Finite Group Databasebeta

← #11803612

Subgroups — #11803612

Order 1152.

1479 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63910C211yesmaximal, characteristic
2C2×C4×#626C211yesmaximal, characteristic, complemented
3C2×#63836C211yesmaximal, characteristic, complemented
4#10592364C211yesmaximal, characteristic, complemented
5C3×#4668C211yesmaximal, characteristic, complemented
6C3×#4649C211yesmaximal, characteristic, complemented
7#10591384C211yesmaximal, characteristic, complemented
8#10591383C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591367C211yesmaximal, characteristic, complemented
11#10591320C211yesmaximal, characteristic, complemented
12#10591305C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic, complemented
14#10591265C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#74385—31nomaximal
17#73763—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63910C418yescomplemented
48C4×#626—24no—
49#63836—24no—
50C32×#95C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C4×#67—31no—
57C2×#895—31no—
58C2×#892—31no—
59C2×#884—31no—
60C2×C4×D12—31no—
61C2×#872—31no—
62C3×#385—31no—
63C3×C4×C4⋊C4—31no—
64#5213—31no—
65#4989—31no—
66#4988—31no—
67#4988—31no—
68#4987—31no—
69#4984—31no—
70#4976—31no—
71#4957—31no—
72#4957—31no—
73#4951—31no—
74#4940—31no—
75#4940—31no—
76#4939—31no—
77#4939—31no—
78#4670—31no—
79#4668—31no—
80#4668D311yescharacteristic, complemented
81#4667—31no—
82#4665—31no—
83#4665—31no—
84#4665—31no—
85#4665—61no—
86#4649D311yescharacteristic, complemented
87C23×C3⋊D3C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—41no—
96C2×C4⋊(C3⋊D3)—41no—
97C2×C4⋊(C3⋊D3)C2×C414yescomplemented
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—41no—
100C2×C4×C3⋊D3—41no—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—41no—
110C2×C3×C4×D3—41no—
111C2×#626—22no—
112C2×#626—22no—
113C2×#626—41no—
114C2×#626—41no—
115C2×#626C2×C414yes—
116C2×#626C2×C414yescomplemented
117C2×#624—22no—
118C2×#624—22no—
119C2×#624C2×C414yescomplemented
120#3752—22no—
121#3752—41no—
122#3752—41no—
123C3×(C2×D3)⋊C4—41no—
124C3×(C2×D3)⋊C4C2×C414yescomplemented
125C3×C4⋊Dic3—41no—
126C3×Dic3⋊C4—22no—
127C3×Dic3⋊C4—22no—
128C3×Dic3⋊C4C2×C414yescomplemented
129C3×C4×Dic3—41no—
130C3×C4×Dic3—41no—
131C3×C4×Dic3D414yescomplemented
132Dic3⋊Dic3—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—41no—
135#3722—22no—
136#3722—22no—
137#3722—41no—
138#3722—41no—
139#3722C2×C414yescomplemented
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—41no—
142Dic32—22no—
143#2324—91noSylow
144C23×C3×C4—31no—
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—61no—
157C22×C4×D3C2×D311yescharacteristic
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C42—31no—
165C2×C3×C42—31no—
166C2×C3×C42—31no—
167C2×#217—31no—
168C2×#217—31no—
169C4×#67—64no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—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—31no—
188C2×(C2×D3)⋊C4—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3C2×D311yescharacteristic
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4C2×D311yescharacteristic
201C2×Dic3⋊C4C2×D311yescharacteristic
202C2×Dic3⋊C4C2×D311yescharacteristic
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3C2×D311yescharacteristic
206C2×C4×Dic3C2×D311yescharacteristic
207C2×C4×Dic3C2×D311yescharacteristic
208#895—38no—
209#892—64no—
210#884—38no—
211C4×D12—64no—
212#872—64no—
213C3×#95—21no—
214C3×#95—31no—
215C3×#95—31no—
216C3×#95C2×D311yescharacteristic
217C3×#95C2×D311yescharacteristic
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—61no—
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C23×C32C2411yescharacteristic
