Finite Group Databasebeta

← #11806896

Subgroups — #11806896

Order 1152.

1807 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×#63979C211yesmaximal, characteristic
3C2×Dic3×#67C211yesmaximal, characteristic, complemented
4C2×C4×#626C211yesmaximal, characteristic, complemented
5C2×#63881C211yesmaximal, characteristic, complemented
6#10592655C211yesmaximal, characteristic, complemented
7C3×#4957C211yesmaximal, characteristic, complemented
8#10591711C211yesmaximal, characteristic, complemented
9#10591707C211yesmaximal, characteristic, complemented
10#10591384C211yesmaximal, characteristic, complemented
11#10591383C211yesmaximal, characteristic, complemented
12#10591381C211yesmaximal, characteristic, complemented
13#10591363C211yesmaximal, characteristic, complemented
14Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#82343—31nomaximal
17#76306—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#67⋊C4—24no—
40#63979C418yescomplemented
41Dic3×#67—24no—
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51C2×Dic32C2211yescharacteristic
52C4×#626—24no—
53#63881—24no—
54#63658C2211yescharacteristic
55#63658C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C2×C3×C4×D4—31no—
59C2×#940—31no—
60C2×#940—31no—
61C2×D4×Dic3—31no—
62C2×C4×#67—31no—
63C2×C4×#67—31no—
64C2×#893—31no—
65C2×#67⋊C4—31no—
66C2×#67⋊C4D311yescharacteristic, complemented
67C2×C4×D12—31no—
68C3×#390—31no—
69#5221—31no—
70#5213—31no—
71#5213—31no—
72#4988—31no—
73Dic3×C4⋊C4—31no—
74Dic3×C4⋊C4—31no—
75#4958—31no—
76#4958—31no—
77#4957—31no—
78#4957—31no—
79#4957—31no—
80#4957D311yescharacteristic, complemented
81#4956—31no—
82#4956—31no—
83#4956—31no—
84#4956—31no—
85#4956—61no—
86#4939—31no—
87C4×Dic3⋊C4—31no—
88C4×Dic3⋊C4—31no—
89C24×C32C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—41no—
96C2×#638—41no—
97C2×#638C2×C414yescomplemented
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—41no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67C2×C414yescomplemented
109C2×C3×#67C2×C414yescomplemented
110C22×C3×Dic3—22no—
111C22×C3×Dic3—22no—
112C22×C3×Dic3—41no—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—41no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#626—22no—
125C2×#626—22no—
126C2×#626C2×C414yescomplemented
127C2×#626C2×C414yescomplemented
128C2×#625—41no—
129C2×#625—41no—
130C2×#625C2×C414yescomplemented
131C2×D3×Dic3—22no—
132C2×D3×Dic3—22no—
133C2×D3×Dic3—41no—
134C32×C22⋊C4—22no—
135#3757—22no—
136#3752—41no—
137C3×#217—41no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×(C2×D3)⋊C4—41no—
141C3×Dic3⋊C4—22no—
142C3×Dic3⋊C4D414yescomplemented
143C3×C4×Dic3—22no—
144C3×C4×Dic3—22no—
145Dic3⋊Dic3—22no—
146Dic3⋊Dic3D414yescomplemented
147#3722—22no—
148#3722—22no—
149(C2×D3)⋊Dic3—22no—
150(C2×D3)⋊Dic3—22no—
151(C2×D3)⋊Dic3—41no—
152Dic32—22no—
153Dic32—22no—
154Dic32C2×C414yescomplemented
155#2366—91noSylow
156C22×C3×D4—31no—
157C22×C3×D4—31no—
158C23×C3×C4—31no—
159C23×C3×C4—31no—
160C22×#67—31no—
161C22×#67—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—61no—
167C22×#67C2×D311yescharacteristic
168C22×#67C2×D311yescharacteristic
169C23×Dic3—31no—
170C23×Dic3C2×D311yescharacteristic
171C22×D12—31no—
172C22×D12—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—61no—
177C22×C4×D3C2×D311yescharacteristic
178C3×C4×D4—64no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C22⋊C4—21no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4C2×D311yescharacteristic
