Finite Group Databasebeta

← #11805527

Subgroups — #11805527

Order 1152.

1493 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#625C211yesmaximal, characteristic
2C2×#63879C211yesmaximal, characteristic
3C2×#63879C211yesmaximal, characteristic
4#10592346C211yesmaximal, characteristic, complemented
5C3×#4668C211yesmaximal, characteristic, complemented
6C3×D3×#95C211yesmaximal, characteristic, complemented
7#10591379C211yesmaximal, characteristic, complemented
8#10591369C211yesmaximal, characteristic, complemented
9D3×C3⋊#95C211yesmaximal, characteristic, complemented
10#10591313C211yesmaximal, characteristic, complemented
11#10591278C211yesmaximal, characteristic, complemented
12#10591277C211yesmaximal, characteristic, complemented
13#10591264C211yesmaximal, characteristic, complemented
14#10591247C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#74394—31nomaximal
17#73369—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C4×#625—24no—
44#63879—24no—
45#63879C418yescomplemented
46C32×#95C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C4×#67—31no—
57C2×C4×#67—31no—
58C2×C4×#67—31no—
59C2×C4×#67—31no—
60C2×#67⋊C4—31no—
61C2×#67⋊C4—31no—
62C3×#385—31no—
63C2×C3×#95—31no—
64#5212—31no—
65#5210—31no—
66#5210—31no—
67C2×C3⋊#95—31no—
68#4989—31no—
69#4987—31no—
70#4976—31no—
71Dic3×C4⋊C4—31no—
72#4950—31no—
73#4942—31no—
74#4668—31no—
75#4668—31no—
76#4668D311yescharacteristic, complemented
77#4667—31no—
78D3×#95—31no—
79D3×#95D311yescharacteristic, complemented
80#4650—31no—
81#4650—31no—
82#4649—31no—
83#4647—31no—
84#4647—31no—
85#4647—31no—
86#4647—61no—
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—41no—
109C2×C3×C4×D3—41no—
110C2×C3×C4×D3—41no—
111C2×C3×C4×D3—41no—
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3C2×C414yescomplemented
114C2×#625C2×C414yes—
115C2×#625D414yes—
116C2×#625Q814yes—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3—41no—
121C2×D3×Dic3—41no—
122C2×D3×Dic3C2×C414yescomplemented
123C4⋊(C3⋊Dic3)—41no—
124#3750—22no—
125#3750—41no—
126#3750C2×C414yescomplemented
127C4×C3⋊Dic3—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4C2×C414yescomplemented
130C3×C4⋊Dic3—41no—
131C3×Dic3⋊C4—22no—
132#3724—22no—
133#3724—41no—
134Dic3⋊Dic3—22no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3C2×C414yescomplemented
139Dic32—22no—
140Dic32C2×C414yescomplemented
141#2349—91noSylow
142C23×C3×C4—31no—
143C23×C3×C4—31no—
144C23×C3×C4—31no—
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C23×Dic3—31no—
149C23×Dic3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3C2×D311yescharacteristic
153C22×C4×D3C2×D311yescharacteristic
154C22×C4×D3C2×D311yescharacteristic
155C22×C4×D3C2×D311yescharacteristic
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C4×#67—38no—
165C4×#67—64no—
166C4×#67—64no—
167C4×#67—64no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4C2×D311yescharacteristic
173C2×(C2×D3)⋊C4C2×D311yescharacteristic
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—61no—
178C2×C4⋊Dic3C2×D311yescharacteristic
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—61no—
191C2×Dic3⋊C4—61no—
192C2×Dic3⋊C4—61no—
193C2×Dic3⋊C4C2×D311yescharacteristic
194C2×C4×Dic3—31no—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—31no—
197C2×C4×Dic3—31no—
198C2×C4×Dic3—31no—
199C2×C4×Dic3—31no—
200C2×C4×Dic3—61no—
201#67⋊C4—38no—
202#67⋊C4—64no—
203C3×#95—21no—
204C3×#95—31no—
205C3×#95—31no—
206C3×#95—31no—
207C3×#95—31no—
208C3×#95C2×D311yescharacteristic
