Finite Group Databasebeta

← #11808226

Subgroups — #11808226

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×Dic3×#67C211yesmaximal, characteristic, complemented
3C2×Dic3×D12C211yesmaximal, characteristic, complemented
4C2×#63880C211yesmaximal, characteristic, complemented
5#10592660C211yesmaximal, characteristic, complemented
6C3×#4960C211yesmaximal, characteristic, complemented
7C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
8#10591724C211yesmaximal, characteristic, complemented
9#10591709C211yesmaximal, characteristic, complemented
10#10591397C211yesmaximal, characteristic, complemented
11#10591391C211yesmaximal, characteristic, complemented
12Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#10591312C211yesmaximal, characteristic, complemented
14#10591293C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#76665—31nomaximal
17#73580—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C2×#3804—24no—
28C2×#3804—24no—
29C2×#3804—24no—
30C22×D3×Dic3C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42Dic3×#67—24no—
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51Dic3×D12—24no—
52#63880—24no—
53#63658C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57#63579C2211yescharacteristic
58#63579C2211yescharacteristic
59C22×#237—31no—
60C22×#235—31no—
61C2×D4×Dic3—31no—
62C2×D4×Dic3—31no—
63C2×C4×#67—31no—
64C2×#67⋊C4—31no—
65C2×C4×D12—31no—
66C2×C4×D12—31no—
67C3×#392—31no—
68C3×C4×C22⋊C4—31no—
69#5223—31no—
70#5223—31no—
71#5222—31no—
72#4961—31no—
73#4961—31no—
74#4961—31no—
75#4961—31no—
76#4961—61no—
77#4960—31no—
78#4960D311yescharacteristic, complemented
79#4947—31no—
80Dic3×C22⋊C4—31no—
81Dic3×C22⋊C4D311yescharacteristic, complemented
82C4×(C2×D3)⋊C4—31no—
83C4×(C2×D3)⋊C4—31no—
84#4673—31no—
85#4672—31no—
86#4671—31no—
87#4666—31no—
88#4656—31no—
89#4656—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×D12—22no—
118C2×C3×D12—22no—
119C2×C3×D12—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×#624—22no—
130C2×#624—22no—
131C2×#624D414yescomplemented
132#3804—232no—
133C2×D3×Dic3—22no—
134C2×D3×Dic3—22no—
135C2×D3×Dic3—22no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C2×D3×Dic3D414yescomplemented
139C32×C22⋊C4—22no—
140#3757—22no—
141#3752—22no—
142#3752—22no—
143C4⋊(C3⋊Dic3)—22no—
144C3×#217—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×C4×Dic3—22no—
148C3×C4×Dic3—22no—
149Dic3⋊Dic3—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—
156Dic32—22no—
157#2388—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C23×C3×C4—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—61no—
167C22×#67C2×D311yescharacteristic
168C22×#67C2×D311yescharacteristic
169C23×Dic3—31no—
170C23×Dic3—31no—
171C23×Dic3C2×D311yescharacteristic
172C2×#237—64no—
173C2×#237—64no—
174C2×#237—64no—
175C2×#235—64no—
176C2×#235—64no—
177C2×#235—64no—
178C22×D12—31no—
179C22×D12—31no—
180C22×D12C2×D311yescharacteristic
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×Dic6—31no—
186C22×Dic6—31no—
187C2×C3×C22⋊C4—21no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4C2×D311yescharacteristic
192C2×C3×C22⋊C4C2×D311yescharacteristic
193C2×C3×C42—31no—
194C2×C3×C42—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—61no—
202C2×#217C2×D311yescharacteristic
203D4×Dic3—64no—
204D4×Dic3—64no—
205C4×#67—64no—
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×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3—31no—
224C2×C4⋊Dic3—61no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—31no—
227C2×C4×Dic3—31no—
228C2×C4×Dic3—31no—
229C2×C4×Dic3C2×D311yescharacteristic
230C2×C4×Dic3C2×D311yescharacteristic
231#67⋊C4—64no—
232C4×D12—64no—
233C4×D12—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—61no—
244C3⋊#95C2×D311yescharacteristic
245C3⋊#95C2×D311yescharacteristic
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#4112yescomplemented
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⋊Dic3—21no—
291C2×C3⋊Dic3C2×D412yes—
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×D12—28no—
314#627—28no—
315#626—28no—
316#626—28no—
317#624—28no—
318D3×Dic3—28no—
319D3×Dic3—44no—
320C22×#41—91no—
321C2×C4×D4—91no—
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—31no—
330#392—91no—
