Finite Group Databasebeta

← #10726665

Subgroups — #10726665

Order 768.

3494 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊C4C211yesmaximal, characteristic
2C2×C3×#396C211yesmaximal, characteristic, complemented
3C2×#4994C211yesmaximal, characteristic, complemented
4C2×#4989C211yesmaximal, characteristic, complemented
5C2×#4989C211yesmaximal, characteristic, complemented
6C2×#4987C211yesmaximal, characteristic, complemented
7C2×#4955C211yesmaximal, characteristic
8C2×#4955C211yesmaximal, characteristic
9#71570C211yesmaximal, characteristic, complemented
10#71570C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71547C211yesmaximal, characteristic, complemented
13#71546C211yesmaximal, characteristic, complemented
14#69428C211yesmaximal, characteristic, complemented
15(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
16#14726—31nomaximal, Sylow
17C25×D3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic, complemented
21C22×C3×C4⋊C4C2211yescharacteristic, complemented
22C22×C3×C4⋊C4C2211yescharacteristic, complemented
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic, complemented
40C22×Dic3⋊C4C2211yescharacteristic, complemented
41C22×Dic3⋊C4C2211yescharacteristic, complemented
42C2×D3×C22⋊C4—24no—
43C2×D3×C22⋊C4—24no—
44C2×D3×C22⋊C4—24no—
45C3×#396—24no—
46C2×C3×#95C2211yescharacteristic, complemented
47C2×C3⋊#95C2211yescharacteristic, complemented
48C2×C3⋊#95C2211yescharacteristic, complemented
49C2×C3⋊#95C2211yescharacteristic, complemented
50C2×C3⋊#95C2211yescharacteristic, complemented
51C2×C3⋊#95C2211yescharacteristic, complemented
52C2×C3⋊#95C2211yescharacteristic, complemented
53C2×C3⋊#95C2211yescharacteristic, complemented
54C2×C3⋊#95C2211yescharacteristic, complemented
55C2×C3⋊#95C2211yescharacteristic, complemented
56#4994—24no—
57#4989—24no—
58#4989—24no—
59#4987—24no—
60#4955—24no—
61#4955—24no—
62C23×C22⋊C4—31no—
63C2×#396—31no—
64C2×#396D311yescharacteristic, complemented
65C2×#385—31no—
66C2×#385—31no—
67C2×#380—31no—
68C2×#379—31no—
69C2×#379—31no—
70#1439—31no—
71#1439—31no—
72#1439—31no—
73#1439—31no—
74#1439—31no—
75#1439—31no—
76C22⋊#95—31no—
77C25×C3C2311yescharacteristic
78C24×D3—22no—
79C24×D3—22no—
80C24×D3—22no—
81C24×D3—22no—
82C24×D3—22no—
83C24×D3—22no—
84C24×D3—22no—
85C24×D3—22no—
86C24×D3—22no—
87C24×D3—22no—
88C24×D3—41no—
89C24×D3—41no—
90C24×D3—41no—
91C24×D3—41no—
92C24×D3Q814yes—
93C24×D3C2311yescharacteristic
94C24×D3C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—41no—
117C22×C4×D3—41no—
118C22×C4×D3—41no—
119C22×C4×D3—41no—
120C22×C4×D3D414yes—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—41no—
129C2×C3×C4⋊C4—41no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—41no—
