Finite Group Databasebeta

← #11812887

Subgroups — #11812887

Order 1152.

1491 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63961C211yesmaximal, characteristic, complemented
2C2×#63958C211yesmaximal, characteristic
3C2×#63952C211yesmaximal, characteristic, complemented
4C2×#63900C211yesmaximal, characteristic, complemented
5#10592655C211yesmaximal, characteristic, complemented
6C3×#4961C211yesmaximal, characteristic, complemented
7C3×#4950C211yesmaximal, characteristic, complemented
8#10591694C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591378C211yesmaximal, characteristic, complemented
11#10591345C211yesmaximal, characteristic, complemented
12#10591324C211yesmaximal, characteristic, complemented
13#10591307C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591249C211yesmaximal, characteristic, complemented
16#77117—31nomaximal
17#74608—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41#63961—24no—
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45#63958—24no—
46C2×Dic32C2211yescharacteristic
47#63952—24no—
48#63900—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#938—31no—
58C2×#935—31no—
59C2×#929—31no—
60C2×C4×#67—31no—
61C2×D3×C4⋊C4—31no—
62C2×D3×C4⋊C4—31no—
63C2×#884—31no—
64C2×#67⋊C4—31no—
65C3×#394—31no—
66C3×#385—31no—
67#4993—31no—
68#4990—31no—
69#4989—31no—
70#4982—31no—
71#4961D311yescharacteristic, complemented
72#4956—31no—
73#4956—31no—
74#4956—31no—
75#4956—31no—
76#4956—61no—
77#4952—31no—
78#4952—31no—
79#4951—31no—
80#4950D311yescharacteristic, complemented
81#4949—31no—
82#4668—31no—
83#4665—31no—
84#4665—31no—
85#4657—31no—
86#4655—31no—
87#4652—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—22no—
94C2×#638—22no—
95C2×#638D414yes—
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—41no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3—22no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#624—22no—
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—41no—
123C2×#624—41no—
124C32×C22⋊C4—22no—
125#3757—22no—
126#3752—22no—
127C3×#217—22no—
128C3×#217—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—41no—
131C3×C4⋊Dic3—22no—
132C3×C4⋊Dic3—22no—
133C3×C4⋊Dic3—41no—
134#3724—22no—
135#3724—22no—
136#3724—22no—
137#3724D414yescomplemented
138Dic3⋊Dic3—22no—
139#3722—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143Dic32—22no—
144#2443—91noSylow
145C22×C3×D4—31no—
146C23×C3×C4—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—61no—
151C22×#67C2×D311yescharacteristic
152C23×Dic3C2×D311yescharacteristic
153C22×D12—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—61no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C22⋊C4—21no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4C2×D311yescharacteristic
170C2×C3×C22⋊C4C2×D311yescharacteristic
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—61no—
177C2×#217C2×D311yescharacteristic
178C2×#217C2×D311yescharacteristic
179#938—64no—
180#935—64no—
181#929—64no—
182C4×#67—64no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3C2×D311yescharacteristic
195C2×C4⋊Dic3C2×D311yescharacteristic
196C2×C4⋊Dic3C2×D311yescharacteristic
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208D3×C4⋊C4—64no—
209D3×C4⋊C4—64no—
210#884—64no—
211#67⋊C4—64no—
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—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—61no—
226C3⋊#95—61no—
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32C2×D412yes—
237C23×C32C2411yescharacteristic
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3C2×D412yes—
243C22×C3⋊D3#4112yes—
244C22×C3⋊D3#4112yes—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4#4112yes—
258#638—28no—
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⋊Dic3C2×D412yes—
267C2×C3⋊Dic3C2×D412yes—
268C4×C3⋊D3—28no—
269C3×#67—44no—
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×Dic3—21no—
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×Dic3—44no—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292#626—44no—
293#624—44no—
294#624—44no—
295C2×#123—91no—
296C2×#121—91no—
297C2×C4×D4—91no—
298C22×C4⋊C4—91no—
299#399—91no—
300#398—91no—
301#397—91no—
302#394—31no—
303#388—91no—
304#387—91no—
305#386—91no—
306#386—91no—
307#386—91no—
308#385—31no—
309#385—91no—
310C24×C3—21no—
311C24×C3—31no—
312C24×C3C22×D311yescharacteristic
313C24×C3C22×D311yescharacteristic
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—61no—
317C23×D3C22×D311yescharacteristic
