Finite Group Databasebeta

← #11808227

Subgroups — #11808227

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×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×Dic3×#67C211yesmaximal, characteristic, complemented
4C2×#63952C211yesmaximal, characteristic, complemented
5#10592922C211yesmaximal, characteristic, complemented
6C3×#5223C211yesmaximal, characteristic, complemented
7#10591724C211yesmaximal, characteristic, complemented
8#10591712C211yesmaximal, characteristic, complemented
9#10591708C211yesmaximal, characteristic, complemented
10Dic3×#217C211yesmaximal, characteristic, complemented
11#10591692C211yesmaximal, characteristic, complemented
12#10591392C211yesmaximal, characteristic, complemented
13Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#10591338C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#82400—31nomaximal
17#76665—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×#627C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C2×#3804—24no—
29C2×#3804—24no—
30C2×#3804—24no—
31C22×D3×Dic3C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C3×D4×Dic3—24no—
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43Dic3×#67—24no—
44C2×#3724C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×#3722C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51C2×Dic32C2211yescharacteristic
52#63952—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×D4×Dic3—31no—
63C2×D4×Dic3D311yescharacteristic, complemented
64C2×C4×#67—31no—
65C2×C4×#67—31no—
66C2×#67⋊C4—31no—
67C3×#392—31no—
68#5223—31no—
69#5223—31no—
70#5223—31no—
71#5223—61no—
72#5223D311yescharacteristic, complemented
73#5222—31no—
74C4×#217—31no—
75#4991—31no—
76#4979—31no—
77#4961—31no—
78#4961—31no—
79#4960—31no—
80#4959—31no—
81#4959—31no—
82#4947—31no—
83#4947—31no—
84Dic3×C22⋊C4—31no—
85Dic3×C22⋊C4—31no—
86C4×(C2×D3)⋊C4—31no—
87C4×(C2×D3)⋊C4—31no—
88#4666—31no—
89#4656—31no—
90C24×C32C2311yescharacteristic
91C24×C32C2311yescharacteristic
92C23×C3⋊D3C2311yescharacteristic
93C23×C3×D3C2311yescharacteristic
94C2×C32×D4—22no—
95C2×C32×D4—22no—
96C2×C32×D4—22no—
97C22×C32×C4C2311yescharacteristic
98C2×#638—22no—
99C2×#638—22no—
100C2×#638—22no—
101C2×#638—22no—
102C2×#638—22no—
103C2×#638—22no—
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C22×C3×Dic3—22no—
114C22×C3×Dic3—22no—
115C22×C3×Dic3—22no—
116C22×C3×Dic3—22no—
117C22×C3×Dic3—22no—
118C22×C3×Dic3D414yescomplemented
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C2×#627—22no—
127C2×#627—22no—
128C2×#627—22no—
129C2×#626—22no—
130C2×#626—22no—
131C2×#626—22no—
132C2×#624—22no—
133C2×#624—22no—
134C2×#624D414yescomplemented
135#3804—232no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C2×D3×Dic3D414yescomplemented
139#3757—22no—
140#3757—22no—
141#3752—22no—
142C3×#217—22no—
143C3×#217—22no—
144C3×#217—22no—
145C3×#217—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×C4⋊Dic3—22no—
148C3×C4×Dic3—22no—
149#3724—22no—
150Dic3⋊Dic3—22no—
151#3722—22no—
152#3722—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—22no—
155Dic32—22no—
156Dic32—22no—
157#2388—91noSylow
158C22×C3×D4—21no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4C2×D311yescharacteristic
162C22×C3×D4C2×D311yescharacteristic
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—61no—
171C22×#67—61no—
172C22×#67C2×D311yescharacteristic
173C22×#67C2×D311yescharacteristic
174C23×Dic3—31no—
175C23×Dic3C2×D311yescharacteristic
176C23×Dic3C2×D311yescharacteristic
177C2×#237—64no—
178C2×#237—64no—
179C2×#237—64no—