137C2×C3×C22⋊C4—41no—
138C2×C3×C22⋊C4D414yes—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—41no—
147C2×#217—41no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—22no—
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—22no—
168C2×(C2×D3)⋊C4—22no—
169C2×(C2×D3)⋊C4—22no—
170C2×(C2×D3)⋊C4—22no—
171C2×(C2×D3)⋊C4—41no—
172C2×(C2×D3)⋊C4—41no—
173C2×(C2×D3)⋊C4—41no—
174C2×(C2×D3)⋊C4—41no—
175C2×(C2×D3)⋊C4D414yes—
176C2×(C2×D3)⋊C4D414yes—
177C2×(C2×D3)⋊C4D414yes—
178C2×C4⋊Dic3—22no—
179C2×C4⋊Dic3—22no—
180C2×C4⋊Dic3—41no—
181C2×Dic3⋊C4—22no—
182C2×Dic3⋊C4—22no—
183C2×Dic3⋊C4—22no—
184C2×Dic3⋊C4—41no—
185C2×Dic3⋊C4—41no—
186C2×Dic3⋊C4—41no—
187D3×C22⋊C4—232no—
188C3×#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—22no—
194C3⋊#95—22no—
195C3⋊#95—22no—
196C3⋊#95—41no—
197C3⋊#95—41no—
198C26—31no—
199C24×C4—31no—
200C24×C4—31no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4C2×D311yescharacteristic, complemented
205C22×C4⋊C4C2×D311yescharacteristic, complemented
206C22×C4⋊C4C2×D311yescharacteristic, complemented
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—64no—
221C22×C22⋊C4—64no—
222C22×C22⋊C4—64no—
223C22×C22⋊C4C2×D311yescharacteristic
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C22⋊C4C2×D311yescharacteristic
226#396—24no—
227#396—64no—
228#385—64no—
229#385—64no—
230#380—64no—
231#379—64no—
232#379—64no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95—31no—
238C2×#95—31no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95C2×D311yescharacteristic, complemented
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3C2×D412yes—
256C24×C3C2×Q812yes—
257C24×C3#4112yes—
258C24×C3C2411yescharacteristic
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—28no—
268C23×D3—28no—
269C23×D3—28no—
270C23×D3—28no—
271C23×D3—28no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—28no—
285C23×D3—28no—
286C23×D3—28no—
287C23×D3—28no—
288C23×D3—44no—
289C23×D3—44no—
290C23×D3—44no—
291C23×D3—44no—
292C23×D3—44no—
293C23×D3—44no—
294C23×D3—44no—
295C23×D3—44no—
296C23×D3—44no—
297C23×D3—44no—
298C23×D3—44no—
299C23×D3—44no—
300C23×D3—44no—
301C23×D3—44no—
302C23×D3—44no—
303C23×D3—44no—
304C23×D3—44no—
305C23×D3—44no—
306C23×D3—44no—
307C23×D3—44no—
308C23×D3—44no—
309C23×D3—44no—
310C23×D3—44no—
311C23×D3—44no—
312C23×D3—44no—
313C23×D3—44no—
314C23×D3C2×D412yes—
315C23×D3C2×D412yes—
316C23×D3C2×D412yes—
317C23×D3C2×D412yes—
318C23×D3C2×Q812yes—
319C23×D3C2×Q812yes—
320C23×D3#4112yes—
321C23×D3#4112yes—
322C23×D3#4112yes—
323C23×D3#4112yes—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4C2×D412yes—
361C22×C3×C4C2×D412yes—
362C22×C3×C4C2×D412yes—