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—121no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4—121no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C2×#67—22no—
338C2×#67—22no—
339C2×#67—34no—
340C2×#67—34no—
341C2×#67—41no—
342C2×#67—64no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—122no—
351C2×#67—122no—
352C22×Dic3—22no—
353C22×Dic3—22no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—41no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—122no—
389C2×C4×D3—122no—
390C2×C4×D3—122no—
391C2×C4×D3—121no—
392C2×C4×D3—121no—
393C2×C4×D3—121no—
394C2×C4×D3—121no—
395C3×C4⋊C4—62no—
396C3×C4⋊C4—62no—
397C3×C4⋊C4—121no—
398C3×C22⋊C4—22no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—42no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—62no—
403C3×C22⋊C4—62no—
404C3×C22⋊C4—121no—
405#217—22no—
406#217—22no—
407#217—62no—
408#217—62no—
409#217—62no—
410#217—62no—
411#217—62no—
412#217—122no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—41no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—62no—
422(C2×D3)⋊C4—122no—
423C4⋊Dic3—22no—
424C4⋊Dic3—22no—
425C4⋊Dic3—41no—
426C4⋊Dic3—62no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434Dic3⋊C4—62no—
435Dic3⋊C4—62no—
436C4×Dic3—62no—
437C4×Dic3—62no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C22×C32C22×D411yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32C2×#4111yescharacteristic
449C22×C32C2×#4111yescharacteristic
450C22×C32H(5,𝔽2)11yescharacteristic
451C22×C322−1+411yescharacteristic
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—22no—
458C2×C3⋊D3#12314yescomplemented
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C32×C4—22no—
467C32×C4—41no—
468C3⋊Dic3—22no—
469C3⋊Dic3—22no—
470C3⋊Dic3—41no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C22×D4—31no—
479C22×D4—91no—
480C22×D4—91no—
481C23×C4—31no—
482C23×C4—91no—
483C23×C4—91no—
484C23×C4—91no—
485#123—184no—
486#121—184no—
487C4×D4—184no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—184no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4D3211yescharacteristic
508C2×C42—91no—
509#95—31no—
510#95—31no—
511#95—31no—
512#95—91no—
513#95—91no—
514#95—91no—
515#95—91no—
516#95—91no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—22no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3D3×D412yes—
545C23×C3D3×D412yes—
546C23×C3C23×D311yescharacteristic
547C23×C3C23×D311yescharacteristic
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—32no—
556C22×D3—32no—
557C22×D3—32no—
558C22×D3—32no—
559C22×D3—32no—
560C22×D3—32no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—121no—
573C22×D3—121no—
574C22×D3—121no—
575C22×D3—121no—
576C3×D4—124no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—22no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
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—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—124no—
615C2×C3×C4#23512yes—
616C2×C3×C4#23712yes—
617#67—44no—
618#67—68no—
619#67—68no—
620#67—128no—
621#67—124no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—44no—
646C2×Dic3—62no—
647C2×Dic3—62no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—121no—
663C2×Dic3—121no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3D3×D412yes—
670C2×Dic3D3×D412yes—
671D12—124no—
672C4×D3—68no—
673C4×D3—68no—
674C4×D3—128no—
675C4×D3—124no—
676C4×D3—124no—
677C4×D3—124no—
678C4×D3—124no—
679C2×C32—42no—
680C2×C32C2×#12311yescharacteristic
681C2×C32#52511yescharacteristic
682C2×C32#53911yescharacteristic
683C2×C32D4211yescharacteristic
684C2×C32#54711yescharacteristic
685C2×C32#54811yescharacteristic
686C2×C32#55311yescharacteristic
687C3⋊D3—24no—
688C3×D3—81no—
689C24—31no—
690C24—91no—
691C24C2×D3211yescharacteristic
692C2×D4—62no—
693C2×D4—62no—
694C2×D4—94no—
695C2×D4—121no—
696C2×D4—182no—
697C2×D4—182no—
698C2×D4—182no—
699C2×D4—182no—
700C2×D4—182no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—62no—
709C22×C4—62no—
710C22×C4—91no—
711C22×C4—91no—
712C22×C4—91no—
713C22×C4—121no—
714C22×C4—182no—
715C22×C4—182no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—182no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—361no—
722C22×C4—361no—
723C22×C4C2×D3211yescharacteristic
724C22×C4C2×D3211yescharacteristic
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—94no—
728C4⋊C4—121no—
729C4⋊C4—182no—
730C4⋊C4—182no—
731C4⋊C4—182no—
732C4⋊C4—182no—
733C22⋊C4—22no—
734C22⋊C4—62no—
735C22⋊C4—62no—
736C22⋊C4—62no—
737C22⋊C4—121no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—182no—
