Finite Group Databasebeta

← #11808224

Subgroups — #11808224

Order 1152.

2049 conjugacy classes of subgroups.

The subgroup lattice has 1127 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C2×#63952C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C2×#63880C211yesmaximal, characteristic, complemented
5#10592659C211yesmaximal, characteristic, complemented
6C3×#4961C211yesmaximal, characteristic, complemented
7C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
8#10591724C211yesmaximal, characteristic, complemented
9#10591712C211yesmaximal, characteristic, complemented
10#10591395C211yesmaximal, characteristic, complemented
11Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#10591338C211yesmaximal, characteristic, complemented
13#10591292C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591205C211yesmaximal, characteristic, complemented
16#76889—31nomaximal
17#73580—31nomaximal
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C2×#3804—24no—
29C2×#3804—24no—
30C2×#3804—24no—
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×#3724C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×#3722C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50#63952—24no—
51#63894—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×C4×#67—31no—
62C2×#893—31no—
63C2×#67⋊C4—31no—
64C2×#67⋊C4—31no—
65C2×C4×D12—31no—
66C2×C4×D12—31no—
67C3×#394—31no—
68C3×C4×C22⋊C4—31no—
69#5223—31no—
70#4979—31no—
71#4961—31no—
72#4961D311yescharacteristic, complemented
73#4960—31no—
74#4960—31no—
75#4960—31no—
76#4960—31no—
77#4960—61no—
78#4959—31no—
79#4959—31no—
80Dic3×C22⋊C4—31no—
81Dic3×C22⋊C4D311yescharacteristic, complemented
82C4×(C2×D3)⋊C4—31no—
83C4×(C2×D3)⋊C4—31no—
84#4673—31no—
85#4673—31no—
86#4672—31no—
87#4671—31no—
88#4666—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—
99C2×#638—22no—
100C2×#638—22no—
101C2×#638—22no—
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—22no—
106C2×C4⋊(C3⋊D3)—22no—
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C22×C3×Dic3—22no—
111C22×C3×Dic3—22no—
112C22×C3×Dic3D414yescomplemented
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
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×#624—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#3752—22no—
141#3752—22no—
142C3×#217—22no—
143C3×#217—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×C4⋊Dic3—22no—
147C3×C4×Dic3—22no—
148C3×C4×Dic3—22no—
149#3724—22no—
150Dic3⋊Dic3—22no—
151#3722—22no—
152#3722—22no—
153#3722—22no—
154#3722—22no—
155(C2×D3)⋊Dic3—22no—
156Dic32—22no—
157#2388—91noSylow
158C22×C3×D4—31no—
159C23×C3×C4—31no—
160C22×#67—31no—
161C22×#67—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—61no—
167C22×#67—61no—
168C22×#67C2×D311yescharacteristic
169C23×Dic3—31no—
170C23×Dic3C2×D311yescharacteristic
171C2×#237—64no—
172C2×#237—64no—
173C2×#237—64no—
174C2×#235—64no—
175C2×#235—64no—
176C2×#235—64no—
177C22×D12—31no—
178C22×D12—31no—
179C22×D12—31no—
180C22×D12—31no—
181C22×D12—61no—
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×Dic6—31no—
188C22×Dic6—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×C3×C42—31no—
199C2×#217—31no—
200C2×#217C2×D311yescharacteristic
201C2×#217C2×D311yescharacteristic
202C4×#67—64no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
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×C4⋊Dic3—31no—
221C2×C4⋊Dic3C2×D311yescharacteristic
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×C4×Dic3—31no—