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
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⋊D3C22×C412yes—
241C22×C3⋊D3C22×C412yes—
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×D3C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C22×C412yes—
257C2×C32×C4C2×D412yes—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C4⋊(C3⋊D3)—44no—
265C4×C3⋊D3—44no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
282C2×C3×Dic3C22×C412yes—
283C2×C3×Dic3C22×C412yes—
284C2×C3×Dic3C2×D412yes—
285C2×C3×Dic3C2×D412yes—
286C2×C3×Dic3#4112yes—
287C3×C4×D3—44no—
288#626—28no—
289#626—44no—
290#624—28no—
291C2×#121—91no—
292C2×C4×D4—91no—
293C2×#117—91no—
294#390—91no—
295#390—91no—
296#390—91no—
297#389—91no—
298#388—91no—
299#388—91no—
300#386—91no—
301#386—91no—
302#385—31no—
303#385—91no—
304#380—91no—
305C4×C4⋊C4—31no—
306C24×C3—31no—
307C23×D3—31no—
308C23×D3—31no—
309C23×D3—31no—
310C23×D3—31no—
311C23×D3—61no—
312C23×D3—61no—
313C23×D3C22×D311yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—62no—
325C22×C3×C4—121no—
326C22×C3×C4—121no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—34no—
334C2×#67—34no—
335C2×#67—62no—
336C2×#67—62no—
337C2×#67—121no—
338C2×#67—121no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C2×D12—34no—
353C2×D12—34no—
354C2×D12—34no—
355C2×D12—34no—
356C2×D12—64no—
357C2×D12—62no—
358C2×D12—62no—
359C2×D12—121no—
360C2×D12—121no—
361C2×D12—121no—
362C2×D12—121no—
363C2×D12—122no—
364C2×D12—122no—
365C2×D12—121no—
366C2×D12—121no—
367C2×C4×D3—22no—
368C2×C4×D3—34no—
369C2×C4×D3—34no—
370C2×C4×D3—41no—
371C2×C4×D3—41no—
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—122no—
379C2×C4×D3—121no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C2×C4×D3—121no—
383C2×C4×D3—122no—
384C2×C4×D3—122no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—62no—
387C3×C4⋊C4—62no—
388C3×C4⋊C4—121no—
389C3×C22⋊C4—34no—
390C3×C22⋊C4—121no—
391C3×C42—34no—
392C3×C42—121no—
393C3×C42—121no—
394#217—62no—
395#217—121no—
396(C2×D3)⋊C4—34no—
397(C2×D3)⋊C4—34no—
398(C2×D3)⋊C4—41no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—122no—
407(C2×D3)⋊C4—121no—
408(C2×D3)⋊C4—121no—
409(C2×D3)⋊C4—121no—
410(C2×D3)⋊C4—121no—
411(C2×D3)⋊C4—121no—
412(C2×D3)⋊C4—121no—
413(C2×D3)⋊C4—121no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4—122no—
416(C2×D3)⋊C4—121no—
417(C2×D3)⋊C4—122no—
418(C2×D3)⋊C4C4×D314yescomplemented
419C4⋊Dic3—41no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422C4⋊Dic3—121no—
423Dic3⋊C4—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—121no—
428Dic3⋊C4C4×D314yescomplemented
429C4×Dic3—41no—
430C4×Dic3—41no—
431C4×Dic3—62no—
432C4×Dic3—62no—
433C4×Dic3D1214yescomplemented
434C22×C32C23×C411yescharacteristic
435C22×C32C22×D411yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32H(5,𝔽2)11yescharacteristic
438C22×C32H(5,𝔽2)11yescharacteristic
439C22×C32H(5,𝔽2)11yescharacteristic
440C22×C322−1+411yescharacteristic
441C2×C3⋊D3—22no—
442C2×C3⋊D3—22no—
443C2×C3⋊D3—22no—
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—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—41no—
465C3⋊Dic3—41no—
466C3⋊Dic3—41no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3C4×D414yes—
474C22×D4—91no—
475C22×D4—91no—
476C22×D4—91no—
477C23×C4—31no—
478C23×C4—91no—
479C23×C4—91no—
480#121—98no—
481C4×D4—184no—
482#117—184no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—91no—
493C2×C22⋊C4—91no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
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×C42—31no—
503C2×C42—31no—
504C2×C42—31no—
505C2×C42—91no—
506#95—31no—
507#95—31no—
508#95—91no—
509#95—91no—
510#95—91no—
511#95D3211yescharacteristic
512C23×C3—21no—
