Finite Group Databasebeta

← #11803614

Subgroups — #11803614

Order 1152.

1453 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#626C211yesmaximal, characteristic, complemented
2C2×#63886C211yesmaximal, characteristic
3C2×#63877C211yesmaximal, characteristic, complemented
4#10592367C211yesmaximal, characteristic, complemented
5C3×#4665C211yesmaximal, characteristic, complemented
6C3×#4649C211yesmaximal, characteristic, complemented
7#10591387C211yesmaximal, characteristic, complemented
8#10591384C211yesmaximal, characteristic, complemented
9#10591383C211yesmaximal, characteristic, complemented
10#10591366C211yesmaximal, characteristic, complemented
11#10591318C211yesmaximal, characteristic, complemented
12#10591279C211yesmaximal, characteristic, complemented
13#10591278C211yesmaximal, characteristic, complemented
14#10591268C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#74665—31nomaximal
17#73763—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C4×#626—24no—
48#63886C418yescomplemented
49#63877—24no—
50C32×#95C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#939—31no—
57C2×C4×#67—31no—
58C2×#895—31no—
59C2×#877—31no—
60C2×C4×D12—31no—
61C2×#872—31no—
62C3×#386—31no—
63C3×C4×C4⋊C4—31no—
64#5221—31no—
65#5210—31no—
66#4988—31no—
67#4987—31no—
68#4984—31no—
69#4957—31no—
70#4957—31no—
71#4956—31no—
72#4944—31no—
73#4942—31no—
74#4940—31no—
75#4940—31no—
76#4939—31no—
77#4939—31no—
78#4669—31no—
79#4668—31no—
80#4668—31no—
81#4668—31no—
82#4668—61no—
83#4665—31no—
84#4665D311yescharacteristic, complemented
85#4649D311yescharacteristic, complemented
86#4647—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—41no—
98C2×C4×C3⋊D3—41no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C2×C3×D12—41no—
106C2×C3×D12—41no—
107C2×C3×D12C2×C414yescomplemented
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—41no—
110C2×C3×C4×D3—41no—
111C2×#626—22no—
112C2×#626—22no—
113C2×#626—41no—
114C2×#626—41no—
115C2×#626C2×C414yes—
116C2×#626C2×C414yescomplemented
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3C2×C414yescomplemented
120#3752—41no—
121#3752C2×C414yescomplemented
122C4⋊(C3⋊Dic3)—41no—
123#3750—22no—
124C3×(C2×D3)⋊C4—22no—
125C3×(C2×D3)⋊C4—41no—
126C3×(C2×D3)⋊C4—41no—
127C3×Dic3⋊C4—22no—
128C3×Dic3⋊C4C2×C414yescomplemented
129C3×C4×Dic3—41no—
130C3×C4×Dic3—41no—
131C3×C4×Dic3D414yescomplemented
132#3724—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—41no—
135#3722—22no—
136#3722—41no—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—41no—
140(C2×D3)⋊Dic3—41no—
141(C2×D3)⋊Dic3C2×C414yescomplemented
142Dic32—22no—
143#2324—91noSylow
144C22×C3×D4—31no—
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C23×Dic3—31no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12C2×D311yescharacteristic
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—61no—
156C22×C4×D3C2×D311yescharacteristic
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C42—31no—
163C2×C3×C42—31no—
164C2×C3×C42—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170#939—38no—
171C4×#67—64no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4—61no—
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—61no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—61no—
202C2×Dic3⋊C4C2×D311yescharacteristic
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3C2×D311yescharacteristic
207C2×C4×Dic3C2×D311yescharacteristic
208C2×C4×Dic3C2×D311yescharacteristic
209#895—38no—
210#877—64no—
211C4×D12—64no—
212#872—64no—
213C3×#95—21no—
214C3×#95—31no—
215C3×#95—31no—
