Finite Group Databasebeta

← #11812920

Subgroups — #11812920

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic
2C2×#63975C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C2×#63883C211yesmaximal, characteristic, complemented
5C3×#4949C211yesmaximal, characteristic, complemented
6C3×#4944C211yesmaximal, characteristic, complemented
7#10591722C211yesmaximal, characteristic, complemented
8#10591722C211yesmaximal, characteristic, complemented
9#10591712C211yesmaximal, characteristic, complemented
10#10591380C211yesmaximal, characteristic, complemented
11#10591374C211yesmaximal, characteristic, complemented
12#10591358C211yesmaximal, characteristic, complemented
13#10591332C211yesmaximal, characteristic, complemented
14#10591290C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic, complemented
16#78103—31nomaximal
17#75848—31nomaximal
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28#64093—24no—
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38#63975—24no—
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47#63894—24no—
48#63883—24no—
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#893—31no—
58C2×D3×C4⋊C4—31no—
59C2×D3×C4⋊C4—31no—
60C2×#884—31no—
61C2×#884—31no—
62C2×#884—61no—
63C2×#883—31no—
64C2×#883—31no—
65C2×C4×D12—31no—
66C3×#399—31no—
67C3×#388—31no—
68#4992—31no—
69#4989—31no—
70#4989—31no—
71#4989—31no—
72#4983—31no—
73#4961—31no—
74#4959—31no—
75#4956—31no—
76#4956—31no—
77#4956—31no—
78#4956—31no—
79#4949D311yescharacteristic, complemented
80#4944D311yescharacteristic, complemented
81#4933—31no—
82#4675—31no—
83#4668—31no—
84#4665—31no—
85#4665—31no—
86#4661—31no—
87#4653—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—22no—
98C2×#638—41no—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)D414yes—
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—41no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—41no—
123C2×#624—41no—
124C32×C22⋊C4—22no—
125#3752—22no—
126#3750—22no—
127C3×#217—22no—
128C3×#217—22no—
129C3×#217—22no—
130C3×#217—41no—
131C3×C4⋊Dic3—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—41no—
135C3×C4×Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3D414yescomplemented
139#3722—22no—
140#3722—22no—
141#3722—22no—
142#3722—22no—
143#3722—22no—
144#2443—91noSylow
145C22×#67—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—61no—
150C22×#67—61no—
151C22×D12—31no—
152C22×D12—31no—
153C22×D12—61no—
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—31no—
161C22×C4×D3—31no—
162C22×C4×D3—61no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—21no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×C3×C22⋊C4C2×D311yescharacteristic
174C2×C3×C42—31no—
175C2×#217C2×D311yescharacteristic
176C2×#217C2×D311yescharacteristic
177C2×#217C2×D311yescharacteristic
178C2×#217C2×D311yescharacteristic
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—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—31no—
191C2×(C2×D3)⋊C4—61no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3C2×D311yescharacteristic
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×Dic3⋊C4C2×D311yescharacteristic
205C2×C4×Dic3C2×D311yescharacteristic
206#893—64no—
207D3×C4⋊C4—64no—
208D3×C4⋊C4—64no—
209#884—64no—
210#884—64no—
211#884—68no—
212#883—64no—
213#883—64no—
214C4×D12—64no—
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—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32C2411yescharacteristic
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⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3C2×D412yes—