180C2×#235—64no—
181C2×#235—64no—
182C2×#235—64no—
183C22×D12—31no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×Dic6—31no—
188C22×Dic6—31no—
189C3×C4×D4—64no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C42—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—61no—
204C2×#217—61no—
205C2×#217C2×D311yescharacteristic
206C2×#217C2×D311yescharacteristic
207C2×#217C2×D311yescharacteristic
208C2×#217C2×D311yescharacteristic
209D4×Dic3—24no—
210D4×Dic3—64no—
211C4×#67—64no—
212C4×#67—64no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—61no—
222C2×(C2×D3)⋊C4C2×D311yescharacteristic
223C2×C4⋊Dic3—31no—
224C2×C4⋊Dic3C2×D311yescharacteristic
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—31no—
227C2×Dic3⋊C4—31no—
228C2×C4×Dic3—31no—
229C2×C4×Dic3—31no—
230C2×C4×Dic3—31no—
231C2×C4×Dic3—31no—
232C2×C4×Dic3C2×D311yescharacteristic
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×C32—21no—
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32C2×D412yes—
260C23×C32#4112yescomplemented
261C23×C32C2411yescharacteristic
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⋊D3C2×D412yes—
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—
276C32×D4—28no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4#4112yescomplemented
280#638—28no—
281#638—28no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D412yes—
290C2×C3⋊Dic3#4112yescomplemented
291C3×#67—28no—
292C3×#67—28no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—28no—
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×Dic3—21no—
309C2×C3×Dic3—44no—
310C2×C3×Dic3C2×D412yes—
311C2×C3×Dic3C2×D412yes—
312C2×C3×Dic3C2×D412yes—
313C2×C3×Dic3C2×D412yes—
314C2×C3×Dic3C2×D412yes—
315C2×C3×Dic3#4112yescomplemented
316#627—28no—
317#626—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—91no—
326#394—91no—
327#394—91no—
328#393—91no—
329#392—31no—
330#392—91no—
331#392—91no—
332C4×C22⋊C4—91no—
333C4×C22⋊C4—91no—
334C4×C22⋊C4—91no—
335C24×C3—21no—
336C24×C3—21no—
337C24×C3—31no—
338C24×C3C22×D311yescharacteristic
339C24×C3C22×D311yescharacteristic
340C24×C3C22×D311yescharacteristic
341C24×C3C22×D311yescharacteristic
342C23×D3—31no—
343C23×D3—31no—
344C23×D3—61no—
345C23×D3C22×D311yescharacteristic
346C2×C3×D4—22no—
347C2×C3×D4—22no—
348C2×C3×D4—22no—
349C2×C3×D4—22no—
350C2×C3×D4—22no—
351C2×C3×D4—22no—
352C2×C3×D4—42no—
353C2×C3×D4—42no—
354C2×C3×D4—42no—
355C2×C3×D4—62no—
356C2×C3×D4—62no—
357C2×C3×D4—62no—
358C2×C3×D4—62no—
359C2×C3×D4—62no—
360C2×C3×D4—62no—
361C22×C3×C4—21no—
362C22×C3×C4—31no—
363C22×C3×C4—34no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—62no—
371C22×C3×C4—62no—
372C22×C3×C4—62no—
373C22×C3×C4—62no—
374C22×C3×C4—62no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—22no—
378C2×#67—22no—
379C2×#67—22no—
380C2×#67—22no—
381C2×#67—22no—
382C2×#67—22no—
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—62no—
394C2×#67—62no—
395C2×#67—62no—
396C2×#67—62no—
397C2×#67—62no—
398C2×#67—122no—
399C2×#67—122no—
400C2×#67—122no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C22×Dic3—22no—
405C22×Dic3—22no—
406C22×Dic3—22no—
407C22×Dic3—22no—
408C22×Dic3—22no—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—34no—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—61no—
417C22×Dic3—61no—
418C22×Dic3—61no—
419C22×Dic3—62no—
420C22×Dic3—62no—
421C22×Dic3#6714yescomplemented
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425C22×Dic3C22×D311yescharacteristic
426C22×Dic3C22×D311yescharacteristic
427C22×Dic3C22×D311yescharacteristic