216C3×#95C2×D311yescharacteristic
217C3×#95C2×D311yescharacteristic
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—61no—
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C23×C32C2411yescharacteristic
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3C22×C412yes—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3C22×C412yes—
248C22×C3×D3C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C22×C412yes—
257C2×C32×C4C2×D412yes—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C22×C412yes—
267C4×C3⋊D3—44no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C22×C412yes—
282C2×C3×Dic3C22×C412yes—
283C2×C3×Dic3C2×D412yes—
284C2×C3×Dic3C2×D412yes—
285C2×C3×Dic3#4112yes—
286C3×D12—44no—
287C3×C4×D3—44no—
288#626—28no—
289#626—44no—
290D3×Dic3—28no—
291C2×#121—91no—
292C2×C4×D4—91no—
293C2×#117—91no—
294#390—91no—
295#390—91no—
296#390—91no—
297#389—91no—
298#388—91no—
299#388—91no—
300#386—31no—
301#386—91no—
302#385—91no—
303#385—91no—
304#380—91no—
305C4×C4⋊C4—31no—
306C24×C3—31no—
307C24×C3—31no—
308C23×D3—31no—
309C23×D3—31no—
310C23×D3—61no—
311C23×D3C22×D311yescharacteristic
312C23×D3C22×D311yescharacteristic
313C2×C3×D4—34no—
314C2×C3×D4—121no—
315C2×C3×D4—121no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—62no—
326C22×C3×C4—121no—
327C22×C3×C4—121no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C2×#67—34no—
335C2×#67—34no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—121no—
339C2×#67—121no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—34no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—62no—
351C22×Dic3—62no—
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C2×D12—34no—
359C2×D12—34no—
360C2×D12—41no—
361C2×D12—41no—
362C2×D12—62no—
363C2×D12—62no—
364C2×D12—121no—
365C2×D12—121no—
366C2×D12C4×D314yescomplemented
367C2×C4×D3—22no—
368C2×C4×D3—34no—
369C2×C4×D3—41no—
370C2×C4×D3—41no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—122no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3—122no—
381C2×C4×D3—122no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—62no—
384C3×C22⋊C4—62no—
385C3×C22⋊C4—121no—
386C3×C22⋊C4—121no—
387C3×C42—34no—
388C3×C42—121no—
389C3×C42—121no—
390#217—34no—
391#217—62no—
392#217—62no—
393#217—121no—
394#217—121no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—34no—
397(C2×D3)⋊C4—34no—
398(C2×D3)⋊C4—34no—
399(C2×D3)⋊C4—41no—
400(C2×D3)⋊C4—41no—
401(C2×D3)⋊C4—64no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4—121no—
408(C2×D3)⋊C4—121no—
409(C2×D3)⋊C4—121no—
410(C2×D3)⋊C4—121no—
411(C2×D3)⋊C4—121no—
412(C2×D3)⋊C4—122no—
413C4⋊Dic3—62no—
414C4⋊Dic3—121no—
415C4⋊Dic3—121no—
416C4⋊Dic3—121no—
417C4⋊Dic3—122no—
418Dic3⋊C4—22no—
419Dic3⋊C4—62no—
420Dic3⋊C4—62no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—122no—
425Dic3⋊C4—121no—
426Dic3⋊C4C4×D314yescomplemented
427C4×Dic3—41no—
428C4×Dic3—41no—
429C4×Dic3—62no—
430C4×Dic3—62no—
431C4×Dic3D1214yescomplemented
432C22×C32C23×C411yescharacteristic
433C22×C32C22×D411yescharacteristic
434C22×C32C2×#4111yescharacteristic
435C22×C32H(5,𝔽2)11yescharacteristic
436C22×C32H(5,𝔽2)11yescharacteristic
437C22×C32H(5,𝔽2)11yescharacteristic
438C22×C322−1+411yescharacteristic
439C2×C3⋊D3—22no—
440C2×C3⋊D3—22no—
441C2×C3⋊D3—22no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C32×C4—22no—
461C32×C4—22no—
462C32×C4—41no—
463C3⋊Dic3—22no—
464C3⋊Dic3—41no—
465C3⋊Dic3—41no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—41no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C3×Dic3C4×D414yes—
472C22×D4—31no—
473C22×D4—91no—
474C22×D4—91no—
