Finite Group Databasebeta

← #11805525

Subgroups — #11805525

Order 1152.

1573 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#626C211yesmaximal, characteristic
2C2×#63881C211yesmaximal, characteristic
3C2×#63881C211yesmaximal, characteristic
4C3⋊D3×#95C211yesmaximal, characteristic, complemented
5C3×#4668C211yesmaximal, characteristic, complemented
6C3×#4647C211yesmaximal, characteristic, complemented
7#10591377C211yesmaximal, characteristic, complemented
8#10591366C211yesmaximal, characteristic, complemented
9D3×C3⋊#95C211yesmaximal, characteristic, complemented
10#10591325C211yesmaximal, characteristic, complemented
11#10591290C211yesmaximal, characteristic, complemented
12#10591290C211yesmaximal, characteristic, complemented
13#10591265C211yesmaximal, characteristic, complemented
14#10591245C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#76203—31nomaximal
17#74394—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C4×#626—24no—
44#63881—24no—
45#63881C418yescomplemented
46C32×#95C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C4×#67—31no—
57C2×#893—31no—
58C2×#893—31no—
59C2×#67⋊C4—31no—
60C2×#67⋊C4—31no—
61C2×C4×D12—31no—
62C3×#389—31no—
63C3×#385—31no—
64C2×C3⋊#95—31no—
65#4989—31no—
66#4989—31no—
67#4989—31no—
68#4987—31no—
69#4987—31no—
70#4987—31no—
71#4984—31no—
72#4977—31no—
73#4976—31no—
74Dic3×C4⋊C4—31no—
75#4950—31no—
76#4942—31no—
77C4×Dic3⋊C4—31no—
78#4668—31no—
79#4668—31no—
80#4668D311yescharacteristic, complemented
81D3×#95—31no—
82D3×#95—31no—
83D3×#95—31no—
84D3×#95—61no—
85#4650—31no—
86#4647D311yescharacteristic, complemented
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—41no—
100C2×C4×C3⋊D3—41no—
101C2×C4×C3⋊D3—41no—
102C2×C4×C3⋊D3—41no—
103C2×C4×C3⋊D3C2×C414yescomplemented
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—41no—
114C2×#626C2×C414yes—
115C2×#626D414yes—
116C2×#626Q814yes—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3—41no—
121C2×D3×Dic3—41no—
122C2×D3×Dic3C2×C414yescomplemented
123C3×(C2×D3)⋊C4—22no—
124C3×(C2×D3)⋊C4C2×C414yescomplemented
125C3×C4⋊Dic3—41no—
126C3×C4⋊Dic3—41no—
127C3×Dic3⋊C4—22no—
128C3×Dic3⋊C4—22no—
129C3×Dic3⋊C4—41no—
130C3×Dic3⋊C4C2×C414yescomplemented
131C3×C4×Dic3—22no—
132Dic3⋊Dic3—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—41no—
135#3722—22no—
136#3722—22no—
137#3722C2×C414yescomplemented
138(C2×D3)⋊Dic3—22no—
139Dic32—22no—
140Dic32C2×C414yescomplemented
141#2349—91noSylow
142C23×C3×C4—31no—
143C22×#67—31no—
144C23×Dic3—31no—
145C23×Dic3—31no—
146C22×D12—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—61no—
156C22×C4×D3—61no—
157C22×C4×D3—61no—
158C22×C4×D3C2×D311yescharacteristic
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C42—31no—
168C2×#217—31no—
169C4×#67—64no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
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)⋊C4C2×D311yescharacteristic
178C2×(C2×D3)⋊C4C2×D311yescharacteristic
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3C2×D311yescharacteristic
183C2×C4⋊Dic3C2×D311yescharacteristic
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4C2×D311yescharacteristic
188C2×Dic3⋊C4C2×D311yescharacteristic
189C2×Dic3⋊C4C2×D311yescharacteristic
190C2×Dic3⋊C4C2×D311yescharacteristic
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3C2×D311yescharacteristic
196#893—38no—
197#893—64no—
198#67⋊C4—38no—
199#67⋊C4—64no—
200C4×D12—64no—
201C3×#95—21no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95C2×D311yescharacteristic
205C3×#95C2×D311yescharacteristic
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—61no—
221C3⋊#95—61no—
222C3⋊#95—61no—