428C22×Dic3C22×D311yescharacteristic
429#237—632no—
430#235—632no—
431C2×D12—62no—
432C2×D12—62no—
433C2×D12—62no—
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
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—62no—
451C3×C22⋊C4—62no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—62no—
454C3×C22⋊C4—62no—
455C3×C42—62no—
456#217—22no—
457#217—22no—
458#217—22no—
459#217—22no—
460#217—62no—
461#217—62no—
462#217—62no—
463#217—62no—
464#217—62no—
465#217—62no—
466#217—122no—
467#217—122no—
468(C2×D3)⋊C4—22no—
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—
478C4⋊Dic3—22no—
479C4⋊Dic3—62no—
480Dic3⋊C4—62no—
481Dic3⋊C4—62no—
482Dic3⋊C4—62no—
483C4×Dic3—22no—
484C4×Dic3—62no—
485C4×Dic3—62no—
486C4×Dic3—62no—
487C4×Dic3—62no—
488C22×C32—22no—
489C22×C32—22no—
490C22×C32—22no—
491C22×C32—22no—
492C22×C32—22no—
493C22×C32—22no—
494C22×C32—41no—
495C22×C32—41no—
496C22×C32—41no—
497C22×C32—41no—
498C22×C32—41no—
499C22×C32—41no—
500C22×C32—41no—
501C22×C32—41no—
502C22×C32C22×D411yescharacteristic
503C22×C32C22×D411yescharacteristic
504C22×C32C22×D411yescharacteristic
505C22×C32C2×#4111yescharacteristic
506C22×C32C2×#4111yescharacteristic
507C22×C32C2×#4111yescharacteristic
508C22×C32C2×#4111yescharacteristic
509C2×C3⋊D3—22no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—22no—
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—
524C3⋊Dic3—22no—
525C3⋊Dic3—22no—
526C3⋊Dic3—41no—
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—31no—
540C22×D4—91no—
541C22×D4—91no—
542C22×D4—91no—
543C22×D4D3211yescharacteristic
544C23×C4—31no—
545C23×C4—31no—
546C23×C4—91no—
547C23×C4—91no—
548C4×D4—64no—
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—31no—
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⋊C4—91no—
566C2×C42—31no—
567C2×C42—91no—
568C2×C42—91no—
569#95—31no—
570#95—91no—
571#95—91no—
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—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—32no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—41no—
612C23×C3—41no—
613C23×C3—41no—
614C23×C3—41no—
615C23×C3—61no—
616C23×C3—61no—
617C23×C3—61no—
618C23×C3—61no—
619C23×C3—61no—
620C23×C3—61no—
621C23×C3#23512yescomplemented
622C23×C3D3×D412yes—
623C23×C3#23712yescomplemented
624C23×C3C2×#6712yes—
625C23×C3C23×D311yescharacteristic
626C23×C3C23×D311yescharacteristic
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—62no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—61no—
642C22×D3—61no—
643C22×D3—61no—
644C22×D3—61no—
645C22×D3—61no—
646C22×D3—61no—
647C22×D3—61no—
648C22×D3—121no—
649C22×D3—121no—
650C22×D3—121no—
651C22×D3—121no—
652C22×D3—121no—
653C22×D3—121no—
654C22×D3D3×D412yes—
655C3×D4—28no—
656C3×D4—28no—
657C3×D4—48no—
658C3×D4—68no—
659C3×D4—68no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—22no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—68no—
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—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—124no—
690C2×C3×C4#23512yescomplemented
691C2×C3×C4#23712yescomplemented
692#67—28no—
693#67—28no—
694#67—68no—
695#67—68no—
696#67—68no—
697#67—68no—
698#67—68no—
699#67—128no—
700#67—128no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—28no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—32no—
721C2×Dic3—44no—
722C2×Dic3—62no—
723C2×Dic3—62no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—61no—
730C2×Dic3—61no—
731C2×Dic3—61no—
732C2×Dic3—68no—
733C2×Dic3—61no—
734C2×Dic3—61no—
735C2×Dic3—61no—