475C23×C4—31no—
476C23×C4—91no—
477C23×C4—91no—
478#121—98no—
479C4×D4—184no—
480#117—184no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—91no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C22⋊C4—31no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—91no—
492C2×C22⋊C4—91no—
493C2×C22⋊C4—91no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C42—31no—
501C2×C42—31no—
502C2×C42—31no—
503C2×C42—91no—
504#95—31no—
505#95—31no—
506#95—91no—
507#95—91no—
508#95—91no—
509#95D3211yescharacteristic
510C23×C3—21no—
511C23×C3—32no—
512C23×C3—32no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3C23×D311yescharacteristic
526C23×C3C23×D311yescharacteristic
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—32no—
540C22×D3—32no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—121no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3C2×C4×D312yes—
561C22×D3C2×C4×D312yes—
562C3×D4—124no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—124no—
605C2×C3×C4C2×C4×D312yes—
606C2×C3×C4C2×C4×D312yes—
607C2×C3×C4C2×D1212yes—
608C2×C3×C4D3×D412yes—
609#67—68no—
610#67—124no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—62no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—68no—
632C2×Dic3—62no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3C2×C4×D312yes—
653C2×Dic3C2×C4×D312yes—
654C2×Dic3C2×D1212yes—
655C2×Dic3C2×D1212yes—
656C2×Dic3#23512yes—
657D12—44no—
658D12—68no—
659D12—124no—
660C4×D3—44no—
661C4×D3—68no—
662C4×D3—124no—
663C4×D3—124no—
664C4×D3—128no—
665C2×C32C2×C4×D411yescharacteristic
666C2×C32#51811yescharacteristic
667C2×C32#52011yescharacteristic
668C2×C32#53511yescharacteristic
669C2×C32#53711yescharacteristic
670C2×C32#54011yescharacteristic
671C2×C32#54211yescharacteristic
672C3⋊D3—42no—
673C3×D3—42no—
674C3×D3—42no—
675C24—31no—
676C24—31no—
677C24—91no—
678C2×D4—34no—
679C2×D4—94no—
680C2×D4—94no—
681C2×D4—121no—
682C2×D4—121no—
683C2×D4—182no—
684C2×D4—182no—
685C2×D4—361no—
686C2×D4—361no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—62no—
694C22×C4—94no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—91no—
698C22×C4—121no—
699C22×C4—121no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—361no—
704C22×C4—361no—
705C22×C4C2×D3211yescharacteristic
706C22×C4C2×D3211yescharacteristic
707C22×C4C2×D3211yescharacteristic
708C4⋊C4—34no—
709C4⋊C4—62no—
710C4⋊C4—182no—
711C4⋊C4—182no—
712C4⋊C4—182no—
713C4⋊C4—361no—
714C4⋊C4—361no—
715C22⋊C4—62no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4—121no—
719C22⋊C4—121no—
720C22⋊C4—182no—
721C22⋊C4—182no—
722C22⋊C4—182no—
723C22⋊C4—361no—
724C22⋊C4—361no—
725C22⋊C4—361no—
726C22⋊C4—361no—
727C42—34no—
728C42—121no—
729C42—121no—
730C42—182no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3C22×C4×D311yescharacteristic
753C22×C3C22×C4×D311yescharacteristic
754C22×C3C22×D1211yescharacteristic
755C22×C3C2×#23511yescharacteristic
756C22×C3C2×D3×D411yescharacteristic
757C22×C3#100411yescharacteristic
758C22×C3#100411yescharacteristic
759C22×C3#100411yescharacteristic
760C22×C3#100411yescharacteristic
761C22×C3#100711yescharacteristic
762C22×C3D3×#4111yescharacteristic
763C22×C3#100911yescharacteristic
764C22×C3#100911yescharacteristic
765C22×C3#101011yescharacteristic
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—64no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—122no—
788C2×D3—122no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—122no—
792C2×D3—122no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—34no—
806C3×C4—42no—
807C3×C4—42no—
808C3×C4—41no—