223C3⋊#95C2×D311yescharacteristic
224C3⋊#95C2×D311yescharacteristic
225C23×C32C2411yescharacteristic
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3C22×C412yes—
231C22×C3⋊D3C2×D412yes—
232C22×C3⋊D3C2×Q812yes—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C22×C412yes—
238C22×C3×D3C2×D412yes—
239C22×C3×D3C2×Q812yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C22×C412yes—
248C2×C32×C4#4112yes—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C22×C412yes—
257C2×C3⋊Dic3#4112yes—
258C4×C3⋊D3—44no—
259C4×C3⋊D3—44no—
260C4×C3⋊D3—44no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
278C2×C3×Dic3C22×C412yes—
279C2×C3×Dic3C22×C412yes—
280C2×C3×Dic3C2×D412yes—
281C2×C3×Dic3C2×Q812yes—
282C3×C4×D3—44no—
283#626C4⋊C4116yescomplemented
284D3×Dic3—44no—
285D3×Dic3—44no—
286C2×C4×D4—91no—
287C2×C4×D4—91no—
288C2×C4×D4—91no—
289#389—31no—
290#389—91no—
291#385—31no—
292#385—91no—
293#385—91no—
294#385—91no—
295#382—91no—
296#380—91no—
297#380—91no—
298C4×C4⋊C4—91no—
299C2×#95—91no—
300C2×#95—91no—
301C24×C3—31no—
302C23×D3—31no—
303C23×D3—31no—
304C23×D3—61no—
305C23×D3C22×D311yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—62no—
317C22×C3×C4—62no—
318C22×C3×C4—121no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—34no—
326C2×#67—34no—
327C2×#67—34no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—34no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—62no—
339C22×Dic3—62no—
340C22×Dic3—121no—
341C22×Dic3—121no—
342C22×Dic3—121no—
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C2×D12—34no—
351C2×D12—34no—
352C2×D12—34no—
353C2×C4×D3—22no—
354C2×C4×D3—22no—
355C2×C4×D3—34no—
356C2×C4×D3—34no—
357C2×C4×D3—34no—
358C2×C4×D3—41no—
359C2×C4×D3—64no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—62no—
366C2×C4×D3—62no—
367C2×C4×D3—64no—
368C2×C4×D3—64no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—122no—
373C2×C4×D3—122no—
374C2×C4×D3—121no—
375C2×C4×D3—121no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C2×C4×D3—121no—
383C2×C4×D3—121no—
384C2×C4×D3—121no—
385C2×C4×D3—122no—
386C2×C4×D3—122no—
387C2×C4×D3—122no—
388C2×C4×D3—122no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—62no—
391C3×C4⋊C4—62no—
392C3×C4⋊C4—121no—
393C3×C4⋊C4—121no—
394C3×C4⋊C4—121no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—62no—
397C3×C42—62no—
398#217—62no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—34no—
401(C2×D3)⋊C4—34no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4C4×D314yescomplemented
408C4⋊Dic3—41no—
409C4⋊Dic3—41no—
410C4⋊Dic3—62no—
411C4⋊Dic3—62no—
412C4⋊Dic3—121no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—41no—
416Dic3⋊C4—62no—
417Dic3⋊C4—62no—
418Dic3⋊C4—121no—
419Dic3⋊C4C4×D314yescomplemented
420C4×Dic3—22no—
421C4×Dic3—34no—
422C4×Dic3—34no—
423C4×Dic3—62no—
424C4×Dic3—62no—
425C22×C32C23×C411yescharacteristic
426C22×C32C22×D411yescharacteristic
427C22×C32C22×Q811yescharacteristic
428C22×C32C2×#4111yescharacteristic
429C22×C32C2×#4111yescharacteristic
430C22×C32H(5,𝔽2)11yescharacteristic
431C22×C32H(5,𝔽2)11yescharacteristic
432C2×C3⋊D3—22no—
433C2×C3⋊D3—22no—
434C2×C3⋊D3—22no—
435C2×C3⋊D3—22no—
436C2×C3⋊D3—22no—
437C2×C3⋊D3—22no—
438C2×C3⋊D3C2×C4⋊C414yes—
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3C2×C4⋊C414yes—
446C32×C4—22no—
447C32×C4—22no—
448C32×C4—41no—
449C3⋊Dic3—22no—
450C3⋊Dic3—22no—
451C3⋊Dic3—41no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3C2×C4⋊C414yes—
459C22×D4—91no—
460C23×C4—31no—
461C23×C4—91no—
462C23×C4—91no—
463C23×C4—91no—
464C23×C4—91no—
465C23×C4—91no—
466C4×D4—98no—
467C4×D4—184no—
468C4×D4—184no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—91no—