187C2×C3×C22⋊C4C2×D311yescharacteristic
188C2×C3×C42—31no—
189C2×C3×C42—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×#217—31no—
194C2×#217—31no—
195C2×#217—61no—
196C2×#217C2×D311yescharacteristic
197#940—38no—
198#940—38no—
199D4×Dic3—64no—
200C4×#67—64no—
201C4×#67—64no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—61no—
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4C2×D311yescharacteristic
220C2×Dic3⋊C4C2×D311yescharacteristic
221C2×C4×Dic3—31no—
222C2×C4×Dic3—31no—
223C2×C4×Dic3—31no—
224C2×C4×Dic3—31no—
225C2×C4×Dic3—31no—
226C2×C4×Dic3—31no—
227C2×C4×Dic3C2×D311yescharacteristic
228C2×C4×Dic3C2×D311yescharacteristic
229#893—64no—
230#67⋊C4—24no—
231#67⋊C4—64no—
232C4×D12—64no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95—61no—
242C3⋊#95—61no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32C22×C412yes—
250C23×C32C2411yescharacteristic
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C22×C412yes—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3C22×C412yes—
271C22×C3×D3C22×C412yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C2×D412yes—
278#638—44no—
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⋊Dic3C22×C412yes—
287C2×C3⋊Dic3C2×D412yes—
288C4×C3⋊D3—44no—
289C3×#67—28no—
290C3×#67—28no—
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—44no—
302C2×C3×Dic3C22×C412yes—
303C2×C3×Dic3C22×C412yes—
304C2×C3×Dic3C2×D412yes—
305C2×C3×Dic3C2×D412yes—
306C2×C3×Dic3C2×D412yes—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3#4112yes—
309C2×C3×Dic3#4112yes—
310C3×C4×D3—44no—
311#626—28no—
312#626—28no—
313#625—44no—
314D3×Dic3—44no—
315C2×#127—91no—
316C2×C4×D4—31no—
317C2×C4×D4—91no—
318C2×C4×D4—91no—
319C2×C4×D4—91no—
320#390—31no—
321#390—91no—
322#390—91no—
323#390—91no—
324#386—91no—
325#386—91no—
326#386—91no—
327#386—91no—
328C4×C4⋊C4—91no—
329C4×C4⋊C4—91no—
330C24×C3—21no—
331C24×C3—31no—
332C24×C3—31no—
333C24×C3C22×D311yescharacteristic
334C24×C3C22×D311yescharacteristic
335C23×D3—31no—
336C23×D3—31no—
337C23×D3—61no—
338C23×D3C22×D311yescharacteristic
339C23×D3C22×D311yescharacteristic
340C2×C3×D4—34no—
341C2×C3×D4—34no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—62no—
355C22×C3×C4—62no—
356C22×C3×C4—62no—
357C22×C3×C4—62no—
358C22×C3×C4—121no—
359C22×C3×C4—121no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C2×#67—22no—
365C2×#67—22no—
366C2×#67—22no—
367C2×#67—22no—
368C2×#67—34no—
369C2×#67—34no—
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—64no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67—62no—
379C2×#67—121no—
380C2×#67—121no—
381C2×#67—121no—
382C2×#67—121no—
383C2×#67—121no—
384C2×#67—121no—
385C2×#67—121no—
386C2×#67—121no—
387C2×#67—122no—
388C2×#67—122no—
389C2×#67C4×D314yescomplemented
390C2×#67C4×D314yescomplemented
391C22×Dic3—22no—
392C22×Dic3—22no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—41no—
400C22×Dic3—61no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403C22×Dic3—62no—
404C22×Dic3—62no—
405C22×Dic3—121no—
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C2×D12—34no—
413C2×D12—34no—
414C2×D12—62no—
415C2×D12—62no—
416C2×D12—62no—
417C2×D12—62no—
418C2×C4×D3—22no—
419C2×C4×D3—22no—
420C2×C4×D3—41no—
421C2×C4×D3—62no—
422C2×C4×D3—62no—
423C2×C4×D3—62no—
424C2×C4×D3—62no—
425C2×C4×D3—62no—
426C2×C4×D3—62no—
427C2×C4×D3—122no—
428C2×C4×D3—122no—
429C2×C4×D3—121no—
430C2×C4×D3—121no—
431C2×C4×D3—121no—