809C3×C4—41no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—81no—
813C3×C4—121no—
814C3×C4—121no—
815C3×C4—121no—
816Dic3—22no—
817Dic3—22no—
818Dic3—41no—
819Dic3—41no—
820Dic3—41no—
821Dic3—62no—
822Dic3—62no—
823Dic3—122no—
824Dic3—122no—
825Dic3—121no—
826Dic3—121no—
827Dic3—121no—
828Dic3—121no—
829Dic3—241no—
830Dic3C4×D1214yes—
831C32#232411yescharacteristic, complemented, Sylow
832C23—32no—
833C23—32no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—92no—
847C23—181no—
848C23—181no—
849C23—181no—
850C23—181no—
851C23—181no—
852C23—181no—
853C23C22×D3211yescharacteristic
854D4—124no—
855D4—188no—
856D4—364no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—92no—
883C2×C4—124no—
884C2×C4—188no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—364no—
894C2×C4C4×D3212yes—
895C2×C4D3×D1212yes—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—122no—
904C2×C3—122no—
905C2×C3C2×C4×D1211yescharacteristic
906C2×C3#548611yescharacteristic
907C2×C3#551011yescharacteristic
908C2×C3#552511yescharacteristic
909C2×C3C4×D3×D411yescharacteristic
910C2×C3#554511yescharacteristic
911C2×C3#554611yescharacteristic
912C2×C3#556211yescharacteristic
913C2×C3#557411yescharacteristic
914C2×C3#558211yescharacteristic
915C2×C3#559211yescharacteristic
916C2×C3#560811yescharacteristic
917C2×C3#561511yescharacteristic
918C2×C3#566211yescharacteristic
919D3—42no—
920D3—42no—
921D3—124no—
922D3—122no—
923D3—122no—
924C22—62no—
925C22—62no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22—62no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22—121no—
938C22—182no—
939C22—182no—
940C22—182no—
941C22—361no—
942C22—361no—
943C22—361no—
944C22—361no—
945C22C2×C4×D3211yescharacteristic
946C22C2×D3×D1211yescharacteristic
947C22D3×#23511yescharacteristic
948C22#6431311yescharacteristic
949C22#6431411yescharacteristic
950C22#6431411yescharacteristic
951C22#6431511yescharacteristic
952C4—22no—
953C4—22no—
954C4—34no—
955C4—41no—
956C4—62no—
957C4—62no—
958C4—121no—
959C4—121no—
960C4—121no—
961C4—182no—
962C4—361no—
963C4—361no—
964C3—21no—
965C3#7376311yescharacteristic, complemented
966C3#7466511yescharacteristic, complemented
967C2—122no—
968C2—122no—
969C2—362no—
970C2C4×D3×D1211yescharacteristic
971C2#1059408011yescharacteristic
972C2#1059410011yescharacteristic
973C2#1059425411yescharacteristic
974C2#1059436111yescharacteristic
975C2#1059441911yescharacteristic
976C2#1059452211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63886C2
hypercenter#95D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×C4×#626C2semidirect
3. C2×#63877C2semidirect
4. #10592367C2semidirect
5. C3×#4665C2semidirect
6. C3×#4649C2semidirect
7. #10591387C2semidirect
8. #10591384C2semidirect
9. #10591383C2semidirect
10. #10591366C2semidirect
11. #10591318C2semidirect
12. #10591279C2semidirect
13. #10591278C2semidirect
14. #10591268C2semidirect
15. #10591202C2semidirect
48. #63886C4semidirect
84. #4665D3semidirect
85. #4649D3semidirect
107. C2×C3×D12C2×C4semidirect
116. C2×#626C2×C4semidirect
119. C2×D3×Dic3C2×C4semidirect
121. #3752C2×C4semidirect
128. C3×Dic3⋊C4C2×C4semidirect
131. C3×C4×Dic3D4semidirect
141. (C2×D3)⋊Dic3C2×C4semidirect
366. C2×D12C4×D3semidirect
426. Dic3⋊C4C4×D3semidirect
431. C4×Dic3D12semidirect
831. C32#2324semidirect
965. C3#73763semidirect
966. C3#74665semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
C2×#638862
C2×#638772
#105923672
C3×#46652
C3×#46492
#105913872
#105913842
#105913832
#105913662
#105913182
#105912792
#105912782
#105912682
#105912022
#746653
#737633