736C2×Dic3—61no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—121no—
740C2×Dic3—121no—
741C2×Dic3—121no—
742C2×Dic3—121no—
743C2×Dic3—121no—
744C2×Dic3—121no—
745C2×Dic3—121no—
746C2×Dic3D3×D412yes—
747C2×Dic3D3×D412yes—
748C2×Dic3D3×D412yes—
749C2×Dic3#23712yescomplemented
750C2×Dic3C2×#6712yes—
751C2×Dic3C2×#6712yes—
752D12—68no—
753C4×D3—68no—
754C4×D3—68no—
755C4×D3—68no—
756Dic6—68no—
757Dic6—68no—
758C2×C32—42no—
759C2×C32—42no—
760C2×C32C2×#12011yescharacteristic
761C2×C32#52511yescharacteristic
762C2×C32#52511yescharacteristic
763C2×C32#52511yescharacteristic
764C2×C32#53211yescharacteristic
765C2×C32#53211yescharacteristic
766C2×C32#53211yescharacteristic
767C3⋊D3—42no—
768C3×D3—42no—
769C24—31no—
770C24—91no—
771C24C2×D3211yescharacteristic
772C24C2×D3211yescharacteristic
773#41—1832no—
774C2×Q8—182no—
775C2×Q8—182no—
776C2×Q8—182no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—62no—
781C2×D4—62no—
782C2×D4—62no—
783C2×D4—62no—
784C2×D4—62no—
785C2×D4—62no—
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—62no—
806C22×C4—62no—
807C22×C4—62no—
808C22×C4—94no—
809C22×C4—94no—
810C22×C4—91no—
811C22×C4—91no—
812C22×C4—91no—
813C22×C4—182no—
814C22×C4—182no—
815C22×C4—182no—
816C22×C4—182no—
817C22×C4C2×D3211yescharacteristic
818C4⋊C4—62no—
819C4⋊C4—182no—
820C4⋊C4—182no—
821C22⋊C4—62no—
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—182no—
835C42—182no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—21no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3—41no—
862C22×C3—41no—
863C22×C3—41no—
864C22×C3—41no—
865C22×C3—41no—
866C22×C3—41no—
867C22×C3—41no—
868C22×C3—41no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—62no—
878C22×C3—62no—
879C22×C3—62no—
880C22×C3—81no—
881C22×C3—81no—
882C22×C3—81no—
883C22×C3—81no—
884C22×C3—81no—
885C22×C3—81no—
886C22×C3—81no—
887C22×C3—81no—
888C22×C3—121no—
889C22×C3—121no—
890C22×C3—121no—
891C22×C3—121no—
892C22×C3C2×#23511yescharacteristic
893C22×C3C2×#23511yescharacteristic
894C22×C3C2×D3×D411yescharacteristic
895C22×C3C2×D3×D411yescharacteristic
896C22×C3C2×D3×D411yescharacteristic
897C22×C3C2×D3×D411yescharacteristic
898C22×C3C2×D3×D411yescharacteristic
899C22×C3C2×#23711yescharacteristic
900C22×C3C2×#23711yescharacteristic
901C22×C3C2×#23711yescharacteristic
902C22×C3D3×#4111yescharacteristic
903C22×C3D3×#4111yescharacteristic
904C22×C3D3×#4111yescharacteristic
905C22×C3C22×#6711yescharacteristic
906C2×D3—22no—
907C2×D3—22no—
908C2×D3—22no—
909C2×D3—41no—
910C2×D3—41no—
911C2×D3—41no—
912C2×D3—41no—
913C2×D3—62no—
914C2×D3—62no—
915C2×D3—62no—
916C2×D3—62no—
917C2×D3—62no—
918C2×D3—62no—
919C2×D3—122no—
920C2×D3—122no—
921C2×D3—122no—
922C2×D3—121no—
923C2×D3—121no—
924C2×D3—121no—
925C2×D3—121no—
926C2×D3—121no—
927C2×D3—121no—
928C2×D3—121no—
929C2×D3—121no—
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—62no—
939C3×C4—62no—
940C3×C4—62no—
941C3×C4—121no—
942C3×C4—121no—
943C3×C4—121no—
944Dic3—22no—
945Dic3—22no—
946Dic3—22no—
947Dic3—41no—
948Dic3—41no—
949Dic3—41no—
950Dic3—62no—
951Dic3—62no—
952Dic3—62no—
953Dic3—62no—
954Dic3—122no—
955Dic3—122no—
956Dic3—121no—
957Dic3—121no—
958Dic3—241no—
959Dic3#93714yes—
960C32#238811yescharacteristic, complemented, Sylow
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—32no—
974C23—61no—
975C23—61no—
976C23—61no—
977C23—61no—
978C23—61no—
979C23—61no—
980C23—92no—
981C23—181no—
982C23—181no—
983C23—181no—
984C23—181no—
985C23—181no—
986C23—181no—
987C23#380412yescomplemented
988C23D3×#6712yes—
989C23C22×D3211yescharacteristic