226C2×C4×Dic3—31no—
227C2×C4×Dic3C2×D311yescharacteristic
228C2×C4×Dic3C2×D311yescharacteristic
229#893—64no—
230#67⋊C4—64no—
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⋊D3—21no—
262C22×C3⋊D3—21no—
263C22×C3⋊D3—21no—
264C22×C3⋊D3—21no—
265C22×C3⋊D3—21no—
266C22×C3⋊D3—21no—
267C22×C3⋊D3C2×D412yes—
268C22×C3⋊D3#4112yescomplemented
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3C2×D412yes—
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—
283#638—28no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3C2×D412yes—
289C2×C3⋊Dic3#4112yescomplemented
290C4⋊(C3⋊D3)—28no—
291C3×#67—28no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—28no—
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×Dic3—21no—
308C2×C3×Dic3C2×D412yes—
309C2×C3×Dic3C2×D412yes—
310C2×C3×Dic3C2×D412yes—
311C2×C3×Dic3C2×D412yes—
312C2×C3×Dic3C2×D412yes—
313C2×C3×Dic3#4112yescomplemented
314#627—28no—
315#626—28no—
316#626—28no—
317#624—28no—
318#624—44no—
319D3×Dic3—28no—
320C22×#41—91no—
321C2×C4×D4—91no—
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—31no—
333C4×C22⋊C4—91no—
334C4×C22⋊C4—91no—
335C24×C3—21no—
336C24×C3—31no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C23×D3—31no—
340C23×D3—31no—
341C23×D3—31no—
342C23×D3—31no—
343C23×D3—61no—
344C23×D3—61no—
345C23×D3C22×D311yescharacteristic
346C2×C3×D4—62no—
347C2×C3×D4—62no—
348C2×C3×D4—62no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—31no—
352C22×C3×C4—34no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—62no—
360C22×C3×C4—62no—
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C2×#67—22no—
366C2×#67—22no—
367C2×#67—22no—
368C2×#67—62no—
369C2×#67—62no—
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—122no—
387C2×#67—122no—
388C2×#67—122no—
389C2×#67—122no—
390C2×#67—122no—
391C2×#67—122no—
392C22×Dic3—22no—
393C22×Dic3—22no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—34no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—62no—
402C22×Dic3—62no—
403C22×Dic3D1214yescomplemented
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411#237—632no—
412#235—632no—
413C2×D12—62no—
414C2×D12—62no—
415C2×D12—62no—
416C2×D12—62no—
417C2×D12—62no—
418C2×D12—62no—
419C2×D12—62no—
420C2×D12—62no—
421C2×D12—62no—
422C2×D12—62no—
423C2×D12—62no—
424C2×D12—62no—
425C2×D12—122no—
426C2×D12—122no—
427C2×D12—122no—
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×C4×D3—62no—
438C2×C4×D3—62no—
439C2×C4×D3—62no—
440C2×C4×D3—62no—
441C2×C4×D3—62no—
442C2×C4×D3—62no—
443C2×Dic6—62no—
444C2×Dic6—62no—
445C2×Dic6—62no—
446C2×Dic6—62no—
447C2×Dic6—62no—
448C2×Dic6—62no—
449C3×C4⋊C4—62no—
450C3×C22⋊C4—22no—
451C3×C22⋊C4—22no—
452C3×C22⋊C4—42no—
453C3×C22⋊C4—62no—
454C3×C22⋊C4—62no—
455C3×C22⋊C4—62no—
456C3×C22⋊C4—62no—
457C3×C42—62no—
458C3×C42—62no—
459#217—22no—
460#217—22no—
461#217—62no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
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—62no—
473(C2×D3)⋊C4—62no—
474(C2×D3)⋊C4—62no—
475(C2×D3)⋊C4—62no—
476(C2×D3)⋊C4—62no—
477(C2×D3)⋊C4—122no—
478(C2×D3)⋊C4—122no—
479C4⋊Dic3—22no—
480C4⋊Dic3—62no—
481Dic3⋊C4—62no—
482Dic3⋊C4—62no—
483Dic3⋊C4—62no—
484C4×Dic3—22no—
485C4×Dic3—22no—
486C4×Dic3—62no—
487C4×Dic3—62no—
488C22×C32—22no—
489C22×C32—22no—
490C22×C32—22no—
491C22×C32—41no—
492C22×C32—41no—
493C22×C32—41no—
494C22×C32—41no—
495C22×C32C22×D411yescharacteristic
496C22×C32C22×D411yescharacteristic
497C22×C32C22×D411yescharacteristic
498C22×C32C2×#4111yescharacteristic
