—
127C2×#626—22no—
128C2×#626—22no—
129C2×#626—22no—
130C2×#626—22no—
131C2×#626—22no—
132C2×#625—22no—
133C2×#625—22no—
134C2×#625—22no—
135C2×#625—22no—
136C2×#625—22no—
137C2×#625—22no—
138#3798—232no—
139C32×C42—22no—
140#3752—22no—
141#3752—22no—
142C4×C3⋊Dic3—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×C4⋊Dic3—22no—
148C3×C4×Dic3—22no—
149#3724—22no—
150Dic3⋊Dic3—22no—
151#3722—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—22no—
155(C2×D3)⋊Dic3—22no—
156(C2×D3)⋊Dic3—22no—
157#2388—91noSylow
158C22×C3×D4—31no—
159C23×C3×C4—31no—
160C23×C3×C4—31no—
161C23×C3×C4—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—31no—
169C2×#235—64no—
170C2×#235—64no—
171C2×#235—64no—
172C2×#235—64no—
173C2×#235—64no—
174C2×#235—64no—
175C22×D12—31no—
176C22×D12—31no—
177C22×D12—31no—
178C22×D12C2×D311yescharacteristic
179C22×C4×D3—31no—
180C22×C4×D3—31no—
181C22×C4×D3—61no—
182C22×C4×D3C2×D311yescharacteristic
183C22×C4×D3C2×D311yescharacteristic
184C22×C4×D3C2×D311yescharacteristic
185C22×Dic6—31no—
186C22×Dic6—31no—
187C3×C4×D4—64no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C42—21no—
194C2×C3×C42—31no—
195C2×C3×C42C2×D311yescharacteristic
196C2×C3×C42C2×D311yescharacteristic
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C4×#67—64no—
203C4×#67—64no—
204C4×#67—64no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—61no—
217C2×(C2×D3)⋊C4—61no—
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×(C2×D3)⋊C4C2×D311yescharacteristic
221C2×(C2×D3)⋊C4C2×D311yescharacteristic
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3C2×D311yescharacteristic
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—31no—
227C2×C4×Dic3—31no—
228C2×C4×Dic3—31no—
229C2×C4×Dic3—61no—
230C2×C4×Dic3C2×D311yescharacteristic
231C4×D12—24no—
232C4×D12—64no—
233C3×#95—31no—
234C3×#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95—31no—
242C3⋊#95—31no—
243C3⋊#95—61no—
244C3⋊#95—61no—
245C3⋊#95C2×D311yescharacteristic
246C3⋊#95C2×D311yescharacteristic
247C23×C32C2411yescharacteristic
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3C2×D412yes—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
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×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3C2×D412yes—
274C22×C3×D3C2×D412yes—
275C22×C3×D3#4112yescomplemented
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4C2×D412yes—
282C2×C32×C4C2×D412yes—
283C2×C32×C4C2×D412yes—
284C2×C32×C4#4112yescomplemented
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⋊Dic3C2×D412yes—
293C2×C3⋊Dic3#4112yescomplemented
294C4×C3⋊D3—28no—
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—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3C2×D412yes—
309C2×C3×Dic3#4112yescomplemented
310C3×D12—28no—
311C3×C4×D3—28no—
312C3×C4×D3—28no—
313C3×C4×D3—44no—
314#627—28no—
315#626—28no—
316#626—28no—
317#626—28no—
318#625—28no—
319#625—28no—
320C22×#41—91no—
321C2×C4×D4—31no—
322C2×C4×D4—91no—
323C2×C4×D4—91no—
324#395—91no—
325#394—91no—
326#394—91no—
327#394—91no—
328#393—91no—
329#392—91no—
330#392—91no—
331#392—91no—
332C4×C22⋊C4—31no—
333C4×C22⋊C4—91no—
334C4×C22⋊C4—91no—
335C24×C3—31no—
336C24×C3—31no—
337C24×C3—31no—
338C23×D3—31no—
339C23×D3—31no—
340C23×D3—61no—
341C23×D3C22×D311yescharacteristic
342C23×D3C22×D311yescharacteristic
343C23×D3C22×D311yescharacteristic
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C2×C3×D4—62no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—34no—
354C22×C3×C4—34no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—62no—
358C22×C3×C4—62no—
359C22×C3×C4—62no—
360C22×C3×C4—62no—
361C22×C3×C4—62no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C2×#67—62no—
371C2×#67—62no—