513C23×C3—32no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3C23×D311yescharacteristic
521C23×C3C23×D311yescharacteristic
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—32no—
529C22×D3—32no—
530C22×D3—32no—
531C22×D3—32no—
532C22×D3—62no—
533C22×D3—62no—
534C22×D3—62no—
535C22×D3—62no—
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—61no—
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×D3C2×C4×D312yes—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
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—22no—
586C2×C3×C4—22no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—41no—
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—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—61no—
615C2×C3×C4—124no—
616C2×C3×C4C2×C4×D312yes—
617C2×C3×C4C2×C4×D312yes—
618C2×C3×C4C2×D1212yes—
619C2×C3×C4D3×D412yes—
620#67—68no—
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—62no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3C2×C4×D312yes—
656C2×Dic3C2×C4×D312yes—
657C2×Dic3C2×C4×D312yes—
658C2×Dic3C2×D1212yes—
659C2×Dic3C2×D1212yes—
660C2×Dic3#23512yes—
661D12—68no—
662D12—124no—
663D12—124no—
664D12—128no—
665D12—124no—
666C4×D3—44no—
667C4×D3—68no—
668C4×D3—68no—
669C4×D3—124no—
670C4×D3—124no—
671C4×D3—128no—
672C2×C32C2×C4×D411yescharacteristic
673C2×C32#51811yescharacteristic
674C2×C32#52011yescharacteristic
675C2×C32#53511yescharacteristic
676C2×C32#53711yescharacteristic
677C2×C32#54011yescharacteristic
678C2×C32#54211yescharacteristic
679C3⋊D3—42no—
680C3⋊D3—42no—
681C3×D3—42no—
682C24—31no—
683C24—91no—
684C24—91no—
685C2×D4—94no—
686C2×D4—94no—
687C2×D4—94no—
688C2×D4—182no—
689C2×D4—182no—
690C2×D4—361no—
691C2×D4—361no—
692C2×D4—361no—
693C2×D4—361no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—62no—
702C22×C4—94no—
703C22×C4—91no—
704C22×C4—91no—
705C22×C4—121no—
706C22×C4—121no—
707C22×C4—182no—
708C22×C4—182no—
709C22×C4—182no—
710C22×C4—361no—
711C22×C4—361no—
712C22×C4C2×D3211yescharacteristic
713C22×C4C2×D3211yescharacteristic
714C22×C4C2×D3211yescharacteristic
715C4⋊C4—34no—
716C4⋊C4—62no—
717C4⋊C4—62no—
718C4⋊C4—121no—
719C4⋊C4—182no—
720C4⋊C4—182no—
721C4⋊C4—361no—
722C22⋊C4—34no—
723C22⋊C4—94no—
724C22⋊C4—121no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C22⋊C4—361no—
730C22⋊C4—361no—
731C22⋊C4—361no—
732C22⋊C4—361no—
733C22⋊C4—361no—
734C42—34no—
735C42—121no—
736C42—121no—
737C42—182no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—62no—
746C22×C3—62no—
747C22×C3—62no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3C22×C4×D311yescharacteristic
753C22×C3C22×C4×D311yescharacteristic
754C22×C3C22×D1211yescharacteristic
755C22×C3C2×#23511yescharacteristic
756C22×C3C2×D3×D411yescharacteristic
757C22×C3#100411yescharacteristic
758C22×C3#100411yescharacteristic
759C22×C3#100411yescharacteristic
760C22×C3#100711yescharacteristic
761C22×C3#100711yescharacteristic
762C22×C3D3×#4111yescharacteristic
763C22×C3#100911yescharacteristic
764C22×C3#100911yescharacteristic
765C22×C3#100911yescharacteristic
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—22no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—64no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—62no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—62no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—122no—
787C2×D3—122no—
788C2×D3—122no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—122no—
792C2×D3—122no—
793C2×D3—122no—
794C2×D3—122no—
795C2×D3—121no—
796C2×D3—121no—
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—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—34no—
820C3×C4—42no—
821C3×C4—42no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—62no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—81no—
