Finite Group Databasebeta

← #11812850

Subgroups — #11812850

Order 1152.

1467 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#63909C211yesmaximal, characteristic
3C2×#63904C211yesmaximal, characteristic, complemented
4C2×#63897C211yesmaximal, characteristic, complemented
5#10592690C211yesmaximal, characteristic, complemented
6C3×#4982C211yesmaximal, characteristic, complemented
7#10591382C211yesmaximal, characteristic, complemented
8#10591382C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591378C211yesmaximal, characteristic, complemented
11#10591277C211yesmaximal, characteristic, complemented
12#10591266C211yesmaximal, characteristic, complemented
13#10591262C211yesmaximal, characteristic, complemented
14#10591204C211yesmaximal, characteristic, complemented
15#10591203C211yesmaximal, characteristic, complemented
16#82195—31nomaximal
17#77951—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C3×D3×C4⋊C4—24no—
37C2×#3724C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46#63909—24no—
47#63904—24no—
48#63897—24no—
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C22×C3×C4⋊C4—31no—
58C2×#930—31no—
59C2×C4×#67—31no—
60C2×#895—31no—
61C2×#894—31no—
62C2×#894—31no—
63C2×#893—31no—
64C2×D3×C4⋊C4D311yescharacteristic, complemented
65C3×#398—31no—
66#5213—31no—
67#5213—31no—
68#5213—31no—
69#5210—31no—
70#4993—31no—
71#4993—31no—
72#4992—31no—
73#4991—31no—
74#4991—31no—
75#4991—61no—
76#4990—31no—
77#4989—31no—
78#4989—31no—
79#4982D311yescharacteristic, complemented
80#4980—31no—
81#4978—31no—
82#4675—31no—
83#4670—31no—
84#4668—31no—
85#4665—31no—
86#4665—31no—
87#4665—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)—41no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3—41no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626D414yes—
121C2×#624—22no—
122C2×#624—22no—
123C2×#624—41no—
124C32×C4⋊C4—22no—
125#3752—22no—
126#3752—22no—
127#3752—22no—
128#3752—41no—
129C3×C4⋊Dic3—22no—
130C3×C4⋊Dic3—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4D414yescomplemented
135#3724—41no—
136#3722—22no—
137#3722—22no—
138#3722—22no—
139#3722—22no—
140#3722—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143Dic32—22no—
144#2443—91noSylow
145C23×C3×C4—31no—
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—31no—
153C22×D12—31no—
154C22×D12—61no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3C2×D311yescharacteristic
158C22×C4×D3C2×D311yescharacteristic
159C22×C4×D3C2×D311yescharacteristic
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—64no—
168C2×C3×C4⋊C4C2×D311yescharacteristic
169C2×C3×C4⋊C4C2×D311yescharacteristic
170C2×#217—31no—
171C2×#217—31no—
172#930—64no—
173C4×#67—64no—
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—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—61no—
195C2×(C2×D3)⋊C4—61no—
196C2×(C2×D3)⋊C4—61no—
197C2×(C2×D3)⋊C4—61no—
198C2×C4⋊Dic3C2×D311yescharacteristic
199C2×C4⋊Dic3C2×D311yescharacteristic
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4C2×D311yescharacteristic
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×Dic3⋊C4C2×D311yescharacteristic
205C2×Dic3⋊C4C2×D311yescharacteristic
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208#895—64no—
209#894—64no—
210#894—64no—
211#893—64no—
212D3×C4⋊C4—24no—
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—31no—
226C3⋊#95—61no—
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C23×C32C2411yescharacteristic
231C22×C3⋊D3—21no—
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⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3C2×D412yes—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3C2×D412yes—
250C22×C3×D3#4112yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—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×C4C2×D412yes—
260C2×C32×C4#4112yes—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C4⋊(C3⋊D3)—44no—
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×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×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C3×C4×D3—28no—
290C3×C4×D3—44no—
291C3×C4×D3—44no—
292#626—28no—
293#626—44no—
294#624—44no—
295C2×#123—91no—
296C2×#121—91no—
297C2×C4×D4—91no—
298C22×C4⋊C4—31no—
299#399—91no—
300#398—31no—
301#397—91no—
302#394—91no—
303#388—91no—
304#387—91no—
305#386—91no—
306#386—91no—
307#386—91no—
308#385—91no—
309#385—91no—
310C24×C3—31no—
311C23×D3—31no—
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—61no—
316C23×D3—61no—
317C23×D3C22×D311yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
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—62no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4—121no—
336C22×C3×C4—121no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C2×#67—34no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C2×D12—34no—
363C2×D12—62no—