432C2×C4×D3—122no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—62no—
435C3×C22⋊C4—22no—
436C3×C22⋊C4—22no—
437C3×C22⋊C4—42no—
438C3×C22⋊C4—62no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—121no—
441C3×C22⋊C4—121no—
442C3×C42—62no—
443C3×C42—62no—
444#217—41no—
445#217—62no—
446#217—62no—
447#217—62no—
448#217—62no—
449#217—122no—
450#217—121no—
451(C2×D3)⋊C4—22no—
452(C2×D3)⋊C4—22no—
453(C2×D3)⋊C4—41no—
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—121no—
461(C2×D3)⋊C4—121no—
462(C2×D3)⋊C4—121no—
463(C2×D3)⋊C4—122no—
464C4⋊Dic3—34no—
465C4⋊Dic3—62no—
466Dic3⋊C4—22no—
467Dic3⋊C4—34no—
468Dic3⋊C4—62no—
469Dic3⋊C4#6714yescomplemented
470C4×Dic3—22no—
471C4×Dic3—22no—
472C4×Dic3—34no—
473C4×Dic3—34no—
474C4×Dic3—62no—
475C4×Dic3—62no—
476C4×Dic3—62no—
477C4×Dic3—62no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32C23×C411yescharacteristic
486C22×C32C22×D411yescharacteristic
487C22×C32C22×D411yescharacteristic
488C22×C32C2×#4111yescharacteristic
489C22×C32C2×#4111yescharacteristic
490C22×C32H(5,𝔽2)11yescharacteristic
491C22×C32H(5,𝔽2)11yescharacteristic
492C2×C3⋊D3—22no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—41no—
498C2×C3⋊D3—41no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3—41no—
508C2×C3×D3—41no—
509C2×C3×D3—41no—
510C2×C3×D3—41no—
511C2×C3×D3—41no—
512C2×C3×D3—41no—
513C32×C4—22no—
514C32×C4—41no—
515C3⋊Dic3—22no—
516C3⋊Dic3—22no—
517C3⋊Dic3—41no—
518C3×Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3—41no—
521C3×Dic3—41no—
522C3×Dic3C4×D414yescomplemented
523C3×Dic3C4×D414yescomplemented
524C22×D4—31no—
525C22×D4—31no—
526C22×D4—91no—
527C22×D4—91no—
528C22×D4—91no—
529C22×D4—91no—
530C23×C4—31no—
531C23×C4—31no—
532C23×C4—91no—
533C23×C4—91no—
534#127—98no—
535C4×D4—64no—
536C4×D4—184no—
537C4×D4—184no—
538C4×D4—184no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—91no—
548C2×C22⋊C4—91no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4D3211yescharacteristic
555C2×C42—31no—
556C2×C42—31no—
557C2×C42—91no—
558C2×C42—91no—
559C2×C42—91no—
560#95—91no—
561#95—91no—
562#95—91no—
563#95—91no—
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—21no—
577C23×C3—22no—
578C23×C3—32no—
579C23×C3—32no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3C2×C4×D312yes—
599C23×C3C2×C4×D312yes—
600C23×C3C23×D311yescharacteristic
601C23×C3C23×D311yescharacteristic
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—32no—
615C22×D3—32no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—61no—
630C22×D3—61no—
631C22×D3—121no—
632C22×D3—121no—
633C22×D3—121no—
634C22×D3—121no—
635C22×D3C2×C4×D312yes—
636C22×D3C2×C4×D312yes—
637C3×D4—68no—
638C3×D4—68no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—22no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—124no—
674C2×C3×C4—124no—
675C2×C3×C4D3×D412yes—
676C2×C3×C4C2×#6712yes—
677#67—28no—
678#67—28no—
679#67—68no—
680#67—68no—
681#67—124no—
682#67—124no—
683#67—124no—
684#67—124no—
685#67—128no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—32no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—44no—
701C2×Dic3—62no—
702C2×Dic3—62no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—121no—
718C2×Dic3—121no—
719C2×Dic3—121no—
720C2×Dic3—121no—
721C2×Dic3—121no—
722C2×Dic3—121no—
723C2×Dic3—121no—
724C2×Dic3—124no—
725C2×Dic3C2×C4×D312yes—
726C2×Dic3C2×C4×D312yes—
727C2×Dic3#23512yes—
728C2×Dic3D3×D412yes—
729C2×Dic3D3×D412yes—
730C2×Dic3#23712yes—