499C22×C32C2×#4111yescharacteristic
500C22×C32C2×#4111yescharacteristic
501C22×C32C2×#4111yescharacteristic
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—22no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—22no—
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—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—41no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C32×C4—22no—
524C32×C4—41no—
525C3⋊Dic3—22no—
526C3⋊Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—41no—
531C3×Dic3—41no—
532C3×Dic3—41no—
533C3×Dic3#12014yes—
534C2×#41—184no—
535C2×#41—184no—
536C2×#41—184no—
537C22×Q8—91no—
538C22×D4—31no—
539C22×D4—91no—
540C22×D4—91no—
541C22×D4—91no—
542C22×D4—91no—
543C22×D4—91no—
544C23×C4—31no—
545C23×C4—91no—
546C23×C4—91no—
547C23×C4—91no—
548C4×D4—184no—
549C4×D4—184no—
550C4×D4—184no—
551C2×C4⋊C4—31no—
552C2×C4⋊C4—91no—
553C2×C4⋊C4—91no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—31no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4—91no—
562C2×C22⋊C4—91no—
563C2×C22⋊C4—91no—
564C2×C22⋊C4—91no—
565C2×C22⋊C4D3211yescharacteristic
566C2×C42—31no—
567C2×C42—31no—
568C2×C42—91no—
569#95—31no—
570#95—31no—
571#95—31no—
572#95—91no—
573#95—91no—
574#95—91no—
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—21no—
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—22no—
589C23×C3—32no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3C2×D1212yes—
603C23×C3D3×D412yes—
604C23×C3C23×D311yescharacteristic
605C23×C3C23×D311yescharacteristic
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—32no—
615C22×D3—32no—
616C22×D3—62no—
617C22×D3—62no—
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—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—61no—
642C22×D3—121no—
643C22×D3—121no—
644C22×D3—121no—
645C22×D3—121no—
646C22×D3—121no—
647C22×D3—121no—
648C22×D3—121no—
649C22×D3—121no—
650C22×D3—121no—
651C22×D3—121no—
652C22×D3—121no—
653C22×D3—121no—
654C22×D3D3×D412yes—
655C3×D4—68no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—22no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—32no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—68no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4#23512yescomplemented
695C2×C3×C4#23712yescomplemented
696#67—28no—
697#67—68no—
698#67—68no—
699#67—68no—
700#67—68no—
701#67—68no—
702#67—68no—
703#67—128no—
704#67—128no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—28no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—32no—
722C2×Dic3—32no—
723C2×Dic3—32no—
724C2×Dic3—32no—
725C2×Dic3—62no—
726C2×Dic3—62no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—61no—
730C2×Dic3—61no—
731C2×Dic3—61no—
732C2×Dic3—61no—
733C2×Dic3—61no—
734C2×Dic3—61no—
735C2×Dic3—68no—
736C2×Dic3—121no—
737C2×Dic3—121no—
738C2×Dic3—121no—
739C2×Dic3—121no—
740C2×Dic3C2×D1212yes—
741C2×Dic3C2×D1212yes—
742C2×Dic3#23512yescomplemented
743C2×Dic3D3×D412yes—
744C2×Dic3D3×D412yes—
745C2×Dic3D3×D412yes—
746D12—68no—
747D12—68no—
748D12—68no—
749D12—68no—
750D12—128no—
751C4×D3—68no—
752C4×D3—68no—
753C4×D3—68no—
754C4×D3—124no—
755C4×D3—124no—
756Dic6—68no—
757Dic6—68no—
758C2×C32—42no—
759C2×C32C2×#12011yescharacteristic
760C2×C32#52511yescharacteristic
761C2×C32#52511yescharacteristic
762C2×C32#52511yescharacteristic
763C2×C32#53211yescharacteristic
764C2×C32#53211yescharacteristic
765C2×C32#53211yescharacteristic
766C3⋊D3—42no—
767C3⋊D3—42no—
768C3×D3—42no—
769C24—31no—
770C24—91no—
