Finite Group Databasebeta

← #11812905

Subgroups — #11812905

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#63910C211yesmaximal, characteristic
3C2×#63883C211yesmaximal, characteristic, complemented
4C2×#63853C211yesmaximal, characteristic, complemented
5C3×#4940C211yesmaximal, characteristic, complemented
6C3×#4933C211yesmaximal, characteristic, complemented
7#10591387C211yesmaximal, characteristic, complemented
8#10591380C211yesmaximal, characteristic, complemented
9#10591375C211yesmaximal, characteristic, complemented
10#10591353C211yesmaximal, characteristic, complemented
11#10591317C211yesmaximal, characteristic, complemented
12#10591312C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591208C211yesmaximal, characteristic, complemented
16#75848—31nomaximal
17#75319—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46#63910—24no—
47#63883—24no—
48#63853—24no—
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#895—31no—
58C2×#894—31no—
59C2×D3×C4⋊C4—31no—
60C2×D3×C4⋊C4—31no—
61C2×#884—31no—
62C2×#883—31no—
63C2×C4×D12—31no—
64C2×C4×D12—31no—
65C2×C4×D12—61no—
66C3×#388—31no—
67C3×#387—31no—
68#4989—31no—
69#4981—31no—
70#4961—31no—
71#4956—31no—
72#4956—31no—
73#4949—31no—
74#4940D311yescharacteristic, complemented
75#4933D311yescharacteristic, complemented
76#4677—31no—
77#4675—31no—
78#4674—31no—
79#4672—31no—
80#4668—31no—
81#4668—31no—
82#4668—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86#4665—31no—
87#4661—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)D414yes—
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—41no—
104C2×C4×C3⋊D3—41no—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×#626—22no—
113C2×#626—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—41no—
118C2×#624—22no—
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—22no—
123C2×#624—41no—
124C32×C42—22no—
125#3752—22no—
126#3752—22no—
127C4⋊(C3⋊Dic3)—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4D414yescomplemented
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—41no—
138#3722—22no—
139#3722—22no—
140#3722—22no—
141#3722—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—41no—
144#2443—91noSylow
145C22×#67—31no—
146C22×#67—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—61no—
152C22×C4×D3—31no—
153C22×C4×D3—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—
161C22×C4×D3—61no—
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×C22⋊C4—31no—
168C2×C3×C42—21no—
169C2×C3×C42C2×D311yescharacteristic
170C2×C3×C42C2×D311yescharacteristic
171C2×#217—31no—
172C2×#217—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
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—61no—
188C2×(C2×D3)⋊C4—61no—
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—61no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×Dic3⋊C4C2×D311yescharacteristic
205C2×Dic3⋊C4C2×D311yescharacteristic
206#895—64no—
207#894—64no—
208D3×C4⋊C4—64no—
209D3×C4⋊C4—64no—
210#884—64no—
211#883—64no—
212C4×D12—64no—
213C4×D12—64no—
214C4×D12—68no—
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⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C23×C32C2411yescharacteristic
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3C2×D412yes—
243C22×C3⋊D3C2×D412yes—
244C22×C3⋊D3#4112yes—
245C22×C3⋊D3#4112yes—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2×D412yes—
261C2×C32×C4C2×D412yes—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C4⋊(C3⋊D3)—28no—
269C4×C3⋊D3—44no—
270C4×C3⋊D3—44no—
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×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3#4112yes—
292#626—44no—
293#626—44no—
294#624—28no—
295#624—44no—
296C2×#123—91no—
297C2×#121—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300#399—91no—
301#398—91no—
302#397—91no—
303#394—91no—
304#388—31no—
305#387—31no—
306#386—91no—
307#386—91no—
308#386—91no—
309#385—91no—
310#385—91no—
311C24×C3—31no—
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—61no—
317C23×D3—61no—
318C23×D3C22×D311yescharacteristic
319C22×C3×C4—21no—
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×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—62no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—121no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C2×D12—34no—
355C2×D12—34no—
356C2×D12—64no—
357C2×D12—62no—
358C2×D12—62no—
359C2×D12—62no—
360C2×D12—62no—
361C2×D12—64no—
362C2×D12—64no—
363C2×D12—62no—
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—121no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—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—64no—
383C2×C4×D3—64no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—122no—