828C3×C4—121no—
829C3×C4—121no—
830C3×C4—121no—
831Dic3—22no—
832Dic3—22no—
833Dic3—22no—
834Dic3—41no—
835Dic3—41no—
836Dic3—41no—
837Dic3—122no—
838Dic3—121no—
839Dic3—121no—
840Dic3—121no—
841Dic3—121no—
842Dic3—241no—
843Dic3C4×D1214yes—
844C32#232411yescharacteristic, complemented, Sylow
845C23—32no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—92no—
853C23—92no—
854C23—181no—
855C23—181no—
856C23—181no—
857C23—181no—
858C23—181no—
859C23—181no—
860C23—181no—
861C23—181no—
862C23—181no—
863C23—181no—
864C23—181no—
865C23—181no—
866C23C22×D3211yescharacteristic
867D4—188no—
868D4—364no—
869D4—364no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—61no—
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—124no—
899C2×C4—188no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—364no—
907C2×C4C4×D3212yes—
908C2×C4D3×D1212yes—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—122no—
917C2×C3C2×C4×D1211yescharacteristic
918C2×C3#550411yescharacteristic
919C2×C3#551011yescharacteristic
920C2×C3#552511yescharacteristic
921C2×C3C4×D3×D411yescharacteristic
922C2×C3#554511yescharacteristic
923C2×C3#554511yescharacteristic
924C2×C3#556211yescharacteristic
925C2×C3#557411yescharacteristic
926C2×C3#558211yescharacteristic
927C2×C3#559211yescharacteristic
928C2×C3#562911yescharacteristic
929C2×C3#564011yescharacteristic
930C2×C3#566311yescharacteristic
931D3—42no—
932D3—124no—
933D3—122no—
934D3—122no—
935D3—122no—
936D3—122no—
937D3—242no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—182no—
946C22—182no—
947C22—182no—
948C22—182no—
949C22—182no—
950C22—182no—
951C22—361no—
952C22—361no—
953C22—361no—
954C22—361no—
955C22—361no—
956C22—361no—
957C22—361no—
958C22—361no—
959C22C2×C4×D3211yescharacteristic
960C22C2×D3×D1211yescharacteristic
961C22D3×#23511yescharacteristic
962C22#6431411yescharacteristic
963C22#6431411yescharacteristic
964C22#6431411yescharacteristic
965C22#6431611yescharacteristic
966C4—22no—
967C4—22no—
968C4—34no—
969C4—41no—
970C4—62no—
971C4—62no—
972C4—62no—
973C4—121no—
974C4—121no—
975C4—121no—
976C4—361no—
977C4—361no—
978C3—21no—
979C3#7376311yescharacteristic, complemented
980C3#7438511yescharacteristic, complemented
981C2—122no—
982C2—362no—
983C2—362no—
984C2C4×D3×D1211yescharacteristic
985C2#1059408011yescharacteristic
986C2#1059420211yescharacteristic
987C2#1059425611yescharacteristic
988C2#1059432711yescharacteristic
989C2#1059433011yescharacteristic
990C2#1059452311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63910C2
hypercenter#95D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#626C2semidirect
3. C2×#63836C2semidirect
4. #10592364C2semidirect
5. C3×#4668C2semidirect
6. C3×#4649C2semidirect
7. #10591384C2semidirect
8. #10591383C2semidirect
9. #10591382C2semidirect
10. #10591367C2semidirect
11. #10591320C2semidirect
12. #10591305C2semidirect
13. #10591290C2semidirect
14. #10591265C2semidirect
15. #10591194C2semidirect
47. #63910C4semidirect
80. #4668D3semidirect
86. #4649D3semidirect
97. C2×C4⋊(C3⋊D3)C2×C4semidirect
116. C2×#626C2×C4semidirect
119. C2×#624C2×C4semidirect
124. C3×(C2×D3)⋊C4C2×C4semidirect
128. C3×Dic3⋊C4C2×C4semidirect
131. C3×C4×Dic3D4semidirect
139. #3722C2×C4semidirect
418. (C2×D3)⋊C4C4×D3semidirect
428. Dic3⋊C4C4×D3semidirect
433. C4×Dic3D12semidirect
844. C32#2324semidirect
979. C3#73763semidirect
980. C3#74385semidirect

Maximal subgroups

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

subgroupindex
C2×#639102
C2×C4×#6262
C2×#638362
#105923642
C3×#46682
C3×#46492
#105913842
#105913832
#105913822
#105913672
#105913202
#105913052
#105912902
#105912652
#105911942
#743853
#737633