Finite Group Databasebeta

← #11810335

Subgroups — #11810335

Order 1152.

1937 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63981C211yesmaximal, characteristic
3C2×#63969C211yesmaximal, characteristic, complemented
4C2×#63881C211yesmaximal, characteristic, complemented
5C3×#4959C211yesmaximal, characteristic, complemented
6C3×#4952C211yesmaximal, characteristic, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591703C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591364C211yesmaximal, characteristic, complemented
11#10591355C211yesmaximal, characteristic, complemented
12#10591292C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic, complemented
14#10591259C211yesmaximal, characteristic, complemented
15#10591203C211yesmaximal, characteristic, complemented
16#77669—31nomaximal
17#77111—31nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C22⋊C4×C3⋊D3—24no—
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37#63981—24no—
38#63969—24no—
39C2×#3724C2211yescharacteristic, complemented
40C2×#3724C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×#3722C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
49C2×Dic32C2211yescharacteristic, complemented
50#63881—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#937—31no—
58C2×#935—31no—
59C2×#893—31no—
60C2×#883—31no—
61C2×#882—31no—
62C2×#67⋊C4—31no—
63C2×D3×C22⋊C4—31no—
64C2×D3×C22⋊C4—31no—
65C2×D3×C22⋊C4—61no—
66C3×#397—31no—
67C3×#394—31no—
68#4993—31no—
69#4993—31no—
70#4989—31no—
71#4959—31no—
72#4959D311yescharacteristic, complemented
73#4958—31no—
74#4956—31no—
75#4955—31no—
76#4955—31no—
77#4952D311yescharacteristic, complemented
78#4945—31no—
79#4944—31no—
80#4672—31no—
81#4670—31no—
82#4669—31no—
83#4668—31no—
84#4667—31no—
85#4667—31no—
86#4665—31no—
87#4665—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3—22no—
90C23×C3⋊D3—22no—
91C23×C3⋊D3—22no—
92C23×C3⋊D3—22no—
93C23×C3⋊D3—22no—
94C23×C3⋊D3—41no—
95C23×C3⋊D3—41no—
96C23×C3⋊D3C2311yescharacteristic
97C23×C3⋊D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C2×C4×C3⋊D3—22no—
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—22no—
107C2×C4×C3⋊D3—41no—
108C2×C4×C3⋊D3—41no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—41no—
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#626—41no—
124C2×#626D414yes—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—41no—
128C32×C22⋊C4—22no—
129#3757D414yescomplemented
130#3752—22no—
131#3752—22no—
132C3×#217—22no—
133C3×#217—22no—
134C3×#217—41no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—41no—
137C3×Dic3⋊C4—22no—
138C3×Dic3⋊C4—41no—
139#3724—22no—
140#3724—41no—
141Dic3⋊Dic3—22no—
142#3722—22no—
143#3722—22no—
144#3722—22no—
145#3722—22no—
146#3722—22no—
147#3722—41no—
148(C2×D3)⋊Dic3—22no—
149Dic32—22no—
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C24×D3—61no—
154C22×C3×D4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67C2×D311yescharacteristic
158C23×Dic3—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—61no—
167C22×C4×D3—61no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C22⋊C4—21no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4C2×D311yescharacteristic
177C2×C3×C22⋊C4C2×D311yescharacteristic
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—61no—
182C2×#217C2×D311yescharacteristic
183C2×#217C2×D311yescharacteristic
184C2×#217C2×D311yescharacteristic
185#937—64no—
186#935—64no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
207C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