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—62no—
369C2×D12—62no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—122no—
373C2×D12—122no—
374C2×D12—121no—
375C2×D12—121no—
376C2×D12—122no—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—22no—
380C2×C4×D3—22no—
381C2×C4×D3—22no—
382C2×C4×D3—22no—
383C2×C4×D3—22no—
384C2×C4×D3—41no—
385C2×C4×D3—41no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—62no—
390C2×C4×D3—121no—
391C2×C4×D3—121no—
392C3×C4⋊C4—22no—
393C3×C4⋊C4—22no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—42no—
396C3×C4⋊C4—62no—
397C3×C4⋊C4—62no—
398C3×C4⋊C4—62no—
399C3×C4⋊C4—62no—
400C3×C4⋊C4—62no—
401#217—62no—
402#217—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
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—122no—
422(C2×D3)⋊C4—122no—
423(C2×D3)⋊C4—122no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—121no—
426(C2×D3)⋊C4—122no—
427C4⋊Dic3—22no—
428C4⋊Dic3—22no—
429Dic3⋊C4—22no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432Dic3⋊C4—121no—
433Dic3⋊C4—121no—
434Dic3⋊C4#6714yescomplemented
435C4×Dic3—62no—
436C4×Dic3—62no—
437C22×C32C22×D411yescharacteristic
438C22×C32C22×D411yescharacteristic
439C22×C32C2×#4111yescharacteristic
440C22×C32C2×#4111yescharacteristic
441C22×C32C2×#4111yescharacteristic
442C22×C32H(5,𝔽2)11yescharacteristic
443C22×C322−1+411yescharacteristic
444C2×C3⋊D3—22no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—22no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3#12314yescomplemented
465C32×C4—22no—
466C32×C4—22no—
467C32×C4—41no—
468C3⋊Dic3—41no—
469C3⋊Dic3—41no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C22×D4—91no—
478C22×D4—91no—
479C22×D4—91no—
480C23×C4—31no—
481C23×C4—31no—
482C23×C4—31no—
483C23×C4—91no—
484#123—184no—
485#121—184no—
486C4×D4—184no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—64no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4D3211yescharacteristic
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
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×C42—91no—
508#95—31no—
509#95—31no—
510#95—31no—
511#95—91no—
512#95—91no—
513#95—91no—
514#95—91no—
515#95—91no—
516C23×C3—21no—
517C23×C3—32no—
518C23×C3—32no—
519C23×C3—32no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3C23×D311yescharacteristic
525C23×C3C23×D311yescharacteristic
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—32no—
531C22×D3—32no—
532C22×D3—62no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—62no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
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—61no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—121no—
563C22×D3—121no—
564C22×D3—121no—
565C22×D3—121no—
566C22×D3—121no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—121no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3#23512yes—
573C22×D3D3×D412yes—
574C22×D3#23912yes—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
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—21no—
588C2×C3×C4—21no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—68no—
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—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—124no—
621C2×C3×C4—124no—
622C2×C3×C4#23512yes—
623C2×C3×C4D3×D412yes—
624C2×C3×C4#23912yes—
625C2×C3×C4C2×#6712yes—
626#67—68no—
627#67—124no—
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—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—61no—
647C2×Dic3—61no—
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—121no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—121no—
663C2×Dic3—121no—
664C2×Dic3D3×D412yes—
665C2×Dic3C2×#6712yes—
666C2×Dic3C2×#6712yes—
667D12—68no—
668D12—124no—
669D12—124no—
670D12—128no—
671D12—124no—
672C4×D3—28no—
673C4×D3—44no—
674C4×D3—44no—
675C4×D3—124no—
676C4×D3—124no—
677C2×C32C2×#12311yescharacteristic
678C2×C32#52511yescharacteristic
679C2×C32#53911yescharacteristic
680C2×C32D4211yescharacteristic
681C2×C32#54711yescharacteristic
682C2×C32#54811yescharacteristic
683C2×C32#55311yescharacteristic
684C3⋊D3—42no—
685C3⋊D3—81no—
686C3×D3—24no—
687C24—31no—
688C24—91no—
689C24—91no—
690C2×D4—94no—
691C2×D4—182no—
692C2×D4—182no—
693C2×D4—182no—
694C2×D4—182no—
695C2×D4—182no—
696C2×D4—182no—
697C2×D4—182no—
698C2×D4—361no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—62no—
709C22×C4—62no—
710C22×C4—62no—
711C22×C4—62no—
712C22×C4—62no—
713C22×C4—91no—
714C22×C4—91no—
715C22×C4—121no—
716C22×C4—121no—
717C22×C4—182no—
718C22×C4—182no—
719C22×C4—361no—
720C22×C4C2×D3211yescharacteristic
721C22×C4C2×D3211yescharacteristic
722C22×C4C2×D3211yescharacteristic
723C4⋊C4—22no—
724C4⋊C4—34no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—62no—
730C4⋊C4—361no—
731C22⋊C4—182no—
732C22⋊C4—182no—
733C22⋊C4—182no—
734C22⋊C4—182no—
735C22⋊C4—182no—
736C22⋊C4—182no—