390C2×C4×D3—122no—
391C2×C4×D3—121no—
392C2×C4×D3—121no—
393C2×C4×D3—121no—
394C2×C4×D3—121no—
395C2×C4×D3—121no—
396C2×C4×D3—121no—
397C2×C4×D3—122no—
398C2×C4×D3—122no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—62no—
401C3×C4⋊C4—62no—
402C3×C22⋊C4—62no—
403C3×C22⋊C4—62no—
404C3×C22⋊C4—62no—
405C3×C42—24no—
406C3×C42—22no—
407C3×C42—22no—
408#217—62no—
409#217—121no—
410(C2×D3)⋊C4—22no—
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
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—62no—
423(C2×D3)⋊C4—64no—
424(C2×D3)⋊C4—64no—
425(C2×D3)⋊C4—62no—
426(C2×D3)⋊C4—62no—
427(C2×D3)⋊C4—62no—
428(C2×D3)⋊C4—121no—
429C4⋊Dic3—62no—
430C4⋊Dic3—64no—
431C4⋊Dic3—62no—
432C4⋊Dic3—62no—
433C4⋊Dic3—62no—
434C4⋊Dic3—62no—
435C4⋊Dic3—121no—
436Dic3⋊C4—22no—
437Dic3⋊C4—22no—
438Dic3⋊C4—62no—
439Dic3⋊C4—62no—
440Dic3⋊C4—62no—
441Dic3⋊C4—121no—
442Dic3⋊C4D1214yescomplemented
443C22×C32C22×D411yescharacteristic
444C22×C32C22×D411yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32H(5,𝔽2)11yescharacteristic
449C22×C322−1+411yescharacteristic
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
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—22no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3#12314yescomplemented
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C32×C4—22no—
472C32×C4—22no—
473C32×C4—41no—
474C3⋊Dic3—41no—
475C3⋊Dic3—41no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C3×Dic3—22no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C22×D4—91no—
484C22×D4—91no—
485C22×D4—91no—
486C23×C4—91no—
487C23×C4—91no—
488C23×C4—91no—
489C23×C4—91no—
490#123—184no—
491#121—184no—
492C4×D4—184no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—184no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C42D3211yescharacteristic
514#95—31no—
515#95—31no—
516#95—31no—
517#95—31no—
518#95—31no—
519#95—31no—
520#95—91no—
521#95—91no—
522C23×C3—21no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3C23×D311yescharacteristic
531C23×C3C23×D311yescharacteristic
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—32no—
540C22×D3—32no—
541C22×D3—32no—
542C22×D3—32no—
543C22×D3—32no—
544C22×D3—32no—
545C22×D3—32no—
546C22×D3—32no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—62no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—62no—
560C22×D3—62no—
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—121no—
574C22×D3—121no—
575C22×D3—121no—
576C22×D3—121no—
577C22×D3—121no—
578C22×D3—121no—
579C22×D3—121no—
580C22×D3—121no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—22no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—22no—
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—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—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×C4C2×D1212yes—
626C2×C3×C4D3×D412yes—
627C2×C3×C4D3×D412yes—
628C2×C3×C4D3×D412yes—
629#67—124no—
630#67—124no—
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—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—62no—
650C2×Dic3—62no—
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—61no—
663C2×Dic3—121no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3C2×D1212yes—
668C2×Dic3C2×D1212yes—
669C2×Dic3#23512yes—
670D12—68no—
671D12—68no—
672D12—616no—
673D12—124no—
674D12—124no—
675C4×D3—68no—
676C4×D3—68no—
677C4×D3—124no—
678C4×D3—124no—
679C4×D3—124no—
680C4×D3—124no—
681C4×D3—124no—
682C4×D3—124no—
683C4×D3—128no—
684C4×D3—128no—
685C2×C32C2×#12311yescharacteristic
686C2×C32#52511yescharacteristic
687C2×C32#53911yescharacteristic
688C2×C32D4211yescharacteristic
689C2×C32#54711yescharacteristic
690C2×C32#54811yescharacteristic
691C2×C32#55311yescharacteristic
692C3⋊D3—24no—
693C3⋊D3—42no—
694C3×D3—81no—
695C24—31no—
696C24—91no—
697C24—91no—
698C2×D4—94no—
699C2×D4—182no—
700C2×D4—182no—
701C2×D4—182no—
702C2×D4—182no—
703C2×D4—182no—
704C2×D4—182no—
705C2×D4—182no—
706C2×D4—361no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—91no—
715C22×C4—91no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—182no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—182no—
723C22×C4—182no—
724C22×C4—182no—
725C22×C4—361no—
726C22×C4—361no—
727C22×C4—361no—
728C22×C4C2×D3211yescharacteristic
729C22×C4C2×D3211yescharacteristic
730C22×C4C2×D3211yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—62no—
733C4⋊C4—62no—
734C4⋊C4—182no—
735C4⋊C4—182no—
736C4⋊C4—182no—
737C4⋊C4—182no—
738C4⋊C4—361no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—182no—
743C22⋊C4—182no—
744C22⋊C4—182no—
745C22⋊C4—182no—
746C22⋊C4—182no—
747C22⋊C4—182no—
748C22⋊C4—182no—
749C22⋊C4—361no—
750C42—22no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3C22×D1211yescharacteristic