208C2×C4⋊Dic3—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4C2×D311yescharacteristic, complemented
215C2×Dic3⋊C4C2×D311yescharacteristic, complemented
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218#893—64no—
219#883—64no—
220#882—64no—
221#67⋊C4—64no—
222D3×C22⋊C4—64no—
223D3×C22⋊C4—64no—
224D3×C22⋊C4—68no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95C2×D311yescharacteristic, complemented
234C3⋊#95C2×D311yescharacteristic, complemented
235C3⋊#95C2×D311yescharacteristic, complemented
236C3⋊#95C2×D311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32C2×D412yes—
244C23×C32C2411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—28no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—44no—
257C22×C3⋊D3—44no—
258C22×C3⋊D3—44no—
259C22×C3⋊D3—44no—
260C22×C3⋊D3—44no—
261C22×C3⋊D3—44no—
262C22×C3⋊D3C2×D412yes—
263C22×C3⋊D3#4112yes—
264C22×C3⋊D3#4112yes—
265C22×C3⋊D3#4112yes—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3C2×D412yes—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3C2×D412yes—
284C2×C3⋊Dic3C2×D412yes—
285C4×C3⋊D3—44no—
286C4×C3⋊D3—44no—
287C3×#67—44no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
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—21no—
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×Dic3C2×D412yes—
309#626—28no—
310#626—44no—
311D3×Dic3—44no—
312C2×#123—91no—
313C2×#120—91no—
314C2×C4×D4—91no—
315C22×C22⋊C4—91no—
316#399—91no—
317#397—31no—
318#394—31no—
319#394—91no—
320#388—91no—
321#388—91no—
322#386—91no—
323#386—91no—
324#385—91no—
325#380—91no—
326#379—91no—
327C24×C3—21no—
328C24×C3—31no—
329C24×C3C22×D311yescharacteristic
330C24×C3C22×D311yescharacteristic
331C23×D3—31no—
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—61no—
336C23×D3—61no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—62no—
344C23×D3—62no—
345C23×D3—64no—
346C23×D3—64no—
347C23×D3—64no—
348C23×D3—62no—
349C23×D3—62no—
350C23×D3—122no—
351C23×D3—122no—
352C23×D3—121no—
353C23×D3—121no—
354C23×D3—121no—
355C23×D3—121no—
356C23×D3—122no—
357C23×D3—122no—
358C23×D3C22×D311yescharacteristic
359C2×C3×D4—62no—
360C2×C3×D4—62no—
361C2×C3×D4—121no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
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—31no—
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C2×#67—22no—
376C2×#67—22no—
377C2×#67—34no—
378C2×#67—41no—
379C2×#67—62no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—62no—
383C2×#67—121no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—62no—
391C22×Dic3—62no—
392C22×Dic3—121no—
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C2×D12—34no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—62no—
404C2×D12—62no—
405C2×D12—121no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—64no—
416C2×C4×D3—64no—
417C2×C4×D3—62no—
418C2×C4×D3—122no—
419C2×C4×D3—122no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C2×C4×D3—121no—
423C2×C4×D3—121no—
424C2×C4×D3—121no—
425C2×C4×D3—122no—
426C2×C4×D3—122no—
427C3×C4⋊C4—62no—
428C3×C4⋊C4—121no—
429C3×C22⋊C4—24no—
430C3×C22⋊C4—22no—
431C3×C22⋊C4—22no—
432C3×C22⋊C4—62no—
433C3×C22⋊C4—62no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—121no—
436C3×C22⋊C4—121no—
437#217—22no—
438#217—22no—
439#217—34no—
440#217—34no—
441#217—41no—
442#217—64no—
443#217—62no—
444(C2×D3)⋊C4—22no—
445(C2×D3)⋊C4—41no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—62no—
456(C2×D3)⋊C4—62no—
457(C2×D3)⋊C4—62no—
458(C2×D3)⋊C4—62no—
459(C2×D3)⋊C4—62no—
460(C2×D3)⋊C4—64no—
