Finite Group Databasebeta

← #11808247

Subgroups — #11808247

Order 1152.

2007 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×#63904C211yesmaximal, characteristic, complemented
4C2×#63879C211yesmaximal, characteristic, complemented
5#10592658C211yesmaximal, characteristic, complemented
6C3×#4959C211yesmaximal, characteristic, complemented
7#10591724C211yesmaximal, characteristic, complemented
8#10591723C211yesmaximal, characteristic, complemented
9Dic3×#217C211yesmaximal, characteristic, complemented
10#10591393C211yesmaximal, characteristic, complemented
11Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#10591293C211yesmaximal, characteristic, complemented
13#10591291C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591195C211yesmaximal, characteristic, complemented
16#82400—31nomaximal
17#76889—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C2×#3804—24no—
29C2×#3804—24no—
30C2×#3804—24no—
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#67⋊C4—24no—
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51#63904—24no—
52#63879—24no—
53#63658C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58#63579C2211yescharacteristic
59C22×#237—31no—
60C22×#235—31no—
61C2×C3×C4×D4—31no—
62C2×C4×#67—31no—
63C2×C4×#67—31no—
64C2×#893—31no—
65C2×#67⋊C4—31no—
66C2×#67⋊C4D311yescharacteristic, complemented
67C3×#394—31no—
68#5223—31no—
69#5223—31no—
70#5223—31no—
71C4×#217—31no—
72#4991—31no—
73#4979—31no—
74#4979—31no—
75#4960—31no—
76#4960—31no—
77#4960—31no—
78#4959—31no—
79#4959—31no—
80#4959—31no—
81#4959—61no—
82#4959D311yescharacteristic, complemented
83#4947—31no—
84Dic3×C22⋊C4—31no—
85Dic3×C22⋊C4—31no—
86C4×(C2×D3)⋊C4—31no—
87C4×(C2×D3)⋊C4—31no—
88#4673—31no—
89#4666—31no—
90C24×C32C2311yescharacteristic
91C23×C3⋊D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C23×C3×D3C2311yescharacteristic
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×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3—22no—
110C22×C3×Dic3D414yescomplemented
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
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×#625—22no—
130C2×#625—22no—
131C2×#625—22no—
132C2×#624—22no—
133C2×#624—22no—
134C2×#624D414yescomplemented
135#3804—232no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C2×D3×Dic3D414yescomplemented
139C32×C22⋊C4—22no—
140#3757—22no—
141#3752—22no—
142#3752—22no—
143#3750—22no—
144C3×#217—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×(C2×D3)⋊C4—22no—
148C3×Dic3⋊C4—22no—
149C3×Dic3⋊C4—22no—
150C3×C4×Dic3—22no—
151#3722—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—22no—
155Dic32—22no—
156Dic32—22no—
157#2388—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—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—61no—
169C22×#67C2×D311yescharacteristic
170C22×#67C2×D311yescharacteristic
171C23×Dic3—31no—
172C23×Dic3C2×D311yescharacteristic
173C2×#237—64no—
174C2×#237—64no—
175C2×#237—64no—
176C2×#235—64no—
177C2×#235—64no—
178C2×#235—64no—
179C22×D12—31no—
180C22×D12—31no—
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3C2×D311yescharacteristic
185C22×Dic6—31no—
186C22×Dic6—31no—
187C3×C4×D4—64no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C22⋊C4—21no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4C2×D311yescharacteristic
196C2×C3×C22⋊C4C2×D311yescharacteristic
197C2×C3×C42—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—61no—
204C2×#217C2×D311yescharacteristic