331#392—91no—
332C4×C22⋊C4—31no—
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—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—62no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—31no—
357C22×C3×C4—34no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
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—122no—
388C2×#67—122no—
389C2×#67—122no—
390C22×Dic3—22no—
391C22×Dic3—22no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—34no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—61no—
402C22×Dic3—62no—
403C22×Dic3—62no—
404C22×Dic3—62no—
405C22×Dic3—62no—
406C22×Dic3—62no—
407C22×Dic3D1214yescomplemented
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414#237—632no—
415#235—632no—
416C2×D12—22no—
417C2×D12—22no—
418C2×D12—22no—
419C2×D12—62no—
420C2×D12—62no—
421C2×D12—62no—
422C2×D12—62no—
423C2×D12—62no—
424C2×D12—62no—
425C2×C4×D3—34no—
426C2×C4×D3—34no—
427C2×C4×D3—34no—
428C2×C4×D3—62no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
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×C22⋊C4—22no—
444C3×C22⋊C4—22no—
445C3×C22⋊C4—42no—
446C3×C22⋊C4—62no—
447C3×C22⋊C4—62no—
448C3×C22⋊C4—62no—
449C3×C42—62no—
450C3×C42—62no—
451#217—22no—
452#217—62no—
453#217—62no—
454#217—62no—
455#217—62no—
456#217—62no—
457#217—62no—
458#217—122no—
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—62no—
468(C2×D3)⋊C4—62no—
469(C2×D3)⋊C4—62no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—122no—
472(C2×D3)⋊C4—122no—
473C4⋊Dic3—62no—
474C4⋊Dic3—62no—
475C4⋊Dic3—62no—
476C4⋊Dic3—62no—
477C4⋊Dic3—122no—
478Dic3⋊C4—62no—
479Dic3⋊C4—62no—
480C4×Dic3—22no—
481C4×Dic3—22no—
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—22no—
520C32×C4—41no—
521C3⋊Dic3—22no—
522C3⋊Dic3—41no—
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—31no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C23×C4—31no—
541C23×C4—91no—
542C23×C4—91no—
543C23×C4—91no—
544C4×D4—184no—
545C4×D4—184no—
546C4×D4—184no—
547C2×C4⋊C4—91no—
548C2×C4⋊C4—91no—
549C2×C4⋊C4—91no—
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×C22⋊C4D3211yescharacteristic
562C2×C42—31no—
563C2×C42—31no—
564C2×C42—91no—
565#95—31no—
566#95—31no—
567#95—31no—
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×C3C2×D1212yes—
606C23×C3D3×D412yes—
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×D3D3×D412yes—
643C22×D3#23712yescomplemented
644C3×D4—68no—
645C3×D4—68no—
646C3×D4—68no—
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—22no—
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—68no—
671C2×C3×C4—61no—
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#23512yescomplemented
683C2×C3×C4#23712yescomplemented
684#67—28no—
685#67—28no—
686#67—68no—
687#67—68no—
688#67—68no—
689#67—68no—
690#67—128no—
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—28no—
700C2×Dic3—21no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—32no—
704C2×Dic3—32no—
705C2×Dic3—62no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—68no—
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—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—121no—
724C2×Dic3—121no—
725C2×Dic3—121no—
726C2×Dic3—121no—
727C2×Dic3—121no—
728C2×Dic3—121no—
729C2×Dic3—121no—
730C2×Dic3—121no—
731C2×Dic3—124no—
732C2×Dic3C2×D1212yes—
733C2×Dic3C2×D1212yes—
734C2×Dic3#23512yescomplemented
735C2×Dic3D3×D412yes—
736C2×Dic3D3×D412yes—
737C2×Dic3D3×D412yes—
738C2×Dic3#23712yescomplemented
739D12—28no—
740D12—68no—
741D12—68no—
742C4×D3—68no—
743C4×D3—68no—
744C4×D3—68no—
745C4×D3—124no—
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—62no—
774C2×D4—62no—
775C2×D4—62no—
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—94no—
795C22×C4—94no—
796C22×C4—91no—
797C22×C4—91no—
798C22×C4—91no—
799C22×C4—182no—
800C22×C4—182no—
801C22×C4—182no—
802C22×C4—182no—
803C22×C4—182no—
804C22×C4—182no—
805C22×C4—182no—
806C22×C4C2×D3211yescharacteristic
807C22×C4C2×D3211yescharacteristic
808C4⋊C4—182no—
809C4⋊C4—182no—
810C4⋊C4—182no—
811C22⋊C4—22no—
812C22⋊C4—62no—
813C22⋊C4—62no—
814C22⋊C4—62no—
815C22⋊C4—182no—
816C22⋊C4—182no—
817C22⋊C4—182no—
818C22⋊C4—182no—
819C22⋊C4—182no—
820C22⋊C4—182no—
821C22⋊C4—182no—
822C22⋊C4—182no—
823C42—62no—
824C42—62no—