461(C2×D3)⋊C4—64no—
462(C2×D3)⋊C4—62no—
463(C2×D3)⋊C4—121no—
464(C2×D3)⋊C4—121no—
465C4⋊Dic3—62no—
466Dic3⋊C4—22no—
467Dic3⋊C4—41no—
468Dic3⋊C4—62no—
469Dic3⋊C4—62no—
470Dic3⋊C4—62no—
471Dic3⋊C4—121no—
472Dic3⋊C4—121no—
473C4×Dic3—62no—
474C4×Dic3—62no—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32C22×D411yescharacteristic
483C22×C32C22×D411yescharacteristic
484C22×C32C2×#4111yescharacteristic
485C22×C32C2×#4111yescharacteristic
486C22×C32C2×#4111yescharacteristic
487C22×C32H(5,𝔽2)11yescharacteristic
488C22×C32H(5,𝔽2)11yescharacteristic
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—22no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—416no—
499C2×C3⋊D3—41no—
500C2×C3⋊D3—41no—
501C2×C3⋊D3—41no—
502C2×C3⋊D3—41no—
503C2×C3⋊D3#12314yescomplemented
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—41no—
508C2×C3×D3—41no—
509C2×C3×D3—41no—
510C2×C3×D3—41no—
511C32×C4—41no—
512C32×C4—41no—
513C3⋊Dic3—22no—
514C3⋊Dic3—22no—
515C3×Dic3—22no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C3×Dic3—41no—
519C3×Dic3—41no—
520C3×Dic3—41no—
521C3×Dic3—41no—
522C25—91no—
523C22×D4—31no—
524C22×D4—91no—
525C22×D4—91no—
526C23×C4—91no—
527C23×C4—91no—
528C23×C4—91no—
529#123—184no—
530#120—184no—
531C4×D4—184no—
532C2×C4⋊C4—31no—
533C2×C4⋊C4—31no—
534C2×C4⋊C4—91no—
535C2×C4⋊C4—91no—
536C2×C4⋊C4—91no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—31no—
541C2×C22⋊C4—31no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—91no—
547C2×C22⋊C4—91no—
548C2×C22⋊C4—91no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—184no—
553C2×C22⋊C4D3211yescharacteristic
554C2×C42—91no—
555#95—31no—
556#95—31no—
557#95—31no—
558#95—31no—
559#95—91no—
560#95—91no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—22no—
577C23×C3—32no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3D3×D412yes—
589C23×C3D3×D412yes—
590C23×C3C23×D311yescharacteristic
591C23×C3C23×D311yescharacteristic
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—32no—
599C22×D3—32no—
600C22×D3—32no—
601C22×D3—32no—
602C22×D3—32no—
603C22×D3—32no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—62no—
607C22×D3—62no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—62no—
623C22×D3—616no—
624C22×D3—68no—
625C22×D3—68no—
626C22×D3—62no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—121no—
640C22×D3—121no—
641C22×D3—121no—
642C22×D3—121no—
643C22×D3—124no—
644C22×D3—124no—
645C22×D3—124no—
646C22×D3—124no—
647C22×D3—124no—
648C22×D3—124no—
649C22×D3—124no—
650C22×D3—124no—
651C22×D3—124no—
652C22×D3—124no—
653C22×D3—128no—
654C22×D3—128no—
655C22×D3—128no—
656C22×D3—128no—
657C22×D3—128no—
658C22×D3—128no—
659C22×D3—124no—
660C22×D3—124no—
661C22×D3D3×D412yes—
662C3×D4—124no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—32no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
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—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702#67—44no—
703#67—68no—
704#67—124no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
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—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—32no—
726C2×Dic3—32no—
727C2×Dic3—32no—
728C2×Dic3—32no—
729C2×Dic3—62no—
730C2×Dic3—62no—
731C2×Dic3—61no—
732C2×Dic3—61no—
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—124no—
744C2×Dic3D3×D412yes—
745D12—68no—
746D12—124no—
747C4×D3—124no—
748C4×D3—124no—
749C4×D3—124no—
750C4×D3—124no—
751C4×D3—124no—
752C4×D3—128no—
753C4×D3—128no—
754C2×C32—42no—