363C22×C3×C4C2×D412yes—
364C22×C3×C4C2×D412yes—
365C22×C3×C4C2×D412yes—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3—21no—
386C22×Dic3—21no—
387C22×Dic3—21no—
388C22×Dic3—21no—
389C22×Dic3—21no—
390C22×Dic3—21no—
391C22×Dic3—21no—
392C22×Dic3—21no—
393C22×Dic3—21no—
394C22×Dic3—21no—
395C22×Dic3—21no—
396C22×Dic3—21no—
397C22×Dic3—21no—
398C22×Dic3—21no—
399C22×Dic3—21no—
400C22×Dic3—21no—
401C22×Dic3—21no—
402C22×Dic3—21no—
403C22×Dic3—21no—
404C22×Dic3C2×D412yes—
405C22×Dic3C2×D412yes—
406C22×Dic3C2×D412yes—
407C22×Dic3C2×D412yes—
408C2×C4×D3—28no—
409C2×C4×D3—28no—
410C2×C4×D3—28no—
411C2×C4×D3—44no—
412C2×C4×D3—44no—
413C2×C4×D3—44no—
414C2×C4×D3—44no—
415C2×C4×D3—44no—
416C2×C4×D3—44no—
417C2×C4×D3—44no—
418C2×C4×D3—44no—
419C2×C4×D3—44no—
420C2×C4×D3—44no—
421C2×C4×D3—44no—
422C3×C4⋊C4—44no—
423C3×C4⋊C4—44no—
424C3×C4⋊C4—44no—
425C3×C22⋊C4—28no—
426C3×C22⋊C4—44no—
427C3×C22⋊C4—44no—
428#217—28no—
429#217—44no—
430#217—44no—
431(C2×D3)⋊C4—28no—
432(C2×D3)⋊C4—28no—
433(C2×D3)⋊C4—28no—
434(C2×D3)⋊C4—28no—
435(C2×D3)⋊C4—44no—
436(C2×D3)⋊C4—44no—
437(C2×D3)⋊C4—44no—
438(C2×D3)⋊C4—44no—
439(C2×D3)⋊C4—44no—
440(C2×D3)⋊C4—44no—
441C4⋊Dic3—44no—
442Dic3⋊C4—44no—
443Dic3⋊C4—44no—
444C25—31no—
445C25—31no—
446C25—34no—
447C25—62no—
448C25—62no—
449C25—62no—
450C25—62no—
451C25—62no—
452C25—62no—
453C25—62no—
454C25—62no—
455C25—62no—
456C25—62no—
457C25—121no—
458C25—121no—
459C25—121no—
460C25—121no—
461C25C22×D311yescharacteristic
462C23×C4—31no—
463C23×C4—31no—
464C23×C4—31no—
465C23×C4—31no—
466C23×C4—34no—
467C23×C4—31no—
468C23×C4—31no—
469C23×C4—62no—
470C23×C4—62no—
471C23×C4—62no—
472C23×C4—62no—
473C23×C4—62no—
474C23×C4—62no—
475C23×C4—62no—
476C23×C4—62no—
477C23×C4—62no—
478C23×C4—121no—
479C23×C4—121no—
480C23×C4—121no—
481C23×C4—121no—
482C23×C4C22×D311yescharacteristic
483C23×C4C22×D311yescharacteristic
484C23×C4C22×D311yescharacteristic
485C23×C4C22×D311yescharacteristic
486C23×C4C22×D311yescharacteristic
487C23×C4C22×D311yescharacteristic
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—62no—
498C2×C4⋊C4—62no—
499C2×C4⋊C4—62no—
500C2×C4⋊C4—62no—
501C2×C4⋊C4—62no—
502C2×C4⋊C4—121no—
503C2×C4⋊C4—121no—
504C2×C4⋊C4—121no—
505C2×C4⋊C4—121no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—34no—
513C2×C22⋊C4—34no—
514C2×C22⋊C4—34no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—632no—
518C2×C22⋊C4—62no—
519C2×C22⋊C4—62no—
520C2×C22⋊C4—62no—
521C2×C22⋊C4—62no—
522C2×C22⋊C4—62no—
523C2×C22⋊C4—62no—
524C2×C22⋊C4—62no—
525C2×C22⋊C4—62no—
526C2×C22⋊C4—62no—
527C2×C22⋊C4—62no—
528C2×C22⋊C4—62no—
529C2×C22⋊C4—62no—
530C2×C22⋊C4—62no—
531C2×C22⋊C4—62no—
532C2×C22⋊C4—62no—
533C2×C22⋊C4—62no—
534C2×C22⋊C4—62no—