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—62no—
383C2×#67—62no—
384C2×#67—62no—
385C2×#67—62no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—62no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—61no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405#235—632no—
406#235—632no—
407C2×D12—22no—
408C2×D12—22no—
409C2×D12—22no—
410C2×D12—62no—
411C2×D12—62no—
412C2×D12—62no—
413C2×D12—62no—
414C2×D12—62no—
415C2×D12—62no—
416C2×D12—62no—
417C2×D12—62no—
418C2×D12—62no—
419C2×C4×D3—22no—
420C2×C4×D3—22no—
421C2×C4×D3—22no—
422C2×C4×D3—22no—
423C2×C4×D3—22no—
424C2×C4×D3—22no—
425C2×C4×D3—22no—
426C2×C4×D3—34no—
427C2×C4×D3—34no—
428C2×C4×D3—64no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—62no—
432C2×C4×D3—62no—
433C2×C4×D3—122no—
434C2×C4×D3—122no—
435C2×C4×D3D1214yescomplemented
436C2×C4×D3#6714yescomplemented
437C2×Dic6—62no—
438C2×Dic6—62no—
439C2×Dic6—62no—
440C2×Dic6—62no—
441C2×Dic6—62no—
442C2×Dic6—62no—
443C3×C4⋊C4—62no—
444C3×C22⋊C4—62no—
445C3×C22⋊C4—62no—
446C3×C22⋊C4—62no—
447C3×C22⋊C4—62no—
448C3×C42—22no—
449C3×C42—22no—
450C3×C42—42no—
451C3×C42—62no—
452#217—62no—
453#217—62no—
454#217—62no—
455#217—62no—
456#217—62no—
457(C2×D3)⋊C4—22no—
458(C2×D3)⋊C4—22no—
459(C2×D3)⋊C4—22no—
460(C2×D3)⋊C4—22no—
461(C2×D3)⋊C4—62no—
462(C2×D3)⋊C4—62no—
463(C2×D3)⋊C4—62no—
464(C2×D3)⋊C4—62no—
465(C2×D3)⋊C4—62no—
466(C2×D3)⋊C4—62no—
467(C2×D3)⋊C4—64no—
468(C2×D3)⋊C4—64no—
469(C2×D3)⋊C4—62no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—62no—
473(C2×D3)⋊C4—62no—
474C4⋊Dic3—22no—
475C4⋊Dic3—62no—
476Dic3⋊C4—62no—
477Dic3⋊C4—62no—
478Dic3⋊C4—62no—
479C4×Dic3—22no—
480C4×Dic3—62no—
481C4×Dic3—62no—
482C4×Dic3—122no—
483C22×C32C22×D411yescharacteristic
484C22×C32C22×D411yescharacteristic
485C22×C32C22×D411yescharacteristic
486C22×C32C2×#4111yescharacteristic
487C22×C32C2×#4111yescharacteristic
488C22×C32C2×#4111yescharacteristic
489C22×C32C2×#4111yescharacteristic
490C2×C3⋊D3—22no—
491C2×C3⋊D3—22no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3—41no—
494C2×C3⋊D3—41no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
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—22no—
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—
513C2×C3×D3—41no—
514C2×C3×D3—41no—
515C2×C3×D3—41no—
516C2×C3×D3—41no—
517C2×C3×D3—41no—
518C32×C4—22no—
519C32×C4—41no—
520C32×C4#12014yes—
521C3⋊Dic3—22no—
522C3⋊Dic3—22no—
523C3⋊Dic3—41no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—41no—
528C3×Dic3—41no—
529C2×#41—184no—
530C2×#41—184no—
531C2×#41—184no—
532C22×Q8—91no—
533C22×D4—31no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C23×C4—31no—
540C23×C4—31no—
541C23×C4—31no—
542C23×C4—91no—
543C4×D4—64no—
544C4×D4—184no—
545C4×D4—184no—
546C2×C4⋊C4—31no—
547C2×C4⋊C4—91no—
548C2×C4⋊C4—91no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—91no—
561C2×C42—31no—
562C2×C42—91no—
563C2×C42D3211yescharacteristic
564#95—31no—
565#95—31no—
566#95—91no—
567#95—91no—
568#95—91no—
569#95—91no—
570C23×C3—21no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—32no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3C23×D311yescharacteristic
593C23×C3C23×D311yescharacteristic
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
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—32no—
613C22×D3—32no—
614C22×D3—62no—
615C22×D3—62no—
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×D3C2×D1212yes—
634C22×D3#23512yescomplemented
635C22×D3C2×#6712yes—
636C3×D4—68no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—22no—
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—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—68no—
666C2×C3×C4—68no—
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—124no—
674C2×C3×C4C2×D1212yes—