205C4×#67—64no—
206C4×#67—64no—
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×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—61no—
224C2×Dic3⋊C4C2×D311yescharacteristic
225C2×Dic3⋊C4C2×D311yescharacteristic
226C2×C4×Dic3—31no—
227C2×C4×Dic3—31no—
228C2×C4×Dic3—31no—
229C2×C4×Dic3—31no—
230C2×C4×Dic3C2×D311yescharacteristic
231#893—64no—
232#67⋊C4—24no—
233#67⋊C4—64no—
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—31no—
244C3⋊#95—31no—
245C3⋊#95—61no—
246C3⋊#95C2×D311yescharacteristic
247C23×C32—21no—
248C23×C32—21no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32C2×D412yes—
254C23×C32C2411yescharacteristic
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⋊D3C2×D412yes—
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×D3—21no—
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×C4—21no—
282#638—28no—
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#4112yescomplemented
292C3×#67—28no—
293C3×#67—28no—
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—21no—
302C2×C3×Dic3—28no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D412yes—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3C2×D412yes—
309C2×C3×Dic3C2×D412yes—
310C2×C3×Dic3C2×D412yes—
311C2×C3×Dic3#4112yescomplemented
312C2×C3×Dic3#4112yescomplemented
313C3×C4×D3—44no—
314#627—28no—
315#626—28no—
316#626—28no—
317#625—28no—
318#624—28no—
319D3×Dic3—28no—
320C22×#41—91no—
321C2×C4×D4—31no—
322C2×C4×D4—91no—
323C2×C4×D4—91no—
324#395—91no—
325#394—31no—
326#394—91no—
327#394—91no—
328#393—91no—
329#392—91no—
330#392—91no—
331#392—91no—
332C4×C22⋊C4—91no—
333C4×C22⋊C4—91no—
334C4×C22⋊C4—91no—
335C24×C3—21no—
336C24×C3—31no—
337C24×C3—31no—
338C24×C3C22×D311yescharacteristic
339C24×C3C22×D311yescharacteristic
340C23×D3—31no—
341C23×D3—31no—
342C23×D3—61no—
343C23×D3C22×D311yescharacteristic
344C23×D3C22×D311yescharacteristic
345C2×C3×D4—62no—
346C2×C3×D4—62no—
347C2×C3×D4—62no—
348C2×C3×D4—62no—
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—31no—
354C22×C3×C4—34no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—62no—
361C22×C3×C4—62no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4—62no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—22no—
370C2×#67—22no—
371C2×#67—22no—
372C2×#67—22no—
373C2×#67—22no—
374C2×#67—22no—
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—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—122no—
394C2×#67—122no—
395C2×#67—122no—
396C22×Dic3—22no—
397C22×Dic3—22no—
398C22×Dic3—31no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—34no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—61no—
406C22×Dic3—61no—
407C22×Dic3—61no—
408C22×Dic3—62no—
409C22×Dic3—62no—
410C22×Dic3#6714yescomplemented
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D311yescharacteristic
417#237—632no—
418#235—632no—
419C2×D12—62no—
420C2×D12—62no—
421C2×D12—62no—
422C2×D12—62no—
423C2×D12—62no—
424C2×D12—62no—
425C2×C4×D3—22no—
426C2×C4×D3—22no—
427C2×C4×D3—22no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—62no—
432C2×C4×D3—62no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×Dic6—62no—
438C2×Dic6—62no—
439C2×Dic6—62no—
440C2×Dic6—62no—
441C2×Dic6—62no—
442C2×Dic6—62no—
443C3×C4⋊C4—62no—
444C3×C4⋊C4—62no—
445C3×C22⋊C4—22no—
446C3×C22⋊C4—22no—
447C3×C22⋊C4—42no—
448C3×C22⋊C4—62no—
449C3×C22⋊C4—62no—
450C3×C22⋊C4—62no—
451C3×C22⋊C4—62no—
452C3×C42—62no—
453#217—22no—
454#217—62no—
455#217—62no—
456#217—62no—