731C2×Dic3C2×#6712yes—
732C2×Dic3C2×#6712yes—
733D12—68no—
734D12—68no—
735C4×D3—44no—
736C4×D3—124no—
737C4×D3—124no—
738C4×D3—124no—
739C4×D3—128no—
740C2×C32—42no—
741C2×C32C2×C4×D411yescharacteristic
742C2×C32C2×C4×D411yescharacteristic
743C2×C32#51811yescharacteristic
744C2×C32D4211yescharacteristic
745C2×C32#55011yescharacteristic
746C2×C32#55011yescharacteristic
747C2×C32#55911yescharacteristic
748C3⋊D3—42no—
749C3×D3—42no—
750C3×D3—42no—
751C24—31no—
752C24—31no—
753C24—91no—
754C24C2×D3211yescharacteristic
755C2×D4—34no—
756C2×D4—34no—
757C2×D4—62no—
758C2×D4—62no—
759C2×D4—62no—
760C2×D4—62no—
761C2×D4—94no—
762C2×D4—94no—
763C2×D4—94no—
764C2×D4—94no—
765C2×D4—182no—
766C2×D4—182no—
767C2×D4—182no—
768C2×D4—182no—
769C2×D4—361no—
770C2×D4—361no—
771C2×D4—361no—
772C2×D4—361no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—31no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—62no—
780C22×C4—62no—
781C22×C4—62no—
782C22×C4—62no—
783C22×C4—91no—
784C22×C4—91no—
785C22×C4—91no—
786C22×C4—121no—
787C22×C4—121no—
788C22×C4—182no—
789C22×C4—182no—
790C22×C4—182no—
791C22×C4—182no—
792C22×C4—361no—
793C22×C4—361no—
794C22×C4C2×D3211yescharacteristic
795C22×C4C2×D3211yescharacteristic
796C4⋊C4—34no—
797C4⋊C4—62no—
798C4⋊C4—94no—
799C4⋊C4—182no—
800C22⋊C4—22no—
801C22⋊C4—62no—
802C22⋊C4—62no—
803C22⋊C4—121no—
804C22⋊C4—121no—
805C22⋊C4—182no—
806C22⋊C4—182no—
807C22⋊C4—182no—
808C22⋊C4—182no—
809C22⋊C4—182no—
810C22⋊C4—361no—
811C22⋊C4—361no—
812C42—62no—
813C42—62no—
814C42—94no—
815C42—182no—
816C42—182no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—81no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3—121no—
859C22×C3C22×C4×D311yescharacteristic
860C22×C3C22×C4×D311yescharacteristic
861C22×C3C2×#23511yescharacteristic
862C22×C3C2×D3×D411yescharacteristic
863C22×C3C2×D3×D411yescharacteristic
864C22×C3C2×D3×D411yescharacteristic
865C22×C3C2×#23711yescharacteristic
866C22×C3#100411yescharacteristic
867C22×C3#100411yescharacteristic
868C22×C3D3×#4111yescharacteristic
869C22×C3D3×#4111yescharacteristic
870C22×C3#100911yescharacteristic
871C22×C3#100911yescharacteristic
872C22×C3C22×#6711yescharacteristic
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—41no—
886C2×D3—41no—
887C2×D3—64no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—122no—
895C2×D3—122no—
896C2×D3—122no—
897C2×D3—122no—
898C2×D3—122no—
899C2×D3—122no—
900C2×D3—121no—
901C2×D3—121no—
902C2×D3—121no—
903C2×D3—121no—
904C2×D3—121no—
905C2×D3—121no—
906C2×D3—121no—
907C2×D3—121no—
908C3×C4—22no—
909C3×C4—22no—
910C3×C4—34no—
911C3×C4—34no—
912C3×C4—42no—
913C3×C4—41no—
914C3×C4—41no—
915C3×C4—62no—
916C3×C4—62no—
917C3×C4—81no—
918C3×C4—121no—
919C3×C4—121no—
920Dic3—22no—
921Dic3—22no—
922Dic3—41no—
923Dic3—41no—
924Dic3—62no—
925Dic3—62no—
926Dic3—62no—
927Dic3—62no—
928Dic3—122no—
929Dic3—122no—
930Dic3—121no—
931Dic3—121no—
932Dic3—241no—
933Dic3#67⋊C414yescomplemented
934Dic3C4×#6714yescomplemented
935C32#236611yescharacteristic, complemented, Sylow
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—32no—
943C23—32no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—92no—
957C23—181no—
958C23—181no—
959C23—181no—
960C23—181no—
961C23—181no—
962C23—181no—
963C23C4×D3212yes—
964C23C22×D3211yescharacteristic
965D4—68no—
966D4—68no—
967D4—188no—
968D4—188no—
969D4—364no—
970D4—364no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—32no—
977C2×C4—32no—