481C2×C22⋊C4—91no—
482C2×C22⋊C4—91no—
483C2×C22⋊C4—91no—
484C2×C42—31no—
485C2×C42—91no—
486C2×C42—91no—
487#95—31no—
488#95—31no—
489#95—91no—
490#95—91no—
491#95—91no—
492#95—91no—
493#95—91no—
494#95—91no—
495#95—91no—
496#95D3211yescharacteristic
497C23×C3—21no—
498C23×C3—32no—
499C23×C3—32no—
500C23×C3—32no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3C23×D311yescharacteristic
506C23×C3C23×D311yescharacteristic
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—32no—
512C22×D3—32no—
513C22×D3—32no—
514C22×D3—32no—
515C22×D3—32no—
516C22×D3—32no—
517C22×D3—62no—
518C22×D3—62no—
519C22×D3—62no—
520C22×D3—62no—
521C22×D3—62no—
522C22×D3—62no—
523C22×D3—62no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3C2×C4×D312yes—
533C22×D3D3×D412yes—
534C22×D3D3×Q812yes—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—22no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—32no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—32no—
556C2×C3×C4—32no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—124no—
580C2×C3×C4C2×C4×D312yes—
581C2×C3×C4C2×C4×D312yes—
582C2×C3×C4#23712yes—
583C2×C3×C4#23912yes—
584#67—316no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—32no—
602C2×Dic3—32no—
603C2×Dic3—32no—
604C2×Dic3—32no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—62no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—121no—
627C2×Dic3—121no—
628C2×Dic3—124no—
629C2×Dic3—124no—
630C2×Dic3C2×C4×D312yes—
631C2×Dic3C2×C4×D312yes—
632C2×Dic3C2×C4×D312yes—
633C2×Dic3D3×D412yes—
634C2×Dic3D3×Q812yes—
635D12—316no—
636C4×D3—44no—
637C4×D3—124no—
638C4×D3—124no—
639C4×D3—124no—
640C4×D3—124no—
641C4×D3—124no—
642C4×D3—124no—
643C4×D3—124no—
644C4×D3—124no—
645C4×D3—128no—
646C4×D3—128no—
647C4×D3—128no—
648C2×C32C22×C4⋊C411yescharacteristic
649C2×C32C4×#4111yescharacteristic
650C2×C32#51811yescharacteristic
651C2×C32#54611yescharacteristic
652C2×C32#54611yescharacteristic
653C2×C32#55411yescharacteristic
654C2×C32#55411yescharacteristic
655C3⋊D3—24no—
656C3×D3—24no—
657C24—31no—
658C24—91no—
659C2×D4—94no—
660C2×D4—94no—
661C2×D4—94no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—94no—
672C22×C4—91no—
673C22×C4—91no—
674C22×C4—94no—
675C22×C4—91no—
676C22×C4—121no—
677C22×C4—182no—
678C22×C4—182no—
679C22×C4—182no—
680C22×C4—182no—
681C22×C4—182no—
682C22×C4—182no—
683C22×C4—361no—
684C22×C4—361no—
685C22×C4—361no—
686C22×C4—361no—
687C22×C4—361no—
688C22×C4—361no—
689C22×C4—361no—
690C22×C4C2×D3211yescharacteristic
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3211yescharacteristic
693C4⋊C4—34no—
694C4⋊C4—62no—
695C4⋊C4—62no—
696C4⋊C4—121no—
697C4⋊C4—121no—
698C4⋊C4—121no—
699C4⋊C4—182no—
700C4⋊C4—182no—
701C4⋊C4—361no—
702C22⋊C4—34no—
703C22⋊C4—62no—
704C22⋊C4—94no—
705C22⋊C4—182no—
706C22⋊C4—182no—
707C22⋊C4—182no—
708C42—62no—
709C42—94no—
710C42—182no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—34no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3C22×C4×D311yescharacteristic
726C22×C3C22×C4×D311yescharacteristic
727C22×C3C2×D3×D411yescharacteristic
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C2×#23711yescharacteristic
730C22×C3#100411yescharacteristic
731C22×C3#100411yescharacteristic
732C22×C3C2×D3×Q811yescharacteristic
733C22×C3C2×D3×Q811yescharacteristic
734C22×C3C2×#23911yescharacteristic
735C22×C3D3×#4111yescharacteristic
736C22×C3D3×#4111yescharacteristic
737C22×C3#100911yescharacteristic
738C22×C3#100911yescharacteristic
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—34no—
746C2×D3—34no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—64no—