457#217—62no—
458#217—62no—
459#217—122no—
460(C2×D3)⋊C4—22no—
461(C2×D3)⋊C4—22no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—62no—
464(C2×D3)⋊C4—62no—
465(C2×D3)⋊C4—62no—
466(C2×D3)⋊C4—62no—
467(C2×D3)⋊C4—62no—
468(C2×D3)⋊C4—62no—
469(C2×D3)⋊C4—62no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—122no—
473(C2×D3)⋊C4—122no—
474Dic3⋊C4—22no—
475Dic3⋊C4—22no—
476Dic3⋊C4—62no—
477Dic3⋊C4—62no—
478Dic3⋊C4—122no—
479C4×Dic3—22no—
480C4×Dic3—62no—
481C4×Dic3—62no—
482C4×Dic3—62no—
483C4×Dic3—62no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—41no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32—41no—
491C22×C32C22×D411yescharacteristic
492C22×C32C22×D411yescharacteristic
493C22×C32C22×D411yescharacteristic
494C22×C32C2×#4111yescharacteristic
495C22×C32C2×#4111yescharacteristic
496C22×C32C2×#4111yescharacteristic
497C22×C32C2×#4111yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—41no—
502C2×C3⋊D3—41no—
503C2×C3⋊D3—41no—
504C2×C3⋊D3—41no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
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—
518C2×C3×D3—41no—
519C32×C4—41no—
520C32×C4—41no—
521C3⋊Dic3—22no—
522C3⋊Dic3—22no—
523C3⋊Dic3—41no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—41no—
529C3×Dic3#12014yes—
530C2×#41—184no—
531C2×#41—184no—
532C2×#41—184no—
533C22×Q8—91no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C23×C4—31no—
541C23×C4—31no—
542C23×C4—91no—
543C23×C4—91no—
544C4×D4—64no—
545C4×D4—184no—
546C4×D4—184no—
547C2×C4⋊C4—31no—
548C2×C4⋊C4—31no—
549C2×C4⋊C4—91no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—31no—
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×C22⋊C4D3211yescharacteristic
562C2×C42—31no—
563C2×C42—91no—
564C2×C42—91no—
565#95—31no—
566#95—91no—
567#95—91no—
568#95—91no—
569#95—91no—
570#95—91no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—22no—
585C23×C3—32no—
586C23×C3—32no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3D3×D412yes—
606C23×C3C2×#6712yes—
607C23×C3C23×D311yescharacteristic
608C23×C3C23×D311yescharacteristic
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—32no—
622C22×D3—32no—
623C22×D3—62no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—121no—
637C22×D3—121no—
638C22×D3—121no—
639C22×D3—121no—
640C22×D3—121no—
641C22×D3—121no—
642C22×D3#23512yescomplemented
643C22×D3D3×D412yes—
644C3×D4—68no—
645C3×D4—68no—
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—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—68no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—124no—
684#67—28no—
685#67—28no—
686#67—68no—
687#67—68no—
688#67—68no—
689#67—68no—
690#67—68no—
691#67—68no—
692#67—128no—
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—28no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
705C2×Dic3—32no—
706C2×Dic3—32no—
707C2×Dic3—32no—
708C2×Dic3—32no—
709C2×Dic3—62no—
710C2×Dic3—62no—
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—68no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—121no—
727C2×Dic3—121no—
728C2×Dic3—121no—
729C2×Dic3—121no—
730C2×Dic3—121no—
731C2×Dic3—121no—
732C2×Dic3—121no—
733C2×Dic3#23512yescomplemented
734C2×Dic3D3×D412yes—
735C2×Dic3D3×D412yes—
736C2×Dic3D3×D412yes—
737C2×Dic3#23712yescomplemented
738C2×Dic3C2×#6712yes—
739C2×Dic3C2×#6712yes—
740D12—68no—
741D12—68no—
742C4×D3—44no—
743C4×D3—68no—
744C4×D3—68no—
745C4×D3—68no—
746Dic6—68no—
747Dic6—68no—
748C2×C32—42no—
749C2×C32C2×#12011yescharacteristic