535C2×C22⋊C4—62no—
536C2×C22⋊C4—62no—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—62no—
539C2×C22⋊C4—62no—
540C2×C22⋊C4—62no—
541C2×C22⋊C4—62no—
542C2×C22⋊C4—62no—
543C2×C22⋊C4—62no—
544C2×C22⋊C4—62no—
545C2×C22⋊C4—62no—
546C2×C22⋊C4—62no—
547C2×C22⋊C4—62no—
548C2×C22⋊C4—121no—
549C2×C22⋊C4—121no—
550C2×C22⋊C4—121no—
551C2×C22⋊C4—121no—
552C2×C22⋊C4—121no—
553C2×C22⋊C4—121no—
554C2×C22⋊C4#6714yes—
555#95—22no—
556#95—62no—
557#95—62no—
558#95—62no—
559#95—62no—
560#95—62no—
561#95—62no—
562#95—62no—
563#95—121no—
564#95—121no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3C22⋊Q814yes—
600C23×C3C22×D411yescharacteristic
601C23×C3C22×D411yescharacteristic
602C23×C3C22×D411yescharacteristic
603C23×C3C22×D411yescharacteristic
604C23×C3C22×D411yescharacteristic
605C23×C3C22×Q811yescharacteristic
606C23×C3C2×#4111yescharacteristic
607C23×C3C2×#4111yescharacteristic
608C23×C3C2×#4111yescharacteristic
609C23×C3C2×#4111yescharacteristic
610C23×C3C2×#4111yescharacteristic
611C23×C3H(5,𝔽2)11yescharacteristic
612C23×C3H(5,𝔽2)11yescharacteristic
613C23×C3H(5,𝔽2)11yescharacteristic
614C23×C3H(5,𝔽2)11yescharacteristic
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—22no—
643C22×D3—232no—
644C22×D3—22no—
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—22no—
651C22×D3—22no—
652C22×D3—22no—
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—416no—
663C22×D3—416no—
664C22×D3—416no—
665C22×D3—416no—
666C22×D3—416no—
667C22×D3—416no—
668C22×D3—416no—
669C22×D3—416no—
670C22×D3—416no—
671C22×D3—416no—
672C22×D3—416no—
673C22×D3—416no—
674C22×D3—416no—
675C22×D3—41no—
676C22×D3—41no—
677C22×D3—41no—
678C22×D3—41no—
679C22×D3—41no—
680C22×D3—41no—
681C22×D3—41no—
682C22×D3—41no—
683C22×D3—41no—
684C22×D3—41no—
685C22×D3—41no—
686C22×D3—41no—
687C22×D3—41no—
688C22×D3—41no—
689C22×D3—41no—
690C22×D3—41no—
691C22×D3—416no—
692C22×D3#12114yes—
693C22×D3#12114yes—
694C22×D3#12114yes—
695C22×D3C22⋊Q814yes—
696C22×D3C22⋊Q814yes—
697C22×D3C22⋊Q814yes—
698C22×D3C22⋊Q814yes—
699C22×D3#12614yes—
700C2×C3×C4—22no—
701C2×C3×C4—22no—
702C2×C3×C4—22no—
703C2×C3×C4—22no—
704C2×C3×C4—22no—
705C2×C3×C4—22no—
706C2×C3×C4—22no—
707C2×C3×C4—22no—
708C2×C3×C4—22no—
709C2×C3×C4—22no—
710C2×C3×C4—22no—
711C2×C3×C4—22no—
712C2×C3×C4—22no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—41no—
716C2×C3×C4—41no—
717C2×C3×C4—41no—
718C2×C3×C4—41no—
719C2×C3×C4—41no—
720C2×C3×C4—41no—
721C2×C3×C4—41no—
722C2×C3×C4—41no—
723C2×C3×C4—41no—
724C2×C3×C4—41no—
725C2×C3×C4—41no—
726C2×C3×C4—41no—
727C2×C3×C4—41no—
728C2×C3×C4—41no—
729C2×C3×C4—41no—
730C2×C3×C4—41no—
731C2×C3×C4—41no—
732C2×C3×C4—41no—
733C2×C3×C4—41no—
734C2×C3×C4—41no—
735C2×C3×C4—41no—