771C24—91no—
772C24C2×D3211yescharacteristic
773#41—1832no—
774C2×Q8—182no—
775C2×Q8—182no—
776C2×Q8—182no—
777C2×D4—62no—
778C2×D4—62no—
779C2×D4—62no—
780C2×D4—182no—
781C2×D4—182no—
782C2×D4—182no—
783C2×D4—182no—
784C2×D4—182no—
785C2×D4—182no—
786C2×D4—182no—
787C2×D4—182no—
788C2×D4—182no—
789C2×D4—182no—
790C2×D4—182no—
791C2×D4—182no—
792C2×D4—182no—
793C2×D4—182no—
794C2×D4—182no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—34no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—62no—
804C22×C4—62no—
805C22×C4—94no—
806C22×C4—94no—
807C22×C4—91no—
808C22×C4—91no—
809C22×C4—182no—
810C22×C4—182no—
811C22×C4—182no—
812C22×C4—182no—
813C22×C4—182no—
814C22×C4—182no—
815C22×C4—182no—
816C22×C4C2×D3211yescharacteristic
817C22×C4C2×D3211yescharacteristic
818C4⋊C4—62no—
819C4⋊C4—182no—
820C4⋊C4—182no—
821C22⋊C4—22no—
822C22⋊C4—62no—
823C22⋊C4—62no—
824C22⋊C4—62no—
825C22⋊C4—62no—
826C22⋊C4—182no—
827C22⋊C4—182no—
828C22⋊C4—182no—
829C22⋊C4—182no—
830C22⋊C4—182no—
831C22⋊C4—182no—
832C22⋊C4—182no—
833C42—62no—
834C42—62no—
835C42—182no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3—41no—
859C22×C3—41no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—81no—
864C22×C3—81no—
865C22×C3—81no—
866C22×C3—81no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3—121no—
870C22×C3—121no—
871C22×C3C22×D1211yescharacteristic
872C22×C3C2×#23511yescharacteristic
873C22×C3C2×#23511yescharacteristic
874C22×C3C2×D3×D411yescharacteristic
875C22×C3C2×D3×D411yescharacteristic
876C22×C3C2×D3×D411yescharacteristic
877C22×C3C2×D3×D411yescharacteristic
878C22×C3C2×D3×D411yescharacteristic
879C22×C3C2×#23711yescharacteristic
880C22×C3D3×#4111yescharacteristic
881C22×C3D3×#4111yescharacteristic
882C22×C3D3×#4111yescharacteristic
883C22×C3D3×#4111yescharacteristic
884C22×C3D3×#4111yescharacteristic
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—41no—
889C2×D3—41no—
890C2×D3—41no—
891C2×D3—41no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—62no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—122no—
905C2×D3—122no—
906C2×D3—122no—
907C2×D3—122no—
908C2×D3—122no—
909C2×D3—122no—
910C2×D3—121no—
911C2×D3—121no—
912C2×D3—121no—
913C2×D3—121no—
914C2×D3—121no—
915C2×D3—121no—
916C2×D3—121no—
917C2×D3—121no—
918C2×D3—121no—
919C2×D3—121no—
920C2×D3—121no—
921C2×D3—121no—
922C2×D3—121no—
923C2×D3—121no—
924C2×D3—121no—
925C2×D3—121no—
926C2×D3—241no—
927C2×D3—241no—
928C2×D3—241no—
929C2×D3—241no—
930C2×D3—241no—
931C2×D3—241no—
932C2×D3—241no—
933C2×D3—241no—
934C3×C4—22no—
935C3×C4—22no—
936C3×C4—34no—
937C3×C4—42no—
938C3×C4—41no—
939C3×C4—41no—
940C3×C4—62no—
941C3×C4—62no—
942C3×C4—62no—
943C3×C4—81no—
944C3×C4—121no—
945C3×C4—121no—
946C3×C4—121no—
947Dic3—22no—
948Dic3—22no—
949Dic3—22no—
950Dic3—41no—
951Dic3—41no—
952Dic3—41no—
953Dic3—62no—
954Dic3—62no—
955Dic3—62no—
956Dic3—62no—
957Dic3—122no—
958Dic3—122no—
959Dic3#88214yes—
960C32#238811yescharacteristic, complemented, Sylow
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—32no—
968C23—61no—
969C23—61no—
970C23—61no—
971C23—61no—
972C23—61no—
973C23—61no—
974C23—92no—
975C23—92no—
976C23—181no—
977C23—181no—
978C23—181no—
979C23—181no—
980C23—181no—
981C23—181no—
982C23—181no—
983C23—181no—
984C23—181no—
985C23—181no—
986C23—181no—
987C23—181no—
988C23D3×D1212yes—
989C23C22×D3211yescharacteristic
990Q8—188no—
991D4—68no—
992D4—188no—
993D4—188no—
994D4—188no—
995D4—188no—