209C3×#95C2×D311yescharacteristic
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⋊#95C2×D311yescharacteristic
222C3⋊#95C2×D311yescharacteristic
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×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3C22×C412yes—
235C22×C3×D3C22×C412yes—
236C22×C3×D3C2×D412yes—
237C22×C3×D3C2×D412yes—
238C22×C3×D3C2×Q812yes—
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⋊Dic3—21no—
257C2×C3⋊Dic3C22×C412yes—
258C2×C3⋊Dic3C22×C412yes—
259C2×C3⋊Dic3C2×D412yes—
260C2×C3⋊Dic3C2×Q812yes—
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×Dic3C22×C412yes—
277C2×C3×Dic3C22×C412yes—
278C2×C3×Dic3#4112yes—
279C3×C4×D3—44no—
280C3×C4×D3—44no—
281C3×C4×D3—44no—
282C3×C4×D3—44no—
283#625C4⋊C4116yescomplemented
284D3×Dic3—44no—
285D3×Dic3—44no—
286C2×C4×D4—91no—
287C2×C4×D4—91no—
288C2×C4×D4—91no—
289#389—91no—
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—31no—
300C2×#95—91no—
301C24×C3—31no—
302C24×C3—31no—
303C23×D3C22×D311yescharacteristic
304C23×D3C22×D311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—34no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—62no—
316C22×C3×C4—62no—
317C22×C3×C4—62no—
318C22×C3×C4—62no—
319C22×C3×C4—62no—
320C22×C3×C4—62no—
321C22×C3×C4—121no—
322C22×C3×C4—121no—
323C22×C3×C4—121no—
324C22×C3×C4—121no—
325C22×C3×C4—121no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—34no—
333C2×#67—34no—
334C2×#67—34no—
335C2×#67—34no—
336C2×#67—34no—
337C2×#67—34no—
338C22×Dic3—31no—
339C22×Dic3—31no—
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—61no—
351C22×Dic3—62no—
352C22×Dic3—62no—
353C22×Dic3—121no—
354C22×Dic3—121no—
355C22×Dic3—121no—
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C2×C4×D3—22no—
363C2×C4×D3—22no—
364C2×C4×D3—22no—
365C2×C4×D3—22no—
366C2×C4×D3—22no—
367C2×C4×D3—22no—
368C2×C4×D3—34no—
369C2×C4×D3—41no—
370C2×C4×D3—41no—
371C2×C4×D3—41no—
372C2×C4×D3—41no—
373C2×C4×D3—41no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C2×C4×D3C4×D314yescomplemented
380C3×C4⋊C4—62no—
381C3×C4⋊C4—121no—
382C3×C22⋊C4—34no—
383C3×C22⋊C4—62no—
384#217—34no—
385#217—62no—
386#217—62no—
387#217—62no—
388(C2×D3)⋊C4—22no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4C4×D314yescomplemented
394C4⋊Dic3—41no—
395C4⋊Dic3—62no—
396C4⋊Dic3—121no—
397C4⋊Dic3—121no—
398C4⋊Dic3—122no—
399Dic3⋊C4—22no—
400Dic3⋊C4—34no—
401Dic3⋊C4—34no—
402Dic3⋊C4—64no—
403Dic3⋊C4—62no—
404Dic3⋊C4—62no—
405Dic3⋊C4—62no—
406Dic3⋊C4—62no—
407Dic3⋊C4—62no—
408Dic3⋊C4—122no—
409Dic3⋊C4—121no—
410Dic3⋊C4—121no—
411Dic3⋊C4—121no—
412Dic3⋊C4—121no—
413Dic3⋊C4—122no—
414C4×Dic3—34no—
415C4×Dic3—34no—
416C4×Dic3—62no—
417C4×Dic3—62no—
418C4×Dic3—62no—
419C4×Dic3—62no—
420C4×Dic3—122no—
421C22×C32C23×C411yescharacteristic
422C22×C32C22×D411yescharacteristic
423C22×C32C22×Q811yescharacteristic
424C22×C32C2×#4111yescharacteristic
425C22×C32C2×#4111yescharacteristic
426C22×C32H(5,𝔽2)11yescharacteristic
427C22×C32H(5,𝔽2)11yescharacteristic
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
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×D3—22no—
439C2×C3×D3—22no—
440C2×C3×D3C2×C4⋊C414yes—
441C2×C3×D3C2×C4⋊C414yes—
442C32×C4—22no—
443C32×C4—22no—
444C32×C4—41no—
445C3⋊Dic3—22no—
446C3⋊Dic3—41no—
447C3⋊Dic3—41no—
448C3⋊Dic3C2×C4⋊C414yes—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C22×D4—91no—
456C23×C4—31no—
457C23×C4—31no—
458C23×C4—31no—
459C23×C4—31no—
460C23×C4—91no—
461C23×C4—91no—
462C4×D4—98no—
463C4×D4—184no—