736C2×C3×C4—41no—
737C2×C3×C4—41no—
738C2×C3×C4—41no—
739C2×C3×C4—41no—
740C2×C3×C4—41no—
741C2×C3×C4#12014yes—
742C2×Dic3—22no—
743C2×Dic3—22no—
744C2×Dic3—22no—
745C2×Dic3—22no—
746C2×Dic3—22no—
747C2×Dic3—22no—
748C2×Dic3—22no—
749C2×Dic3—22no—
750C2×Dic3—22no—
751C2×Dic3—22no—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—41no—
755C2×Dic3—41no—
756C2×Dic3—41no—
757C2×Dic3—41no—
758C2×Dic3—41no—
759C2×Dic3—41no—
760C2×Dic3—41no—
761C2×Dic3—41no—
762C2×Dic3—41no—
763C2×Dic3—41no—
764C2×Dic3—41no—
765C2×Dic3—41no—
766C2×Dic3—41no—
767C2×Dic3—41no—
768C2×Dic3—41no—
769C2×Dic3—41no—
770C2×Dic3—41no—
771C2×Dic3—41no—
772C2×Dic3—41no—
773C2×Dic3—41no—
774C2×Dic3—41no—
775C2×Dic3—41no—
776C2×Dic3—41no—
777C2×Dic3—41no—
778C2×Dic3—41no—
779C2×Dic3—41no—
780C2×Dic3—41no—
781C2×Dic3—41no—
782C2×Dic3—41no—
783C2×Dic3—41no—
784C4×D3—416no—
785C4×D3—416no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—32no—
799C24—32no—
800C24—32no—
801C24—32no—
802C24—32no—
803C24—32no—
804C24—32no—
805C24—32no—
806C24—32no—
807C24—32no—
808C24—68no—
809C24—68no—
810C24—68no—
811C24—68no—
812C24—68no—
813C24—68no—
814C24—68no—
815C24—68no—
816C24—61no—
817C24—61no—
818C24—61no—
819C24—61no—
820C24—61no—
821C24—61no—
822C24—61no—
823C24—61no—
824C24—68no—
825C24—61no—
826C24—61no—
827C24—61no—
828C24—61no—
829C24—61no—
830C24—61no—
831C24—61no—
832C24—61no—
833C24—61no—
834C24—61no—
835C24—61no—
836C24—61no—
837C24—124no—
838C24—124no—
839C24—124no—
840C24—124no—
841C24—124no—
842C24—124no—
843C24—124no—
844C24—124no—
845C24—124no—
846C24—124no—
847C24—124no—
848C24—124no—
849C24—124no—
850C24—124no—
851C24—124no—
852C24—124no—
853C24—124no—
854C24—124no—
855C24—124no—
856C24—124no—
857C24—124no—
858C24—124no—
859C24—124no—
860C24—124no—
861C24—124no—
862C24—124no—
863C24D3×Q812yes—
864C24#23912yes—
865C24C2×#6712yes—
866C24C23×D311yescharacteristic
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—32no—
904C22×C4—32no—
905C22×C4—32no—
906C22×C4—32no—
907C22×C4—68no—
908C22×C4—68no—
909C22×C4—61no—
910C22×C4—61no—
911C22×C4—61no—
912C22×C4—61no—
913C22×C4—61no—
914C22×C4—61no—
915C22×C4—61no—
916C22×C4—61no—
917C22×C4—61no—
918C22×C4—61no—
919C22×C4—61no—
920C22×C4—61no—
921C22×C4—61no—
922C22×C4—61no—
923C22×C4—61no—
924C22×C4—61no—
925C22×C4—61no—
926C22×C4—61no—
927C22×C4—61no—
928C22×C4—61no—
929C22×C4—61no—
930C22×C4—61no—
931C22×C4—61no—
932C22×C4—61no—
933C22×C4—68no—
934C22×C4—61no—
935C22×C4—61no—
936C22×C4—61no—
937C22×C4—61no—
938C22×C4—61no—
939C22×C4—61no—
940C22×C4—61no—
941C22×C4—61no—
942C22×C4—61no—
943C22×C4—61no—
944C22×C4—61no—
945C22×C4—61no—
946C22×C4—61no—
947C22×C4—61no—
948C22×C4—124no—
949C22×C4—124no—