990Q8—188no—
991D4—28no—
992D4—68no—
993D4—68no—
994D4—188no—
995D4—188no—
996D4—188no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—32no—
1000C2×C4—32no—
1001C2×C4—32no—
1002C2×C4—32no—
1003C2×C4—32no—
1004C2×C4—32no—
1005C2×C4—68no—
1006C2×C4—61no—
1007C2×C4—61no—
1008C2×C4—61no—
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—92no—
1022C2×C4—92no—
1023C2×C4—124no—
1024C2×C4—188no—
1025C2×C4—188no—
1026C2×C4—181no—
1027C2×C4—181no—
1028C2×C4—181no—
1029C2×C4—181no—
1030C2×C4—181no—
1031C2×C4—181no—
1032C2×C4—181no—
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—42no—
1044C2×C3—42no—
1045C2×C3—82no—
1046C2×C3—82no—
1047C2×C3—122no—
1048C2×C3#554711yescharacteristic
1049C2×C3#554711yescharacteristic
1050C2×C3#554811yescharacteristic
1051C2×C3#554811yescharacteristic
1052C2×C3#558611yescharacteristic
1053C2×C3#558611yescharacteristic
1054C2×C3D3×#12011yescharacteristic
1055C2×C3#559611yescharacteristic
1056C2×C3#559611yescharacteristic
1057C2×C3#560611yescharacteristic
1058C2×C3#571611yescharacteristic
1059C2×C3#579111yescharacteristic
1060C2×C3C2×#93711yescharacteristic
1061C2×C3#583211yescharacteristic
1062D3—42no—
1063D3—122no—
1064D3—122no—
1065D3—242no—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—41no—
1073C22—41no—
1074C22—41no—
1075C22—41no—
1076C22—41no—
1077C22—41no—
1078C22—41no—
1079C22—41no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—121no—
1084C22—121no—
1085C22—121no—
1086C22—121no—
1087C22—182no—
1088C22—182no—
1089C22—182no—
1090C22—361no—
1091C22—361no—
1092C22—361no—
1093C22—361no—
1094C22D32×D411yescharacteristic
1095C22D32×D411yescharacteristic
1096C22D3×#23711yescharacteristic
1097C22#6431211yescharacteristic
1098C22C2×#380411yescharacteristic
1099C22C2×#380411yescharacteristic
1100C22C2×D3×#6711yescharacteristic
1101C4—22no—
1102C4—34no—
1103C4—62no—
1104C4—62no—
1105C4—62no—
1106C4—121no—
1107C4—121no—
1108C4—121no—
1109C4—182no—
1110C4—182no—
1111C4—361no—
1112C3—21no—
1113C3#7666511yescharacteristic, complemented
1114C3#8240011yescharacteristic, complemented
1115C2—42no—
1116C2—42no—
1117C2—122no—
1118C2—362no—
1119C2#1059512911yescharacteristic
1120C2#1059513111yescharacteristic
1121C2#1059513811yescharacteristic
1122C2#1059513911yescharacteristic
1123C2#1059515511yescharacteristic
1124C2D3×#93711yescharacteristic
1125C2#1059549811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3804C2semidirect
2. C2×C3×D4×Dic3C2semidirect
3. C2×Dic3×#67C2semidirect
4. C2×#63952C2semidirect
5. #10592922C2semidirect
6. C3×#5223C2semidirect
7. #10591724C2semidirect
8. #10591712C2semidirect
9. #10591708C2semidirect
10. Dic3×#217C2semidirect
11. #10591692C2semidirect
12. #10591392C2semidirect
13. Dic3×(C2×D3)⋊C4C2semidirect
14. #10591338C2semidirect
15. #10591233C2semidirect
63. C2×D4×Dic3D3semidirect
72. #5223D3semidirect
118. C22×C3×Dic3D4semidirect
134. C2×#624D4semidirect
138. C2×D3×Dic3D4semidirect
260. C23×C32#41semidirect
279. C2×C32×C4#41semidirect
290. C2×C3⋊Dic3#41semidirect
315. C2×C3×Dic3#41semidirect
421. C22×Dic3#67semidirect
621. C23×C3#235semidirect
623. C23×C3#237semidirect
690. C2×C3×C4#235semidirect
691. C2×C3×C4#237semidirect
749. C2×Dic3#237semidirect
960. C32#2388semidirect
987. C23#3804semidirect
1033. C2×C4#3804semidirect
1113. C3#76665semidirect
1114. 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×D4×Dic32
C2×Dic3×#672
C2×#639522
#105929222
C3×#52232
#105917242
#105917122
#105917082
Dic3×#2172
#105916922
#105913922
Dic3×(C2×D3)⋊C42
#105913382
#105912332
#824003
#766653