755C2×C32C2×#12311yescharacteristic
756C2×C32#52511yescharacteristic
757C2×C32#53811yescharacteristic
758C2×C32D4211yescharacteristic
759C2×C32#54611yescharacteristic
760C2×C32#54611yescharacteristic
761C2×C32#55111yescharacteristic
762C3⋊D3—24no—
763C3⋊D3—42no—
764C3×D3—42no—
765C24—31no—
766C24—91no—
767C24—91no—
768C24—182no—
769C24—182no—
770C24—182no—
771C24—182no—
772C24—182no—
773C24—361no—
774C24—361no—
775C24C2×D3211yescharacteristic
776C2×D4—62no—
777C2×D4—62no—
778C2×D4—94no—
779C2×D4—121no—
780C2×D4—182no—
781C2×D4—182no—
782C2×D4—182no—
783C2×D4—182no—
784C2×D4—361no—
785C22×C4—31no—
786C22×C4—31no—
787C22×C4—31no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—31no—
791C22×C4—31no—
792C22×C4—91no—
793C22×C4—91no—
794C22×C4—182no—
795C22×C4—182no—
796C22×C4—182no—
797C22×C4—182no—
798C22×C4—182no—
799C22×C4—182no—
800C22×C4—361no—
801C22×C4—361no—
802C22×C4—361no—
803C22×C4C2×D3211yescharacteristic
804C22×C4C2×D3211yescharacteristic
805C4⋊C4—62no—
806C4⋊C4—121no—
807C4⋊C4—182no—
808C4⋊C4—182no—
809C4⋊C4—361no—
810C22⋊C4—22no—
811C22⋊C4—62no—
812C22⋊C4—62no—
813C22⋊C4—62no—
814C22⋊C4—94no—
815C22⋊C4—121no—
816C22⋊C4—121no—
817C22⋊C4—182no—
818C22⋊C4—182no—
819C22⋊C4—182no—
820C22⋊C4—182no—
821C22⋊C4—182no—
822C22⋊C4—182no—
823C22⋊C4—182no—
824C22⋊C4—182no—
825C22⋊C4—361no—
826C42—182no—
827C22×C3—24no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3C2×D3×D411yescharacteristic
863C22×C3C2×D3×D411yescharacteristic
864C22×C3C2×D3×D411yescharacteristic
865C22×C3C2×D3×D411yescharacteristic
866C22×C3#100411yescharacteristic
867C22×C3#100411yescharacteristic
868C22×C3D3×#4111yescharacteristic
869C22×C3D3×#4111yescharacteristic
870C22×C3D3×#4111yescharacteristic
871C22×C3D3×#4111yescharacteristic
872C22×C3D3×#4111yescharacteristic
873C22×C3D3×#4111yescharacteristic
874C22×C3#100911yescharacteristic
875C22×C3#100911yescharacteristic
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—34no—
880C2×D3—34no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—64no—
886C2×D3—64no—
887C2×D3—64no—
888C2×D3—64no—
889C2×D3—64no—
890C2×D3—64no—
891C2×D3—64no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—62no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—64no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—62no—
908C2×D3—62no—
909C2×D3—62no—
910C2×D3—62no—
911C2×D3—122no—
912C2×D3—122no—
913C2×D3—1232no—
914C2×D3—1216no—
915C2×D3—1216no—
916C2×D3—122no—
917C2×D3—122no—
918C2×D3—122no—
919C2×D3—122no—
920C2×D3—121no—
921C2×D3—121no—
922C2×D3—121no—
923C2×D3—121no—
924C2×D3—121no—
925C2×D3—121no—
926C2×D3—121no—
927C2×D3—121no—
928C3×C4—42no—
929C3×C4—42no—
930C3×C4—41no—
931C3×C4—41no—
932C3×C4—41no—
933C3×C4—41no—
934C3×C4—62no—
935C3×C4—121no—
936C3×C4—121no—
937C3×C4—121no—
938C3×C4—121no—
939C3×C4—121no—
940C3×C4—121no—
941Dic3—22no—
942Dic3—41no—
943Dic3—41no—
944Dic3—41no—
945Dic3—41no—
946Dic3—41no—
947Dic3—41no—
948Dic3—62no—
949Dic3—62no—
950Dic3—62no—
951Dic3—62no—
952Dic3—122no—
953Dic3—122no—
954C32#241811yescharacteristic, complemented, Sylow
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—32no—
962C23—61no—
963C23—61no—
964C23—61no—
965C23—61no—
966C23—61no—
967C23—61no—
968C23—92no—
969C23—92no—
970C23—92no—
971C23—92no—
972C23—188no—
973C23—181no—
974C23—181no—
975C23—181no—
976C23—181no—
977C23—181no—
978C23—181no—
979C23—181no—
980C23—181no—
981C23—181no—
982C23—181no—
983C23—364no—
984C23—364no—
985C23—364no—
986C23—364no—
987C23—364no—
988C23—364no—
989C23#381112yes—
990C23C22×D3211yescharacteristic