737C22⋊C4—182no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—361no—
742C42—182no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—34no—
751C22×C3—62no—
752C22×C3—62no—
753C22×C3—62no—
754C22×C3—62no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3C2×#23511yescharacteristic
758C22×C3C2×#23511yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C22×C3C2×D3×D411yescharacteristic
762C22×C3#100411yescharacteristic
763C22×C3C2×#23911yescharacteristic
764C22×C3C2×#23911yescharacteristic
765C22×C3#100711yescharacteristic
766C22×C3#100711yescharacteristic
767C22×C3D3×#4111yescharacteristic
768C22×C3D3×#4111yescharacteristic
769C22×C3#100911yescharacteristic
770C22×C3C22×#6711yescharacteristic
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—62no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—62no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—122no—
784C2×D3—122no—
785C2×D3—122no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—122no—
795C2×D3—122no—
796C2×D3—122no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—121no—
811C2×D3—241no—
812C2×D3—241no—
813C2×D3—241no—
814C2×D3—241no—
815C2×D3—241no—
816C2×D3—241no—
817C2×D3—241no—
818C2×D3—241no—
819C2×D3#89414yescomplemented
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—42no—
825C3×C4—42no—
826C3×C4—41no—
827C3×C4—41no—
828C3×C4—62no—
829C3×C4—62no—
830C3×C4—62no—
831C3×C4—81no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4—121no—
835C3×C4—121no—
836Dic3—22no—
837Dic3—22no—
838Dic3—22no—
839Dic3—41no—
840Dic3—41no—
841Dic3—41no—
842Dic3—41no—
843Dic3—121no—
844Dic3—121no—
845Dic3—121no—
846Dic3—121no—
847Dic3—241no—
848Dic3—241no—
849C32#244311yescharacteristic, complemented, Sylow
850C23—32no—
851C23—32no—
852C23—32no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—92no—
858C23—181no—
859C23—181no—
860C23—181no—
861C23—181no—
862C23—181no—
863C23—181no—
864C23—181no—
865C23—181no—
866C23—181no—
867C23—181no—
868C23—181no—
869C23—181no—
870C23—181no—
871C23C22×D3211yescharacteristic
872D4—188no—
873D4—364no—
874D4—364no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—32no—
885C2×C4—68no—
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—61no—
904C2×C4—124no—
905C2×C4—124no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—364no—
913C2×C4#379912yes—
914C2×C4D3×#6712yes—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—64no—
923C2×C3C2×#89411yescharacteristic
924C2×C3#550711yescharacteristic
925C2×C3#551411yescharacteristic
926C2×C3#551511yescharacteristic
927C2×C3#560911yescharacteristic
928C2×C3#562711yescharacteristic
929C2×C3#563311yescharacteristic
930C2×C3D3×#12311yescharacteristic
931C2×C3#569211yescharacteristic
932C2×C3#569511yescharacteristic
933C2×C3#572611yescharacteristic
934C2×C3#579111yescharacteristic
935C2×C3D4×#6711yescharacteristic
936C2×C3#581711yescharacteristic
937D3—24no—
938D3—122no—
939D3—122no—
940D3—242no—
941D3—242no—
942D3—241no—
943D3—241no—
944C22—34no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—182no—
952C22—182no—
953C22—182no—
954C22—361no—
955C22—361no—
956C22—361no—
957C22—361no—
958C22—361no—
959C22—361no—
960C22—361no—
961C22—361no—
962C22—361no—
963C22—361no—
964C22—361no—
965C22C2×#379911yescharacteristic
966C22D3×#23511yescharacteristic
967C22D32×D411yescharacteristic
968C22#6431411yescharacteristic
969C22#6431611yescharacteristic
970C22D3×#23911yescharacteristic
971C22C2×D3×#6711yescharacteristic
972C4—22no—
973C4—22no—
974C4—41no—
975C4—62no—
976C4—62no—
977C4—62no—
978C4—121no—
979C4—121no—
980C4—121no—
981C4—121no—
982C4—361no—
983C4—361no—
984C3—21no—
985C3#7795111yescharacteristic, complemented
986C3#8219511yescharacteristic, complemented
987C2—64no—
988C2—362no—
989C2—721no—
990C2#1059451711yescharacteristic
991C2#1059454211yescharacteristic
992C2#1059456211yescharacteristic
993C2D3×#89411yescharacteristic
994C2#1059500511yescharacteristic
995C2#1059529111yescharacteristic
996C2#1059540211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63909C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C4⋊C4C2semidirect
3. C2×#63904C2semidirect
4. C2×#63897C2semidirect
5. #10592690C2semidirect
6. C3×#4982C2semidirect
7. #10591382C2semidirect
8. #10591382C2semidirect
9. #10591382C2semidirect
10. #10591378C2semidirect
11. #10591277C2semidirect
12. #10591266C2semidirect
13. #10591262C2semidirect
14. #10591204C2semidirect
15. #10591203C2semidirect
64. C2×D3×C4⋊C4D3semidirect
79. #4982D3semidirect
134. C3×Dic3⋊C4D4semidirect
434. Dic3⋊C4#67semidirect
464. C2×C3×D3#123semidirect
819. C2×D3#894semidirect
849. C32#2443semidirect
985. C3#77951semidirect
986. C3#82195semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×#639092
C2×#639042
C2×#638972
#105926902
C3×#49822
#105913822
#105913782
#105912772
#105912662
#105912622
#105912042
#105912032
#821953
#779513