464C4×D4—184no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—91no—
468C2×C4⋊C4—91no—
469C2×C4⋊C4—91no—
470C2×C4⋊C4—91no—
471C2×C4⋊C4—91no—
472C2×C4⋊C4—91no—
473C2×C4⋊C4—91no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—31no—
476C2×C22⋊C4—91no—
477C2×C22⋊C4—91no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4—91no—
480C2×C42—91no—
481C2×C42—91no—
482C2×C42—91no—
483#95—31no—
484#95—31no—
485#95—31no—
486#95—31no—
487#95—91no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95—91no—
492#95D3211yescharacteristic
493C23×C3—21no—
494C23×C3—32no—
495C23×C3—32no—
496C23×C3—32no—
497C23×C3—32no—
498C23×C3—32no—
499C23×C3—32no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3C23×D311yescharacteristic
509C23×C3C23×D311yescharacteristic
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3C2×C4×D312yes—
519C22×D3C2×C4×D312yes—
520C22×D3D3×D412yes—
521C22×D3D3×D412yes—
522C22×D3D3×Q812yes—
523C22×D3D3×Q812yes—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—124no—
566C2×C3×C4—124no—
567C2×C3×C4—124no—
568C2×C3×C4—124no—
569C2×C3×C4C2×C4×D312yes—
570C2×C3×C4C2×C4×D312yes—
571C2×C3×C4#23512yes—
572C2×C3×C4#23712yes—
573#67—316no—
574#67—316no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
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—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—121no—
620C2×Dic3—121no—
621C2×Dic3—121no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—124no—
627C2×Dic3—124no—
628C2×Dic3C2×C4×D312yes—
629C2×Dic3C2×C4×D312yes—
630C2×Dic3#23512yes—
631C4×D3—44no—
632C4×D3—44no—
633C4×D3—44no—
634C4×D3—44no—
635C4×D3—124no—
636C4×D3—124no—
637C2×C32C22×C4⋊C411yescharacteristic
638C2×C32C4×#4111yescharacteristic
639C2×C32#51811yescharacteristic
640C2×C32#54611yescharacteristic
641C2×C32#54611yescharacteristic
642C2×C32#55411yescharacteristic
643C2×C32#55411yescharacteristic
644C3×D3—24no—
645C3×D3—24no—
646C24—31no—
647C24—31no—
648C2×D4—94no—
649C2×D4—94no—
650C2×D4—94no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—34no—
655C22×C4—31no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—94no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—91no—
668C22×C4—91no—
669C22×C4—121no—
670C22×C4—121no—
671C22×C4—121no—
672C22×C4—121no—
673C22×C4—121no—
674C22×C4—182no—
675C22×C4—182no—
676C22×C4—361no—
677C22×C4—361no—
678C22×C4—361no—
679C22×C4C2×D3211yescharacteristic
680C22×C4C2×D3211yescharacteristic
681C22×C4C2×D3211yescharacteristic
682C4⋊C4—62no—
683C4⋊C4—94no—
684C4⋊C4—121no—
685C4⋊C4—182no—
686C4⋊C4—182no—
687C4⋊C4—182no—
688C4⋊C4—361no—
689C4⋊C4—361no—
690C4⋊C4—361no—
691C22⋊C4—34no—
692C22⋊C4—62no—
693C22⋊C4—94no—
694C22⋊C4—182no—
695C22⋊C4—182no—
696C22⋊C4—182no—
697C42—94no—
698C42—182no—
699C42—182no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—34no—
708C22×C3—34no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3C22×C4×D311yescharacteristic
722C22×C3C22×C4×D311yescharacteristic
723C22×C3C2×#23511yescharacteristic
724C22×C3C2×#23511yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C2×D3×D411yescharacteristic
727C22×C3C2×#23711yescharacteristic
728C22×C3#100411yescharacteristic
729C22×C3#100411yescharacteristic
730C22×C3#100411yescharacteristic
731C22×C3C2×D3×Q811yescharacteristic
732C22×C3C2×D3×Q811yescharacteristic
733C22×C3D3×#4111yescharacteristic
734C22×C3#100911yescharacteristic
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3D3×C4⋊C414yes—
748C2×D3D3×C4⋊C414yes—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—42no—