250C22×C3⋊D3C2×D412yes—
251C22×C3⋊D3#4112yes—
252C22×C3⋊D3#4112yes—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C2×D412yes—
259#638—44no—
260#638—44no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D412yes—
267C4⋊(C3⋊D3)—28no—
268C4×C3⋊D3—44no—
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×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—21no—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3#4112yes—
293#624—28no—
294#624—44no—
295#624—44no—
296C2×#123—91no—
297C2×#121—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300#399—31no—
301#398—91no—
302#397—91no—
303#394—91no—
304#388—31no—
305#387—91no—
306#386—91no—
307#386—91no—
308#386—91no—
309#385—91no—
310#385—91no—
311C24×C3—21no—
312C24×C3C22×D311yescharacteristic
313C24×C3C22×D311yescharacteristic
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—31no—
317C23×D3—31no—
318C23×D3—61no—
319C23×D3—61no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
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×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C2×#67—62no—
335C2×#67—62no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—64no—
345C2×#67—64no—
346C2×#67—122no—
347C2×#67—122no—
348C2×#67—122no—
349C2×#67—121no—
350C2×#67—121no—
351C2×#67—122no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C2×D12—34no—
367C2×D12—34no—
368C2×D12—64no—
369C2×D12—62no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—122no—
374C2×D12—122no—
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—62no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—64no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—122no—
395C2×C4×D3—121no—
396C2×C4×D3—121no—
397C2×C4×D3—121no—
398C2×C4×D3—121no—
399C2×C4×D3—121no—
400C2×C4×D3—121no—
401C2×C4×D3—122no—
402C3×C4⋊C4—62no—
403C3×C4⋊C4—62no—
404C3×C4⋊C4—62no—
405C3×C4⋊C4—121no—
406C3×C22⋊C4—24no—
407C3×C22⋊C4—22no—
408C3×C22⋊C4—22no—
409C3×C22⋊C4—62no—
410C3×C22⋊C4—62no—
411C3×C22⋊C4—62no—
412C3×C22⋊C4—121no—
413C3×C42—62no—
414#217—22no—
415#217—22no—
416#217—22no—
417#217—41no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—62no—
422(C2×D3)⋊C4—62no—
423(C2×D3)⋊C4—62no—
424(C2×D3)⋊C4—62no—
425(C2×D3)⋊C4—62no—
426(C2×D3)⋊C4—62no—
427(C2×D3)⋊C4—62no—
428(C2×D3)⋊C4—64no—
429(C2×D3)⋊C4—62no—
430(C2×D3)⋊C4—62no—
431C4⋊Dic3—22no—
432C4⋊Dic3—34no—
433C4⋊Dic3—62no—
434C4⋊Dic3—62no—
435Dic3⋊C4—22no—
436Dic3⋊C4—22no—
437Dic3⋊C4—34no—
438Dic3⋊C4—41no—
439Dic3⋊C4—62no—
440Dic3⋊C4—62no—
441Dic3⋊C4—64no—
442Dic3⋊C4—62no—
443Dic3⋊C4—62no—
444C4×Dic3—22no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32C22×D411yescharacteristic
453C22×C32C22×D411yescharacteristic
454C22×C32C2×#4111yescharacteristic
455C22×C32C2×#4111yescharacteristic
456C22×C32C2×#4111yescharacteristic
457C22×C32H(5,𝔽2)11yescharacteristic
458C22×C322−1+411yescharacteristic
459C2×C3⋊D3—22no—
460C2×C3⋊D3—22no—
461C2×C3⋊D3—22no—
462C2×C3⋊D3—22no—
463C2×C3⋊D3—22no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—22no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3#12314yescomplemented
473C32×C4—22no—
474C32×C4—41no—
475C3⋊Dic3—22no—
476C3⋊Dic3—41no—
477C3×Dic3—22no—
478C3×Dic3—22no—
479C3×Dic3—22no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C22×D4—91no—
486C22×D4—91no—
487C22×D4—91no—
488C23×C4—91no—
489C23×C4—91no—
490C23×C4—91no—
491C23×C4—91no—
492#123—184no—
493#121—184no—
494C4×D4—184no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—184no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4D3211yescharacteristic
515C2×C42—31no—
516#95—31no—
517#95—31no—
518#95—31no—
519#95—91no—
520#95—91no—