742C22⋊C4—182no—
743C22⋊C4—182no—
744C42—182no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—81no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3C2×#23511yescharacteristic
781C22×C3C2×D3×D411yescharacteristic
782C22×C3C2×D3×D411yescharacteristic
783C22×C3C2×D3×D411yescharacteristic
784C22×C3C2×D3×D411yescharacteristic
785C22×C3C2×#23711yescharacteristic
786C22×C3#100411yescharacteristic
787C22×C3#100411yescharacteristic
788C22×C3#100711yescharacteristic
789C22×C3D3×#4111yescharacteristic
790C22×C3D3×#4111yescharacteristic
791C22×C3D3×#4111yescharacteristic
792C22×C3D3×#4111yescharacteristic
793C22×C3#101011yescharacteristic
794C2×D3—34no—
795C2×D3—34no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—41no—
803C2×D3—64no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—62no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—122no—
817C2×D3—122no—
818C2×D3—122no—
819C2×D3—122no—
820C2×D3—122no—
821C2×D3—122no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—42no—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—62no—
828C3×C4—62no—
829C3×C4—81no—
830C3×C4—121no—
831C3×C4—121no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4—121no—
835Dic3—22no—
836Dic3—22no—
837Dic3—41no—
838Dic3—41no—
839Dic3—41no—
840Dic3—41no—
841Dic3—41no—
842Dic3—62no—
843Dic3—62no—
844Dic3—62no—
845Dic3—62no—
846Dic3—122no—
847Dic3—122no—
848Dic3—121no—
849Dic3—121no—
850Dic3—241no—
851C32#244311yescharacteristic, complemented, Sylow
852C23—21no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—92no—
866C23—92no—
867C23—92no—
868C23—181no—
869C23—181no—
870C23—181no—
871C23—181no—
872C23#380212yes—
873C23C22×D3211yescharacteristic
874D4—124no—
875D4—188no—
876D4—364no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—92no—
904C2×C4—92no—
905C2×C4—124no—
906C2×C4—188no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—181no—
913C2×C4—181no—
914C2×C4—364no—
915C2×C4—364no—
916C2×C4#380412yes—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—42no—
925C2×C3—42no—
926C2×C3—82no—
927C2×C3—241no—
928C2×C3#550711yescharacteristic
929C2×C3#554711yescharacteristic
930C2×C3#555811yescharacteristic
931C2×C3#559011yescharacteristic
932C2×C3#559011yescharacteristic
933C2×C3#560611yescharacteristic
934C2×C3#561111yescharacteristic
935C2×C3#561411yescharacteristic
936C2×C3#563311yescharacteristic
937C2×C3#563811yescharacteristic
938C2×C3D3×#12311yescharacteristic
939C2×C3D3×#12311yescharacteristic
940C2×C3#566011yescharacteristic
941C2×C3#567711yescharacteristic
942D3—64no—
943D3—64no—
944D3—81no—
945D3—124no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—94no—
954C22—121no—
955C22—121no—
956C22—121no—
957C22—121no—
958C22—121no—
959C22—121no—
960C22—121no—
961C22—182no—
962C22—182no—
963C22—182no—
964C22—182no—
965C22—182no—
966C22—182no—
967C22#6429711yescharacteristic
968C22C2×#380211yescharacteristic
969C22D32×D411yescharacteristic
970C22#6431211yescharacteristic
971C22#6431211yescharacteristic
972C22#6431311yescharacteristic
973C22C2×#380411yescharacteristic
974C4—22no—
975C4—41no—
976C4—62no—
977C4—62no—
978C4—121no—
979C4—121no—
980C4—121no—
981C4—121no—
982C4—121no—
983C4—182no—
984C4—182no—
985C4—361no—
986C3—21no—
987C3#7460811yescharacteristic, complemented
988C3#7711711yescharacteristic, complemented
989C2—42no—
990C2—184no—
991C2—241no—
992C2#1059404111yescharacteristic
993C2#1059407511yescharacteristic
994C2#1059427111yescharacteristic
995C2#1059429511yescharacteristic
996C2#1059492811yescharacteristic
997C2#1059512211yescharacteristic
998C2#1059513811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63958C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#63961C2semidirect
3. C2×#63952C2semidirect
4. C2×#63900C2semidirect
5. #10592655C2semidirect
6. C3×#4961C2semidirect
7. C3×#4950C2semidirect
8. #10591694C2semidirect
9. #10591387C2semidirect
10. #10591378C2semidirect
11. #10591345C2semidirect
12. #10591324C2semidirect
13. #10591307C2semidirect
14. #10591275C2semidirect
15. #10591249C2semidirect
71. #4961D3semidirect
80. #4950D3semidirect
137. #3724D4semidirect
458. C2×C3⋊D3#123semidirect
851. C32#2443semidirect
987. C3#74608semidirect
988. C3#77117semidirect

Maximal subgroups

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

subgroupindex
C2×#639612
C2×#639582
C2×#639522
C2×#639002
#105926552
C3×#49612
C3×#49502
#105916942
#105913872
#105913782
#105913452
#105913242
#105913072
#105912752
#105912492
#771173
#746083