996D4—188no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—32no—
1003C2×C4—32no—
1004C2×C4—32no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—32no—
1008C2×C4—68no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—92no—
1025C2×C4—92no—
1026C2×C4—188no—
1027C2×C4—188no—
1028C2×C4—181no—
1029C2×C4—181no—
1030C2×C4—181no—
1031C2×C4—181no—
1032C2×C4—364no—
1033C2×C4#380412yescomplemented
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—21no—
1039C2×C3—21no—
1040C2×C3—21no—
1041C2×C3—42no—
1042C2×C3—42no—
1043C2×C3—82no—
1044C2×C3—122no—
1045C2×C3#547711yescharacteristic
1046C2×C3C2×#88211yescharacteristic
1047C2×C3#552411yescharacteristic
1048C2×C3#554711yescharacteristic
1049C2×C3#554711yescharacteristic
1050C2×C3#554811yescharacteristic
1051C2×C3#554811yescharacteristic
1052C2×C3D3×#12011yescharacteristic
1053C2×C3#559611yescharacteristic
1054C2×C3#559611yescharacteristic
1055C2×C3#560611yescharacteristic
1056C2×C3#565611yescharacteristic
1057C2×C3#565611yescharacteristic
1058C2×C3#566811yescharacteristic
1059D3—42no—
1060D3—122no—
1061D3—122no—
1062D3—122no—
1063D3—122no—
1064D3—242no—
1065D3—242no—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—41no—
1070C22—41no—
1071C22—41no—
1072C22—41no—
1073C22—62no—
1074C22—62no—
1075C22—62no—
1076C22—121no—
1077C22—121no—
1078C22—121no—
1079C22—121no—
1080C22—182no—
1081C22—182no—
1082C22—182no—
1083C22—182no—
1084C22—182no—
1085C22—182no—
1086C22—361no—
1087C22—361no—
1088C22—361no—
1089C22—361no—
1090C22—361no—
1091C22—361no—
1092C22—361no—
1093C22—361no—
1094C22C2×D3×D1211yescharacteristic
1095C22D3×#23511yescharacteristic
1096C22D32×D411yescharacteristic
1097C22D32×D411yescharacteristic
1098C22#6431211yescharacteristic
1099C22#6431211yescharacteristic
1100C22C2×#380411yescharacteristic
1101C4—22no—
1102C4—34no—
1103C4—41no—
1104C4—62no—
1105C4—62no—
1106C4—62no—
1107C4—121no—
1108C4—121no—
1109C4—121no—
1110C4—182no—
1111C4—182no—
1112C3—21no—
1113C3#7358011yescharacteristic, complemented
1114C3#7688911yescharacteristic, complemented
1115C2—42no—
1116C2—122no—
1117C2—362no—
1118C2—362no—
1119C2#1059406811yescharacteristic
1120C2#1059407911yescharacteristic
1121C2D3×#88211yescharacteristic
1122C2#1059426611yescharacteristic
1123C2#1059491011yescharacteristic
1124C2#1059513111yescharacteristic
1125C2#1059513811yescharacteristic
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×#63952C2semidirect
3. C2×#63894C2semidirect
4. C2×#63880C2semidirect
5. #10592659C2semidirect
6. C3×#4961C2semidirect
7. C3×Dic3×C22⋊C4C2semidirect
8. #10591724C2semidirect
9. #10591712C2semidirect
10. #10591395C2semidirect
11. Dic3×(C2×D3)⋊C4C2semidirect
12. #10591338C2semidirect
13. #10591292C2semidirect
14. #10591233C2semidirect
15. #10591205C2semidirect
72. #4961D3semidirect
81. Dic3×C22⋊C4D3semidirect
112. C22×C3×Dic3D4semidirect
134. C2×#624D4semidirect
138. C2×D3×Dic3D4semidirect
268. C22×C3⋊D3#41semidirect
281. C2×C32×C4#41semidirect
289. C2×C3⋊Dic3#41semidirect
313. C2×C3×Dic3#41semidirect
403. C22×Dic3D12semidirect
694. C2×C3×C4#235semidirect
695. C2×C3×C4#237semidirect
742. C2×Dic3#235semidirect
960. C32#2388semidirect
1033. C2×C4#3804semidirect
1113. C3#73580semidirect
1114. C3#76889semidirect

Maximal subgroups

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

subgroupindex
C22×#38042
C2×#639522
C2×#638942
C2×#638802
#105926592
C3×#49612
C3×Dic3×C22⋊C42
#105917242
#105917122
#105913952
Dic3×(C2×D3)⋊C42
#105913382
#105912922
#105912332
#105912052
#768893
#735803