675C2×C3×C4#23512yescomplemented
676C2×C3×C4#23512yescomplemented
677C2×C3×C4D3×D412yes—
678C2×C3×C4D3×D412yes—
679C2×C3×C4D3×D412yes—
680C2×C3×C4D3×D412yes—
681C2×C3×C4C2×#6712yes—
682#67—68no—
683#67—68no—
684#67—68no—
685#67—68no—
686#67—68no—
687#67—68no—
688#67—68no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—32no—
704C2×Dic3—32no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—62no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—121no—
723C2×Dic3—121no—
724C2×Dic3—121no—
725C2×Dic3—121no—
726C2×Dic3—121no—
727C2×Dic3—121no—
728C2×Dic3C2×D1212yes—
729C2×Dic3#23512yescomplemented
730C2×Dic3C2×#6712yes—
731D12—28no—
732D12—68no—
733D12—68no—
734D12—68no—
735C4×D3—28no—
736C4×D3—28no—
737C4×D3—44no—
738C4×D3—68no—
739C4×D3—68no—
740C4×D3—128no—
741Dic6—68no—
742Dic6—68no—
743C2×C32C2×#12011yescharacteristic
744C2×C32#52511yescharacteristic
745C2×C32#52511yescharacteristic
746C2×C32#52511yescharacteristic
747C2×C32#53211yescharacteristic
748C2×C32#53211yescharacteristic
749C2×C32#53211yescharacteristic
750C3⋊D3—42no—
751C3×D3—42no—
752C3×D3—42no—
753C3×D3—42no—
754C24—31no—
755C24—31no—
756C24—31no—
757C24—91no—
758#41—1832no—
759C2×Q8—182no—
760C2×Q8—182no—
761C2×Q8—182no—
762C2×D4—62no—
763C2×D4—62no—
764C2×D4—62no—
765C2×D4—182no—
766C2×D4—182no—
767C2×D4—182no—
768C2×D4—182no—
769C2×D4—182no—
770C2×D4—182no—
771C2×D4—182no—
772C2×D4—182no—
773C2×D4—182no—
774C2×D4—182no—
775C2×D4—182no—
776C2×D4—182no—
777C2×D4—182no—
778C2×D4—182no—
779C2×D4—182no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—34no—
784C22×C4—34no—
785C22×C4—31no—
786C22×C4—31no—
787C22×C4—62no—
788C22×C4—62no—
789C22×C4—62no—
790C22×C4—62no—
791C22×C4—62no—
792C22×C4—62no—
793C22×C4—62no—
794C22×C4—91no—
795C22×C4—91no—
796C22×C4—94no—
797C22×C4—91no—
798C22×C4—182no—
799C22×C4—182no—
800C22×C4C2×D3211yescharacteristic
801C22×C4C2×D3211yescharacteristic
802C22×C4C2×D3211yescharacteristic
803C4⋊C4—62no—
804C4⋊C4—182no—
805C4⋊C4—182no—
806C22⋊C4—62no—
807C22⋊C4—62no—
808C22⋊C4—62no—
809C22⋊C4—62no—
810C22⋊C4—182no—
811C22⋊C4—182no—
812C22⋊C4—182no—
813C22⋊C4—182no—
814C22⋊C4—182no—
815C22⋊C4—182no—
816C22⋊C4—182no—
817C22⋊C4—182no—
818C42—22no—
819C42—62no—
820C42—182no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—121no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3—121no—
848C22×C3—121no—
849C22×C3C22×D1211yescharacteristic
850C22×C3C2×#23511yescharacteristic
851C22×C3C2×#23511yescharacteristic
852C22×C3C2×#23511yescharacteristic
853C22×C3C2×#23511yescharacteristic
854C22×C3C2×D3×D411yescharacteristic
855C22×C3C2×D3×D411yescharacteristic
856C22×C3C2×D3×D411yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C22×C3D3×#4111yescharacteristic
859C22×C3D3×#4111yescharacteristic
860C22×C3D3×#4111yescharacteristic
861C22×C3D3×#4111yescharacteristic
862C22×C3C22×#6711yescharacteristic
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3—41no—
884C2×D3—64no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—122no—
892C2×D3—122no—
893C2×D3—122no—
894C2×D3—122no—
895C2×D3—122no—
896C2×D3—122no—
897C2×D3—121no—
898C2×D3—121no—
899C2×D3—121no—
900C2×D3—121no—
901C2×D3—121no—
902C2×D3—121no—
903C2×D3—121no—
904C2×D3—121no—
905C3×C4—22no—
906C3×C4—22no—
907C3×C4—24no—
908C3×C4—42no—
909C3×C4—42no—
910C3×C4—41no—
911C3×C4—41no—
912C3×C4—62no—
913C3×C4—62no—
914C3×C4—62no—
915C3×C4—121no—
916C3×C4—121no—
917C3×C4#88214yes—
918C3×C4#93714yes—
919Dic3—22no—
920Dic3—22no—
921Dic3—22no—
922Dic3—41no—
923Dic3—41no—
924Dic3—62no—
925Dic3—62no—
926Dic3—62no—
927Dic3—62no—
928Dic3—122no—
929Dic3—122no—
930Dic3—122no—
931Dic3—121no—
932Dic3—121no—
933C32#238811yescharacteristic, complemented, Sylow
934C23—32no—
935C23—32no—
936C23—32no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