751C2×D3—64no—
752C2×D3—64no—
753C2×D3—64no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—62no—
766C2×D3D3×C4⋊C414yes—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—34no—
772C3×C4—42no—
773C3×C4—42no—
774C3×C4—42no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—121no—
780C3×C4—121no—
781C3×C4—121no—
782C3×C4—121no—
783Dic3—22no—
784Dic3—22no—
785Dic3—41no—
786Dic3—41no—
787Dic3—41no—
788Dic3—41no—
789Dic3—62no—
790Dic3—62no—
791Dic3—62no—
792Dic3—62no—
793Dic3—122no—
794Dic3—122no—
795Dic3—122no—
796Dic3—121no—
797Dic3—121no—
798Dic3D3×C4⋊C414yes—
799C32#234911yescharacteristic, complemented, Sylow
800C23—32no—
801C23—32no—
802C23—32no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—92no—
808C23—92no—
809C23—92no—
810C23—181no—
811C23—181no—
812C23—181no—
813C23—181no—
814C23C22×D3211yescharacteristic
815D4—916no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—92no—
845C2×C4—92no—
846C2×C4—124no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—181no—
853C2×C4—181no—
854C2×C4—364no—
855C2×C4—364no—
856C2×C4—364no—
857C2×C4—364no—
858C2×C4—364no—
859C2×C4#379612yes—
860C2×C4C4×D3212yes—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—64no—
869C2×C3C2×D3×C4⋊C411yescharacteristic
870C2×C3C2×D3×C4⋊C411yescharacteristic
871C2×C3C4×#23711yescharacteristic
872C2×C3#554511yescharacteristic
873C2×C3#554511yescharacteristic
874C2×C3C4×#23911yescharacteristic
875C2×C3#559111yescharacteristic
876C2×C3#561211yescharacteristic
877C2×C3#563011yescharacteristic
878C2×C3#563511yescharacteristic
879C2×C3#563611yescharacteristic
880C2×C3#565411yescharacteristic
881C2×C3#569011yescharacteristic
882C2×C3#573011yescharacteristic
883D3—24no—
884D3—68no—
885D3—64no—
886D3—64no—
887C22—34no—
888C22—62no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22—62no—
893C22—62no—
894C22—94no—
895C22—182no—
896C22—182no—
897C22—182no—
898C22—182no—
899C22—182no—
900C22—182no—
901C22C2×#379611yescharacteristic
902C22C2×C4×D3211yescharacteristic
903C22#6430611yescharacteristic
904C22D32×D411yescharacteristic
905C22#6431411yescharacteristic
906C22#6431411yescharacteristic
907C22D32×Q811yescharacteristic
908C4—22no—
909C4—22no—
910C4—34no—
911C4—41no—
912C4—62no—
913C4—62no—
914C4—121no—
915C4—121no—
916C4—121no—
917C4—121no—
918C4—182no—
919C4—182no—
920C4—361no—
921C3—21no—
922C3#7439411yescharacteristic, complemented
923C3#7620311yescharacteristic, complemented
924C2—64no—
925C2—184no—
926C2C4×#379611yescharacteristic
927C2#1059406311yescharacteristic
928C2#1059425611yescharacteristic
929C2#1059427911yescharacteristic
930C2#1059439311yescharacteristic
931C2#1059439411yescharacteristic
932C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C3⋊D3×#95C2semidirect
5. C3×#4668C2semidirect
6. C3×#4647C2semidirect
7. #10591377C2semidirect
8. #10591366C2semidirect
9. D3×C3⋊#95C2semidirect
10. #10591325C2semidirect
11. #10591290C2semidirect
12. #10591290C2semidirect
13. #10591265C2semidirect
14. #10591245C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
45. #63881C4semidirect
80. #4668D3semidirect
86. #4647D3semidirect
103. C2×C4×C3⋊D3C2×C4semidirect
122. C2×D3×Dic3C2×C4semidirect
124. C3×(C2×D3)⋊C4C2×C4semidirect
130. C3×Dic3⋊C4C2×C4semidirect
137. #3722C2×C4semidirect
140. Dic32C2×C4semidirect
283. #626C4⋊C4semidirect
407. (C2×D3)⋊C4C4×D3semidirect
419. Dic3⋊C4C4×D3semidirect
799. C32#2349semidirect
922. C3#74394semidirect
923. C3#76203semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
C2×#638812
C3⋊D3×#952
C3×#46682
C3×#46472
#105913772
#105913662
D3×C3⋊#952
#105913252
#105912902
#105912652
#105912452
Dic3×Dic3⋊C42
#762033
#743943