766C22×C3C2×#23511yescharacteristic
767C22×C3C2×D3×D411yescharacteristic
768C22×C3C2×D3×D411yescharacteristic
769C22×C3C2×D3×D411yescharacteristic
770C22×C3#100711yescharacteristic
771C22×C3D3×#4111yescharacteristic
772C22×C3D3×#4111yescharacteristic
773C22×C3D3×#4111yescharacteristic
774C22×C3D3×#4111yescharacteristic
775C22×C3D3×#4111yescharacteristic
776C22×C3#100911yescharacteristic
777C22×C3#100911yescharacteristic
778C22×C3#101011yescharacteristic
779C2×D3—34no—
780C2×D3—34no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—64no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—64no—
802C2×D3—62no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—122no—
809C2×D3—122no—
810C2×D3—122no—
811C2×D3—122no—
812C2×D3—122no—
813C2×D3—122no—
814C2×D3—122no—
815C2×D3—122no—
816C2×D3—122no—
817C2×D3—122no—
818C2×D3—122no—
819C2×D3—122no—
820C2×D3—121no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—121no—
828C3×C4—24no—
829C3×C4—24no—
830C3×C4—22no—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—22no—
834C3×C4—42no—
835C3×C4—41no—
836C3×C4—41no—
837C3×C4—62no—
838C3×C4—62no—
839C3×C4—62no—
840C3×C4—121no—
841C3×C4—121no—
842C3×C4—121no—
843C3×C4—121no—
844Dic3—22no—
845Dic3—22no—
846Dic3—22no—
847Dic3—41no—
848Dic3—41no—
849Dic3—41no—
850Dic3—41no—
851Dic3—122no—
852Dic3—122no—
853Dic3—121no—
854Dic3—121no—
855Dic3—121no—
856Dic3—121no—
857C32#244311yescharacteristic, complemented, Sylow
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—92no—
866C23—92no—
867C23—92no—
868C23—92no—
869C23—181no—
870C23—181no—
871C23—181no—
872C23—181no—
873C23—181no—
874C23—181no—
875C23—181no—
876C23—181no—
877C23—181no—
878C23—181no—
879C23C22×D3211yescharacteristic
880D4—188no—
881D4—364no—
882D4—364no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—32no—
891C2×C4—32no—
892C2×C4—32no—
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—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—188no—
912C2×C4—181no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—364no—
919C2×C4—364no—
920C2×C4—364no—
921C2×C4D3×D1212yes—
922C2×C4#381112yes—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—241no—
931C2×C3#552411yescharacteristic
932C2×C3#553011yescharacteristic
933C2×C3#554711yescharacteristic
934C2×C3D4×D1211yescharacteristic
935C2×C3#555111yescharacteristic
936C2×C3#557611yescharacteristic
937C2×C3#560911yescharacteristic
938C2×C3#563111yescharacteristic
939C2×C3D3×#12311yescharacteristic
940C2×C3D3×#12311yescharacteristic
941C2×C3#567711yescharacteristic
942C2×C3#569211yescharacteristic
943C2×C3#570711yescharacteristic
944C2×C3#570911yescharacteristic
945D3—64no—
946D3—64no—
947D3—81no—
948D3—124no—
949D3—124no—
950D3—122no—
951D3—122no—
952C22—94no—
953C22—121no—
954C22—121no—
955C22—121no—
956C22—121no—
957C22—121no—
958C22—121no—
959C22—121no—
960C22—182no—
961C22—182no—
962C22—182no—
963C22—182no—
964C22—182no—
965C22—182no—
966C22—182no—
967C22—182no—
968C22—182no—
969C22—361no—
970C22—361no—
971C22—361no—
972C22—361no—
973C22#6429711yescharacteristic
974C22C2×D3×D1211yescharacteristic
975C22D3×#23511yescharacteristic
976C22#6430611yescharacteristic
977C22#6430611yescharacteristic
978C22#6430811yescharacteristic
979C22C2×#381111yescharacteristic
980C4—22no—
981C4—22no—
982C4—41no—
983C4—62no—
984C4—62no—
985C4—62no—
986C4—121no—
987C4—121no—
988C4—121no—
989C4—121no—
990C4—361no—
991C4—361no—
992C3—21no—
993C3#7531911yescharacteristic, complemented
994C3#7584811yescharacteristic, complemented
995C2—184no—
996C2—241no—
997C2—362no—
998C2#1059390111yescharacteristic
999C2#1059393711yescharacteristic
1000C2#1059394611yescharacteristic
1001C2#1059399711yescharacteristic
1002C2#1059483411yescharacteristic
1003C2#1059507411yescharacteristic
1004C2#1059507911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC2×#63910C2
hypercenterC2×C42D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. C2×#63883C2semidirect
4. C2×#63853C2semidirect
5. C3×#4940C2semidirect
6. C3×#4933C2semidirect
7. #10591387C2semidirect
8. #10591380C2semidirect
9. #10591375C2semidirect
10. #10591353C2semidirect
11. #10591317C2semidirect
12. #10591312C2semidirect
13. #10591290C2semidirect
14. #10591275C2semidirect
15. #10591208C2semidirect
74. #4940D3semidirect
75. #4933D3semidirect
133. C3×Dic3⋊C4D4semidirect
442. Dic3⋊C4D12semidirect
463. C2×C3⋊D3#123semidirect
857. C32#2443semidirect
993. C3#75319semidirect
994. C3#75848semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×#639102
C2×#638832
C2×#638532
C3×#49402
C3×#49332
#105913872
#105913802
#105913752
#105913532
#105913172
#105913122
#105912902
#105912752
#105912082
#758483
#753193