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×C3C22×D1211yescharacteristic
869C22×C3C2×#23511yescharacteristic
870C22×C3C2×#23511yescharacteristic
871C22×C3C2×D3×D411yescharacteristic
872C22×C3C2×D3×D411yescharacteristic
873C22×C3C2×D3×D411yescharacteristic
874C22×C3C2×D3×D411yescharacteristic
875C22×C3C2×D3×D411yescharacteristic
876C22×C3C2×#23711yescharacteristic
877C22×C3C2×#23711yescharacteristic
878C22×C3C2×#23711yescharacteristic
879C22×C3D3×#4111yescharacteristic
880C22×C3D3×#4111yescharacteristic
881C22×C3D3×#4111yescharacteristic
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—22no—
918C3×C4—22no—
919C3×C4—34no—
920C3×C4—42no—
921C3×C4—41no—
922C3×C4—41no—
923C3×C4—62no—
924C3×C4—62no—
925C3×C4—62no—
926C3×C4—62no—
927C3×C4—81no—
928C3×C4—121no—
929Dic3—22no—
930Dic3—22no—
931Dic3—22no—
932Dic3—22no—
933Dic3—41no—
934Dic3—62no—
935Dic3—62no—
936Dic3—122no—
937Dic3—121no—
938Dic3—121no—
939Dic3—121no—
940Dic3—121no—
941Dic3—241no—
942Dic3—241no—
943Dic3#88214yes—
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×D1212yes—
973C23C22×D3211yescharacteristic
974Q8—188no—
975D4—68no—
976D4—68no—
977D4—68no—
978D4—188no—
979D4—188no—
980D4—188no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—32no—
987C2×C4—32no—
988C2×C4—32no—
989C2×C4—32no—
990C2×C4—32no—
991C2×C4—32no—
992C2×C4—32no—
993C2×C4—68no—
994C2×C4—61no—
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—92no—
1006C2×C4—188no—
1007C2×C4—188no—
1008C2×C4—181no—
1009C2×C4—181no—
1010C2×C4—181no—
1011C2×C4—181no—
1012C2×C4—181no—
1013C2×C4—181no—
1014C2×C4—181no—
1015C2×C4—181no—
1016C2×C4—364no—
1017C2×C4#380412yescomplemented
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#547711yescharacteristic
1031C2×C3C2×#88211yescharacteristic
1032C2×C3#552411yescharacteristic
1033C2×C3#554711yescharacteristic
1034C2×C3#554711yescharacteristic
1035C2×C3#554811yescharacteristic
1036C2×C3#554811yescharacteristic
1037C2×C3#558611yescharacteristic
1038C2×C3#558611yescharacteristic
1039C2×C3D3×#12011yescharacteristic
1040C2×C3#559611yescharacteristic
1041C2×C3#559611yescharacteristic
1042C2×C3#560611yescharacteristic
1043C2×C3#571611yescharacteristic
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—
1077C22C2×D3×D1211yescharacteristic
1078C22D3×#23511yescharacteristic
1079C22D32×D411yescharacteristic
1080C22D32×D411yescharacteristic
1081C22D3×#23711yescharacteristic
1082C22D3×#23711yescharacteristic
1083C22C2×#380411yescharacteristic
1084C4—22no—
1085C4—34no—
1086C4—41no—
1087C4—62no—
1088C4—62no—
1089C4—62no—
1090C4—62no—
1091C4—121no—
1092C4—182no—
1093C4—361no—
1094C4—361no—
1095C3—21no—
1096C3#7358011yescharacteristic, complemented
1097C3#7666511yescharacteristic, complemented
1098C2—42no—
1099C2—122no—
1100C2—122no—
1101C2—362no—
1102C2#1059405811yescharacteristic
1103C2#1059407811yescharacteristic
1104C2D3×#88211yescharacteristic
1105C2#1059428611yescharacteristic
1106C2#1059491011yescharacteristic
1107C2#1059512911yescharacteristic
1108C2#1059513911yescharacteristic
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×Dic3×#67C2semidirect
3. C2×Dic3×D12C2semidirect
4. C2×#63880C2semidirect
5. #10592660C2semidirect
6. C3×#4960C2semidirect
7. C3×Dic3×C22⋊C4C2semidirect
8. #10591724C2semidirect
9. #10591709C2semidirect
10. #10591397C2semidirect
11. #10591391C2semidirect
12. Dic3×(C2×D3)⋊C4C2semidirect
13. #10591312C2semidirect
14. #10591293C2semidirect
15. #10591233C2semidirect
78. #4960D3semidirect
81. Dic3×C22⋊C4D3semidirect
110. C22×C3×Dic3D4semidirect
131. C2×#624D4semidirect
138. C2×D3×Dic3D4semidirect
275. C22×C3×D3#41semidirect
281. C2×C32×C4#41semidirect
311. C2×C3×Dic3#41semidirect
312. C2×C3×Dic3#41semidirect
407. C22×Dic3D12semidirect
643. C22×D3#237semidirect
682. C2×C3×C4#235semidirect
683. C2×C3×C4#237semidirect
734. C2×Dic3#235semidirect
738. C2×Dic3#237semidirect
944. C32#2388semidirect
1017. C2×C4#3804semidirect
1096. C3#73580semidirect
1097. C3#76665semidirect

Maximal subgroups

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

subgroupindex
C22×#38042
C2×Dic3×#672
C2×Dic3×D122
C2×#638802
#105926602
C3×#49602
C3×Dic3×C22⋊C42
#105917242
#105917092
#105913972
#105913912
Dic3×(C2×D3)⋊C42
#105913122
#105912932
#105912332
#766653
#735803