991D4—124no—
992D4—188no—
993D4—364no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—32no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
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—181no—
1024C2×C4—181no—
1025C2×C4—181no—
1026C2×C4—181no—
1027C2×C4—364no—
1028C2×C4—364no—
1029C2×C4—364no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—44no—
1038C2×C3—42no—
1039C2×C3—42no—
1040C2×C3—122no—
1041C2×C3#559011yescharacteristic
1042C2×C3#560911yescharacteristic
1043C2×C3#561011yescharacteristic
1044C2×C3#561011yescharacteristic
1045C2×C3#561311yescharacteristic
1046C2×C3D3×#12311yescharacteristic
1047C2×C3D3×#12311yescharacteristic
1048C2×C3#565411yescharacteristic
1049C2×C3#565611yescharacteristic
1050C2×C3#565611yescharacteristic
1051C2×C3#567611yescharacteristic
1052C2×C3#567911yescharacteristic
1053C2×C3#570411yescharacteristic
1054C2×C3#570511yescharacteristic
1055D3—42no—
1056D3—68no—
1057D3—64no—
1058D3—64no—
1059D3—124no—
1060D3—122no—
1061D3—122no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—41no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—94no—
1073C22—121no—
1074C22—121no—
1075C22—121no—
1076C22—121no—
1077C22—182no—
1078C22—182no—
1079C22—182no—
1080C22—182no—
1081C22—182no—
1082C22—182no—
1083C22—182no—
1084C22—182no—
1085C22—182no—
1086C22—3616no—
1087C22—361no—
1088C22—361no—
1089C22—361no—
1090C22—361no—
1091C22#6430611yescharacteristic
1092C22#6430611yescharacteristic
1093C22D32×D411yescharacteristic
1094C22#6431211yescharacteristic
1095C22#6431411yescharacteristic
1096C22#6431411yescharacteristic
1097C22C2×#381111yescharacteristic
1098C4—41no—
1099C4—41no—
1100C4—62no—
1101C4—121no—
1102C4—121no—
1103C4—121no—
1104C4—121no—
1105C4—121no—
1106C4—121no—
1107C4—182no—
1108C4—182no—
1109C3—21no—
1110C3#7711111yescharacteristic, complemented
1111C3#7766911yescharacteristic, complemented
1112C2—42no—
1113C2—122no—
1114C2—184no—
1115C2—362no—
1116C2#1059415311yescharacteristic
1117C2#1059422611yescharacteristic
1118C2#1059426011yescharacteristic
1119C2#1059428511yescharacteristic
1120C2#1059492011yescharacteristic
1121C2#1059516311yescharacteristic
1122C2#1059529211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63981C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2418
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×C22⋊C4×C3⋊D3C2semidirect
3. C2×#63969C2semidirect
4. C2×#63881C2semidirect
5. C3×#4959C2semidirect
6. C3×#4952C2semidirect
7. #10591714C2semidirect
8. #10591703C2semidirect
9. #10591387C2semidirect
10. #10591364C2semidirect
11. #10591355C2semidirect
12. #10591292C2semidirect
13. #10591290C2semidirect
14. #10591259C2semidirect
15. #10591203C2semidirect
24. C22×D3×Dic3C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
39. C2×#3724C22semidirect
40. C2×#3724C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×Dic32C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
72. #4959D3semidirect
77. #4952D3semidirect
129. #3757D4semidirect
206. C2×(C2×D3)⋊C4C2×D3semidirect
207. C2×(C2×D3)⋊C4C2×D3semidirect
214. C2×Dic3⋊C4C2×D3semidirect
215. C2×Dic3⋊C4C2×D3semidirect
233. C3⋊#95C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
236. C3⋊#95C2×D3semidirect
503. C2×C3⋊D3#123semidirect
954. C32#2418semidirect
1110. C3#77111semidirect
1111. C3#77669semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×#639812
C2×#639692
C2×#638812
C3×#49592
C3×#49522
#105917142
#105917032
#105913872
#105913642
#105913552
#105912922
#105912902
#105912592
#105912032
#776693
#771113