754C3×C4—42no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—62no—
758C3×C4—62no—
759C3×C4—62no—
760C3×C4—81no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764Dic3—22no—
765Dic3—22no—
766Dic3—22no—
767Dic3—34no—
768Dic3—34no—
769Dic3—41no—
770Dic3—41no—
771Dic3—41no—
772Dic3—64no—
773Dic3—62no—
774Dic3—62no—
775Dic3—122no—
776Dic3—122no—
777Dic3—121no—
778Dic3—121no—
779Dic3—121no—
780Dic3—121no—
781Dic3—241no—
782C32#234911yescharacteristic, complemented, Sylow
783C23—32no—
784C23—32no—
785C23—32no—
786C23—32no—
787C23—32no—
788C23—32no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23—61no—
793C23—61no—
794C23—61no—
795C23—61no—
796C23—61no—
797C23C22×D3211yescharacteristic
798D4—916no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—92no—
825C2×C4—92no—
826C2×C4—92no—
827C2×C4—92no—
828C2×C4—124no—
829C2×C4—124no—
830C2×C4—124no—
831C2×C4—124no—
832C2×C4—181no—
833C2×C4—181no—
834C2×C4—181no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—364no—
841C2×C4—364no—
842C2×C4#379512yes—
843C2×C4C4×D3212yes—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—64no—
852C2×C3—64no—
853C2×C3C4×#23511yescharacteristic
854C2×C3#548611yescharacteristic
855C2×C3#549011yescharacteristic
856C2×C3#549011yescharacteristic
857C2×C3C2×D3×C4⋊C411yescharacteristic
858C2×C3C2×D3×C4⋊C411yescharacteristic
859C2×C3#551111yescharacteristic
860C2×C3#551111yescharacteristic
861C2×C3C4×#23711yescharacteristic
862C2×C3#554511yescharacteristic
863C2×C3#559111yescharacteristic
864C2×C3#563511yescharacteristic
865C2×C3#563611yescharacteristic
866C2×C3#565411yescharacteristic
867D3—24no—
868D3—24no—
869C22—34no—
870C22—34no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—62no—
879C22—62no—
880C22—62no—
881C22—62no—
882C22—62no—
883C22C2×#379511yescharacteristic
884C22C2×C4×D3211yescharacteristic
885C22D3×#23511yescharacteristic
886C22D32×D411yescharacteristic
887C22#6431311yescharacteristic
888C22#6431411yescharacteristic
889C22D32×Q811yescharacteristic
890C4—22no—
891C4—22no—
892C4—41no—
893C4—62no—
894C4—62no—
895C4—62no—
896C4—94no—
897C4—121no—
898C4—121no—
899C4—121no—
900C4—182no—
901C4—361no—
902C4—361no—
903C3—21no—
904C3#7336911yescharacteristic, complemented
905C3#7439411yescharacteristic, complemented
906C2—64no—
907C2—64no—
908C2C4×#379511yescharacteristic
909C2#1059418411yescharacteristic
910C2#1059425411yescharacteristic
911C2#1059427211yescharacteristic
912C2#1059453211yescharacteristic
913C2#1059453311yescharacteristic
914C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
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. #10592346C2semidirect
5. C3×#4668C2semidirect
6. C3×D3×#95C2semidirect
7. #10591379C2semidirect
8. #10591369C2semidirect
9. D3×C3⋊#95C2semidirect
10. #10591313C2semidirect
11. #10591278C2semidirect
12. #10591277C2semidirect
13. #10591264C2semidirect
14. #10591247C2semidirect
15. #10591241C2semidirect
45. #63879C4semidirect
76. #4668D3semidirect
79. D3×#95D3semidirect
113. C2×C3×C4×D3C2×C4semidirect
122. C2×D3×Dic3C2×C4semidirect
126. #3750C2×C4semidirect
129. C3×(C2×D3)⋊C4C2×C4semidirect
138. (C2×D3)⋊Dic3C2×C4semidirect
140. Dic32C2×C4semidirect
283. #625C4⋊C4semidirect
379. C2×C4×D3C4×D3semidirect
393. (C2×D3)⋊C4C4×D3semidirect
782. C32#2349semidirect
904. C3#73369semidirect
905. C3#74394semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
C2×#638792
#105923462
C3×#46682
C3×D3×#952
#105913792
#105913692
D3×C3⋊#952
#105913132
#105912782
#105912772
#105912642
#105912472
#105912412
#743943
#733693