978C2×C4—32no—
979C2×C4—32no—
980C2×C4—32no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—32no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—92no—
995C2×C4—92no—
996C2×C4—124no—
997C2×C4—124no—
998C2×C4—181no—
999C2×C4—181no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4—181no—
1004C2×C4—181no—
1005C2×C4—364no—
1006C2×C4—364no—
1007C2×C4D3×#6712yes—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—42no—
1016C2×C3—42no—
1017C2×C3—82no—
1018C2×C3—122no—
1019C2×C3—122no—
1020C2×C3C2×#67⋊C411yescharacteristic
1021C2×C3C4×D3×D411yescharacteristic
1022C2×C3C4×D3×D411yescharacteristic
1023C2×C3#554511yescharacteristic
1024C2×C3#554511yescharacteristic
1025C2×C3#555311yescharacteristic
1026C2×C3#555911yescharacteristic
1027C2×C3#559911yescharacteristic
1028C2×C3#560911yescharacteristic
1029C2×C3#568111yescharacteristic
1030C2×C3#571811yescharacteristic
1031C2×C3C2×C4×#6711yescharacteristic
1032C2×C3D4×#6711yescharacteristic
1033C2×C3#583411yescharacteristic
1034D3—42no—
1035D3—42no—
1036D3—124no—
1037D3—122no—
1038D3—122no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—121no—
1053C22—121no—
1054C22—121no—
1055C22—121no—
1056C22—121no—
1057C22—121no—
1058C22—121no—
1059C22—121no—
1060C22—182no—
1061C22—182no—
1062C22—182no—
1063C22—361no—
1064C22—361no—
1065C22—361no—
1066C22—361no—
1067C22C2×C4×D3211yescharacteristic
1068C22D3×#23511yescharacteristic
1069C22D32×D411yescharacteristic
1070C22D3×#23711yescharacteristic
1071C22#6431411yescharacteristic
1072C22#6431411yescharacteristic
1073C22C2×D3×#6711yescharacteristic
1074C4—22no—
1075C4—34no—
1076C4—34no—
1077C4—41no—
1078C4—62no—
1079C4—62no—
1080C4—121no—
1081C4—121no—
1082C4—182no—
1083C4—182no—
1084C4—361no—
1085C3—21no—
1086C3#7630611yescharacteristic, complemented
1087C3#8234311yescharacteristic, complemented
1088C2—42no—
1089C2—122no—
1090C2—122no—
1091C2—362no—
1092C2#1059420011yescharacteristic
1093C2#1059424611yescharacteristic
1094C2D3×#67⋊C411yescharacteristic
1095C2#1059425611yescharacteristic
1096C2C4×D3×#6711yescharacteristic
1097C2#1059515811yescharacteristic
1098C2#1059529111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63979C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2366
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#67⋊C4C2semidirect
3. C2×Dic3×#67C2semidirect
4. C2×C4×#626C2semidirect
5. C2×#63881C2semidirect
6. #10592655C2semidirect
7. C3×#4957C2semidirect
8. #10591711C2semidirect
9. #10591707C2semidirect
10. #10591384C2semidirect
11. #10591383C2semidirect
12. #10591381C2semidirect
13. #10591363C2semidirect
14. Dic3×Dic3⋊C4C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
40. #63979C4semidirect
66. C2×#67⋊C4D3semidirect
80. #4957D3semidirect
97. C2×#638C2×C4semidirect
108. C2×C3×#67C2×C4semidirect
109. C2×C3×#67C2×C4semidirect
126. C2×#626C2×C4semidirect
127. C2×#626C2×C4semidirect
130. C2×#625C2×C4semidirect
142. C3×Dic3⋊C4D4semidirect
146. Dic3⋊Dic3D4semidirect
154. Dic32C2×C4semidirect
389. C2×#67C4×D3semidirect
390. C2×#67C4×D3semidirect
469. Dic3⋊C4#67semidirect
522. C3×Dic3C4×D4semidirect
523. C3×Dic3C4×D4semidirect
933. Dic3#67⋊C4semidirect
934. Dic3C4×#67semidirect
935. C32#2366semidirect
1086. C3#76306semidirect
1087. C3#82343semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×#639792
C2×Dic3×#672
C2×C4×#6262
C2×#638812
#105926552
C3×#49572
#105917112
#105917072
#105913842
#105913832
#105913812
#105913632
Dic3×Dic3⋊C42
#823433
#763063