521#95—91no—
522#95—91no—
523#95—91no—
524C23×C3—22no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3C23×D311yescharacteristic
547C23×C3C23×D311yescharacteristic
548C22×D3—32no—
549C22×D3—32no—
550C22×D3—32no—
551C22×D3—32no—
552C22×D3—32no—
553C22×D3—32no—
554C22×D3—32no—
555C22×D3—32no—
556C22×D3—62no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—61no—
561C22×D3—61no—
562C22×D3—61no—
563C22×D3—61no—
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—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—121no—
581C22×D3—121no—
582C22×D3—121no—
583C22×D3—121no—
584C22×D3—121no—
585C22×D3—121no—
586C22×D3—121no—
587C22×D3—121no—
588C22×D3—121no—
589C22×D3—121no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—22no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—22no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
604C2×C3×C4—32no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4D3×D412yes—
631C2×C3×C4D3×D412yes—
632#67—124no—
633#67—124no—
634#67—128no—
635#67—124no—
636#67—124no—
637#67—128no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—62no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—121no—
676C2×Dic3—121no—
677C2×Dic3#23512yes—
678C2×Dic3D3×D412yes—
679C2×Dic3D3×D412yes—
680D12—68no—
681D12—68no—
682D12—128no—
683C4×D3—68no—
684C4×D3—68no—
685C4×D3—124no—
686C4×D3—124no—
687C4×D3—124no—
688C4×D3—124no—
689C4×D3—124no—
690C4×D3—124no—
691C4×D3—128no—
692C2×C32—81no—
693C2×C32C2×#12311yescharacteristic
694C2×C32#52511yescharacteristic
695C2×C32#53911yescharacteristic
696C2×C32D4211yescharacteristic
697C2×C32#54711yescharacteristic
698C2×C32#54811yescharacteristic
699C2×C32#55311yescharacteristic
700C3⋊D3—24no—
701C3⋊D3—42no—
702C24—91no—
703C24—91no—
704C24C2×D3211yescharacteristic
705C2×D4—94no—
706C2×D4—182no—
707C2×D4—182no—
708C2×D4—182no—
709C2×D4—182no—
710C2×D4—182no—
711C2×D4—182no—
712C2×D4—182no—
713C2×D4—361no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—91no—
723C22×C4—91no—
724C22×C4—182no—
725C22×C4—182no—
726C22×C4—182no—
727C22×C4—182no—
728C22×C4—182no—
729C22×C4—182no—
730C22×C4—182no—
731C22×C4—182no—
732C22×C4—182no—
733C22×C4—361no—
734C22×C4—361no—
735C22×C4—361no—
736C22×C4C2×D3211yescharacteristic
737C22×C4C2×D3211yescharacteristic
738C4⋊C4—62no—
739C4⋊C4—62no—
740C4⋊C4—62no—
741C4⋊C4—94no—
742C4⋊C4—121no—
743C4⋊C4—182no—
744C4⋊C4—182no—
745C4⋊C4—182no—
746C22⋊C4—22no—
747C22⋊C4—62no—
748C22⋊C4—62no—
749C22⋊C4—62no—
750C22⋊C4—121no—
751C22⋊C4—182no—
752C22⋊C4—182no—
753C22⋊C4—182no—
754C22⋊C4—182no—
755C22⋊C4—182no—
756C22⋊C4—182no—
757C42—62no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3C2×#23511yescharacteristic
787C22×C3C2×D3×D411yescharacteristic
788C22×C3C2×D3×D411yescharacteristic
789C22×C3C2×D3×D411yescharacteristic
790C22×C3C2×D3×D411yescharacteristic
791C22×C3#100411yescharacteristic
792C22×C3#100711yescharacteristic
793C22×C3D3×#4111yescharacteristic
794C22×C3D3×#4111yescharacteristic
795C22×C3D3×#4111yescharacteristic
796C22×C3D3×#4111yescharacteristic
797C22×C3D3×#4111yescharacteristic
798C22×C3#100911yescharacteristic
799C22×C3#101011yescharacteristic
800C2×D3—34no—
801C2×D3—34no—
802C2×D3—64no—
803C2×D3—62no—
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—62no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—122no—
822C2×D3—122no—
823C2×D3—122no—
824C2×D3—122no—
825C2×D3—122no—
826C2×D3—122no—
827C2×D3—122no—
828C2×D3—122no—
829C2×D3—122no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3—241no—
841C2×D3—241no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—42no—