750C2×C32#52511yescharacteristic
751C2×C32#52511yescharacteristic
752C2×C32#52511yescharacteristic
753C2×C32#53211yescharacteristic
754C2×C32#53211yescharacteristic
755C2×C32#53211yescharacteristic
756C3⋊D3—42no—
757C3×D3—42no—
758C3×D3—42no—
759C24—31no—
760C24—31no—
761C24—91no—
762C24C2×D3211yescharacteristic
763#41—1832no—
764C2×Q8—182no—
765C2×Q8—182no—
766C2×Q8—182no—
767C2×D4—62no—
768C2×D4—62no—
769C2×D4—62no—
770C2×D4—62no—
771C2×D4—62no—
772C2×D4—62no—
773C2×D4—182no—
774C2×D4—182no—
775C2×D4—182no—
776C2×D4—182no—
777C2×D4—182no—
778C2×D4—182no—
779C2×D4—182no—
780C2×D4—182no—
781C2×D4—182no—
782C2×D4—182no—
783C2×D4—182no—
784C2×D4—182no—
785C22×C4—31no—
786C22×C4—31no—
787C22×C4—31no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—34no—
791C22×C4—31no—
792C22×C4—62no—
793C22×C4—62no—
794C22×C4—62no—
795C22×C4—62no—
796C22×C4—62no—
797C22×C4—94no—
798C22×C4—94no—
799C22×C4—91no—
800C22×C4—91no—
801C22×C4—91no—
802C22×C4—182no—
803C22×C4—182no—
804C22×C4—182no—
805C22×C4—182no—
806C22×C4C2×D3211yescharacteristic
807C22×C4C2×D3211yescharacteristic
808C4⋊C4—62no—
809C4⋊C4—62no—
810C4⋊C4—182no—
811C22⋊C4—22no—
812C22⋊C4—62no—
813C22⋊C4—62no—
814C22⋊C4—62no—
815C22⋊C4—62no—
816C22⋊C4—182no—
817C22⋊C4—182no—
818C22⋊C4—182no—
819C22⋊C4—182no—
820C22⋊C4—182no—
821C22⋊C4—182no—
822C22⋊C4—182no—
823C42—62no—
824C42—182no—
825C42—182no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—81no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—121no—
868C22×C3C2×#23511yescharacteristic
869C22×C3C2×#23511yescharacteristic
870C22×C3C2×D3×D411yescharacteristic
871C22×C3C2×D3×D411yescharacteristic
872C22×C3C2×D3×D411yescharacteristic
873C22×C3C2×D3×D411yescharacteristic
874C22×C3C2×D3×D411yescharacteristic
875C22×C3C2×#23711yescharacteristic
876C22×C3D3×#4111yescharacteristic
877C22×C3D3×#4111yescharacteristic
878C22×C3D3×#4111yescharacteristic
879C22×C3D3×#4111yescharacteristic
880C22×C3D3×#4111yescharacteristic
881C22×C3C22×#6711yescharacteristic
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—41no—
889C2×D3—41no—
890C2×D3—41no—
891C2×D3—41no—
892C2×D3—41no—
893C2×D3—41no—
894C2×D3—41no—
895C2×D3—41no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—62no—
902C2×D3—122no—
903C2×D3—122no—
904C2×D3—122no—
905C2×D3—121no—
906C2×D3—121no—
907C2×D3—121no—
908C2×D3—121no—
909C2×D3—121no—
910C2×D3—121no—
911C2×D3—121no—
912C2×D3—121no—
913C2×D3—241no—
914C2×D3—241no—
915C2×D3—241no—
916C2×D3—241no—
917C3×C4—34no—
918C3×C4—41no—
919C3×C4—41no—
920C3×C4—41no—
921C3×C4—41no—
922C3×C4—62no—
923C3×C4—62no—
924C3×C4—62no—
925C3×C4—62no—
926C3×C4—81no—
927C3×C4—81no—
928C3×C4—121no—
929Dic3—22no—
930Dic3—22no—
931Dic3—22no—
932Dic3—22no—
933Dic3—41no—
934Dic3—62no—
935Dic3—62no—
936Dic3—62no—
937Dic3—62no—
938Dic3—122no—
939Dic3—122no—
940Dic3—121no—
941Dic3—121no—
942Dic3—241no—
943Dic3#93714yes—
944C32#238811yescharacteristic, complemented, Sylow
945C23—21no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—32no—
952C23—32no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—61no—
957C23—61no—
958C23—61no—
959C23—61no—
960C23—61no—
961C23—61no—
962C23—61no—
963C23—61no—
964C23—61no—
965C23—92no—
966C23—181no—
967C23—181no—
968C23—181no—
969C23—181no—
970C23—181no—
971C23—181no—
972C23D3×#6712yes—
973C23C22×D3211yescharacteristic
974Q8—188no—
975D4—68no—
976D4—68no—
977D4—188no—
978D4—188no—
979D4—188no—
980D4—188no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—32no—