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—
962C23C22×D3211yescharacteristic
963Q8—188no—
964D4—68no—
965D4—188no—
966D4—188no—
967D4—188no—
968D4—188no—
969D4—188no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—32no—
976C2×C4—32no—
977C2×C4—32no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—68no—
985C2×C4—68no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—92no—
993C2×C4—92no—
994C2×C4—124no—
995C2×C4—181no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—181no—
999C2×C4—188no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4#379812yescomplemented
1004C2×C4D3×D1212yes—
1005C2×C4#380212yes—
1006C2×C4D3×#6712yes—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—122no—
1015C2×C3—122no—
1016C2×C3—122no—
1017C2×C3#547711yescharacteristic
1018C2×C3C2×#88211yescharacteristic
1019C2×C3#552411yescharacteristic
1020C2×C3#554711yescharacteristic
1021C2×C3#554711yescharacteristic
1022C2×C3#554711yescharacteristic
1023C2×C3#554711yescharacteristic
1024C2×C3#554811yescharacteristic
1025C2×C3#554811yescharacteristic
1026C2×C3#554811yescharacteristic
1027C2×C3#554811yescharacteristic
1028C2×C3#579111yescharacteristic
1029C2×C3C2×#93711yescharacteristic
1030C2×C3#583211yescharacteristic
1031D3—42no—
1032D3—42no—
1033D3—42no—
1034D3—124no—
1035D3—122no—
1036D3—122no—
1037C22—62no—
1038C22—62no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—121no—
1047C22—121no—
1048C22—121no—
1049C22—121no—
1050C22—121no—
1051C22—121no—
1052C22—121no—
1053C22—121no—
1054C22—121no—
1055C22—121no—
1056C22—121no—
1057C22—121no—
1058C22—182no—
1059C22—182no—
1060C22—182no—
1061C22—361no—
1062C22—361no—
1063C22—361no—
1064C22—361no—
1065C22C2×#379811yescharacteristic
1066C22C2×D3×D1211yescharacteristic
1067C22C2×#380211yescharacteristic
1068C22D3×#23511yescharacteristic
1069C22D3×#23511yescharacteristic
1070C22#6430611yescharacteristic
1071C22C2×D3×#6711yescharacteristic
1072C4—22no—
1073C4—41no—
1074C4—62no—
1075C4—62no—
1076C4—62no—
1077C4—121no—
1078C4—121no—
1079C4—182no—
1080C4—182no—
1081C4—361no—
1082C4#6392214yes—
1083C3—21no—
1084C3#7358011yescharacteristic, complemented
1085C3#8240011yescharacteristic, complemented
1086C2—122no—
1087C2—122no—
1088C2—122no—
1089C2—362no—
1090C2#1059396811yescharacteristic
1091C2#1059397211yescharacteristic
1092C2#1059399711yescharacteristic
1093C2#1059400611yescharacteristic
1094C2#1059500211yescharacteristic
1095C2#1059500311yescharacteristic
1096C2C2×#6392211yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3798C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C2×C4×#626C2semidirect
4. C2×C4×#625C2semidirect
5. C4×#3752C2semidirect
6. C3×C4×(C2×D3)⋊C4C2semidirect
7. #10591393C2semidirect
8. #10591392C2semidirect
9. #10591391C2semidirect
10. #10591390C2semidirect
11. #10591389C2semidirect
12. #10591338C2semidirect
13. #10591293C2semidirect
14. #10591292C2semidirect
15. C4×(C2×D3)⋊Dic3C2semidirect
66. C2×C4×D12D3semidirect
85. C4×(C2×D3)⋊C4D3semidirect
102. C2×C4×C3⋊D3D4semidirect
118. C2×C3×C4×D3D4semidirect
119. C2×C3×C4×D3D4semidirect
275. C22×C3×D3#41semidirect
284. C2×C32×C4#41semidirect
293. C2×C3⋊Dic3#41semidirect
309. C2×C3×Dic3#41semidirect
435. C2×C4×D3D12semidirect
436. C2×C4×D3#67semidirect
634. C22×D3#235semidirect
675. C2×C3×C4#235semidirect
676. C2×C3×C4#235semidirect
729. C2×Dic3#235semidirect
933. C32#2388semidirect
1003. C2×C4#3798semidirect
1084. C3#73580semidirect
1085. C3#82400semidirect

Maximal subgroups

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

subgroupindex
C22×#37982
C2×C3×C4×D122
C2×C4×#6262
C2×C4×#6252
C4×#37522
C3×C4×(C2×D3)⋊C42
#105913932
#105913922
#105913912
#105913902
#105913892
#105913382
#105912932
#105912922
C4×(C2×D3)⋊Dic32
#824003
#735803