845C3×C4—42no—
846C3×C4—41no—
847C3×C4—41no—
848C3×C4—62no—
849C3×C4—62no—
850C3×C4—62no—
851C3×C4—121no—
852C3×C4—121no—
853C3×C4—121no—
854C3×C4—121no—
855C3×C4—121no—
856Dic3—22no—
857Dic3—22no—
858Dic3—22no—
859Dic3—41no—
860Dic3—41no—
861Dic3—41no—
862Dic3—41no—
863Dic3—41no—
864Dic3—64no—
865Dic3—62no—
866Dic3—62no—
867Dic3—122no—
868Dic3—121no—
869Dic3—121no—
870C32#244311yescharacteristic, complemented, Sylow
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—92no—
879C23—92no—
880C23—92no—
881C23—92no—
882C23—181no—
883C23—181no—
884C23—181no—
885C23—181no—
886C23—181no—
887C23—181no—
888C23—181no—
889C23—181no—
890C23—181no—
891C23—181no—
892C23C22×D3211yescharacteristic
893D4—188no—
894D4—364no—
895D4—364no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—32no—
902C2×C4—32no—
903C2×C4—32no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—92no—
926C2×C4—188no—
927C2×C4—181no—
928C2×C4—181no—
929C2×C4—181no—
930C2×C4—181no—
931C2×C4—181no—
932C2×C4—364no—
933C2×C4—364no—
934C2×C4—364no—
935C2×C4#381112yes—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—82no—
944C2×C3—81no—
945C2×C3—81no—
946C2×C3#553011yescharacteristic
947C2×C3#554711yescharacteristic
948C2×C3#555111yescharacteristic
949C2×C3#560911yescharacteristic
950C2×C3#563111yescharacteristic
951C2×C3#563311yescharacteristic
952C2×C3#563811yescharacteristic
953C2×C3D3×#12311yescharacteristic
954C2×C3D3×#12311yescharacteristic
955C2×C3#565611yescharacteristic
956C2×C3#566111yescharacteristic
957C2×C3#567711yescharacteristic
958C2×C3#570711yescharacteristic
959C2×C3#571711yescharacteristic
960D3—64no—
961D3—64no—
962D3—124no—
963D3—122no—
964D3—122no—
965D3—242no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—94no—
974C22—182no—
975C22—182no—
976C22—182no—
977C22—182no—
978C22—182no—
979C22—182no—
980C22—182no—
981C22—182no—
982C22—182no—
983C22—361no—
984C22—361no—
985C22—361no—
986C22—361no—
987C22#6429711yescharacteristic
988C22D3×#23511yescharacteristic
989C22D32×D411yescharacteristic
990C22#6431211yescharacteristic
991C22#6431211yescharacteristic
992C22#6431411yescharacteristic
993C22C2×#381111yescharacteristic
994C4—22no—
995C4—41no—
996C4—62no—
997C4—62no—
998C4—62no—
999C4—121no—
1000C4—121no—
1001C4—121no—
1002C4—121no—
1003C4—121no—
1004C4—182no—
1005C4—361no—
1006C3—21no—
1007C3#7584811yescharacteristic, complemented
1008C3#7810311yescharacteristic, complemented
1009C2—81no—
1010C2—184no—
1011C2—362no—
1012C2#1059407511yescharacteristic
1013C2#1059416711yescharacteristic
1014C2#1059420411yescharacteristic
1015C2#1059426611yescharacteristic
1016C2#1059483411yescharacteristic
1017C2#1059516911yescharacteristic
1018C2#1059529711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#64093C2
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
2. C2×#63975C2semidirect
3. C2×#63894C2semidirect
4. C2×#63883C2semidirect
5. C3×#4949C2semidirect
6. C3×#4944C2semidirect
7. #10591722C2semidirect
8. #10591722C2semidirect
9. #10591712C2semidirect
10. #10591380C2semidirect
11. #10591374C2semidirect
12. #10591358C2semidirect
13. #10591332C2semidirect
14. #10591290C2semidirect
15. #10591204C2semidirect
79. #4949D3semidirect
80. #4944D3semidirect
138. Dic3⋊Dic3D4semidirect
472. C2×C3⋊D3#123semidirect
870. C32#2443semidirect
1007. C3#75848semidirect
1008. C3#78103semidirect

Maximal subgroups

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

subgroupindex
C2×#640932
C2×#639752
C2×#638942
C2×#638832
C3×#49492
C3×#49442
#105917222
#105917122
#105913802
#105913742
#105913582
#105913322
#105912902
#105912042
#781033
#758483