988C2×C4—32no—
989C2×C4—32no—
990C2×C4—32no—
991C2×C4—32no—
992C2×C4—32no—
993C2×C4—32no—
994C2×C4—68no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—61no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—92no—
1007C2×C4—92no—
1008C2×C4—124no—
1009C2×C4—188no—
1010C2×C4—188no—
1011C2×C4—181no—
1012C2×C4—181no—
1013C2×C4—181no—
1014C2×C4—181no—
1015C2×C4—181no—
1016C2×C4—181no—
1017C2×C4—181no—
1018C2×C3—21no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—42no—
1026C2×C3—42no—
1027C2×C3—82no—
1028C2×C3—122no—
1029C2×C3—122no—
1030C2×C3#554711yescharacteristic
1031C2×C3#554711yescharacteristic
1032C2×C3#554811yescharacteristic
1033C2×C3#554811yescharacteristic
1034C2×C3D3×#12011yescharacteristic
1035C2×C3#559611yescharacteristic
1036C2×C3#559611yescharacteristic
1037C2×C3#560611yescharacteristic
1038C2×C3#565611yescharacteristic
1039C2×C3#565611yescharacteristic
1040C2×C3#566811yescharacteristic
1041C2×C3#579111yescharacteristic
1042C2×C3C2×#93711yescharacteristic
1043C2×C3#583211yescharacteristic
1044D3—42no—
1045D3—42no—
1046D3—122no—
1047D3—122no—
1048D3—242no—
1049C22—22no—
1050C22—22no—
1051C22—22no—
1052C22—41no—
1053C22—41no—
1054C22—41no—
1055C22—41no—
1056C22—62no—
1057C22—62no—
1058C22—62no—
1059C22—62no—
1060C22—62no—
1061C22—62no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22—121no—
1066C22—121no—
1067C22—121no—
1068C22—121no—
1069C22—121no—
1070C22—182no—
1071C22—182no—
1072C22—182no—
1073C22—361no—
1074C22—361no—
1075C22—361no—
1076C22—361no—
1077C22D3×#23511yescharacteristic
1078C22D3×#23511yescharacteristic
1079C22D32×D411yescharacteristic
1080C22D32×D411yescharacteristic
1081C22D3×#23711yescharacteristic
1082C22#6431211yescharacteristic
1083C22C2×D3×#6711yescharacteristic
1084C4—34no—
1085C4—41no—
1086C4—41no—
1087C4—62no—
1088C4—62no—
1089C4—62no—
1090C4—62no—
1091C4—121no—
1092C4—182no—
1093C4—182no—
1094C4—361no—
1095C3—21no—
1096C3#7688911yescharacteristic, complemented
1097C3#8240011yescharacteristic, complemented
1098C2—42no—
1099C2—122no—
1100C2—122no—
1101C2—362no—
1102C2#1059405811yescharacteristic
1103C2#1059406811yescharacteristic
1104C2#1059426611yescharacteristic
1105C2#1059428611yescharacteristic
1106C2#1059489611yescharacteristic
1107C2#1059515511yescharacteristic
1108C2D3×#93711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3804C2semidirect
2. C2×C3×#67⋊C4C2semidirect
3. C2×#63904C2semidirect
4. C2×#63879C2semidirect
5. #10592658C2semidirect
6. C3×#4959C2semidirect
7. #10591724C2semidirect
8. #10591723C2semidirect
9. Dic3×#217C2semidirect
10. #10591393C2semidirect
11. Dic3×(C2×D3)⋊C4C2semidirect
12. #10591293C2semidirect
13. #10591291C2semidirect
14. #10591233C2semidirect
15. #10591195C2semidirect
66. C2×#67⋊C4D3semidirect
82. #4959D3semidirect
110. C22×C3×Dic3D4semidirect
134. C2×#624D4semidirect
138. C2×D3×Dic3D4semidirect
275. C22×C3×D3#41semidirect
291. C2×C3⋊Dic3#41semidirect
311. C2×C3×Dic3#41semidirect
312. C2×C3×Dic3#41semidirect
410. C22×Dic3#67semidirect
642. C22×D3#235semidirect
733. C2×Dic3#235semidirect
737. C2×Dic3#237semidirect
944. C32#2388semidirect
1096. C3#76889semidirect
1097. C3#82400semidirect

Maximal subgroups

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

subgroupindex
C22×#38042
C2×C3×#67⋊C42
C2×#639042
C2×#638792
#105926582
C3×#49592
#105917242
#105917232
Dic3×#2172
#105913932
Dic3×(C2×D3)⋊C42
#105912932
#105912912
#105912332
#105911952
#824003
#768893