950C22×C4—124no—
951C22×C4—124no—
952C22×C4—124no—
953C22×C4—124no—
954C22×C4—124no—
955C22×C4—124no—
956C22×C4—124no—
957C22×C4—124no—
958C22×C4—124no—
959C22×C4D3×D412yes—
960C22×C4D3×D412yes—
961C22×C4D3×D412yes—
962C22×C4D3×D412yes—
963C22×C4C2×#6712yes—
964C22×C4C2×#6712yes—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—124no—
969C4⋊C4—124no—
970C4⋊C4—124no—
971C22⋊C4—28no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—68no—
975C22⋊C4—68no—
976C22⋊C4—68no—
977C22⋊C4—68no—
978C22⋊C4—68no—
979C22⋊C4—124no—
980C22⋊C4—124no—
981C22⋊C4—124no—
982C22⋊C4—124no—
983C22⋊C4—124no—
984C22⋊C4—124no—
985C22⋊C4—124no—
986C22⋊C4—124no—
987C22×C3—24no—
988C22×C3—24no—
989C22×C3—24no—
990C22×C3—42no—
991C22×C3—42no—
992C22×C3—42no—
993C22×C3—42no—
994C22×C3—42no—
995C22×C3—42no—
996C22×C3—42no—
997C22×C3—42no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—42no—
1002C22×C3C2×#12011yescharacteristic
1003C22×C3C2×#12111yescharacteristic
1004C22×C3C2×#12111yescharacteristic
1005C22×C3C2×#12111yescharacteristic
1006C22×C3C2×C22⋊Q811yescharacteristic
1007C22×C3C2×C22⋊Q811yescharacteristic
1008C22×C3C2×C22⋊Q811yescharacteristic
1009C22×C3C2×C22⋊Q811yescharacteristic
1010C22×C3C2×C22⋊Q811yescharacteristic
1011C22×C3#52511yescharacteristic
1012C22×C3#52511yescharacteristic
1013C22×C3#52511yescharacteristic
1014C22×C3C2×#12611yescharacteristic
1015C22×C3#53411yescharacteristic
1016C22×C3#53511yescharacteristic
1017C22×C3#53811yescharacteristic
1018C22×C3#53811yescharacteristic
1019C22×C3#54311yescharacteristic
1020C22×C3#54311yescharacteristic
1021C22×C3D4211yescharacteristic
1022C22×C3D4211yescharacteristic
1023C22×C3D4211yescharacteristic
1024C22×C3D4211yescharacteristic
1025C22×C3#54611yescharacteristic
1026C22×C3#54611yescharacteristic
1027C22×C3#54611yescharacteristic
1028C22×C3#54611yescharacteristic
1029C22×C3#54611yescharacteristic
1030C22×C3#54611yescharacteristic
1031C22×C3#54611yescharacteristic
1032C22×C3#54611yescharacteristic
1033C22×C3#55111yescharacteristic
1034C22×C3#55111yescharacteristic
1035C22×C3#55111yescharacteristic
1036C22×C3#55111yescharacteristic
1037C2×D3—24no—
1038C2×D3—24no—
1039C2×D3—24no—
1040C2×D3—24no—
1041C2×D3—24no—
1042C2×D3—24no—
1043C2×D3—24no—
1044C2×D3—24no—
1045C2×D3—24no—
1046C2×D3—24no—
1047C2×D3—24no—
1048C2×D3—24no—
1049C2×D3—24no—
1050C2×D3—24no—
1051C2×D3—24no—
1052C2×D3—24no—
1053C2×D3—24no—
1054C2×D3—464no—
1055C2×D3—42no—
1056C2×D3—42no—
1057C2×D3—42no—
1058C2×D3—42no—
1059C2×D3—42no—
1060C2×D3—42no—
1061C2×D3—42no—
1062C2×D3—42no—
1063C2×D3—42no—
1064C2×D3—42no—
1065C2×D3—42no—
1066C2×D3—42no—
1067C2×D3#39618yescomplemented
1068C3×C4—24no—
1069C3×C4—42no—
1070C3×C4—42no—
1071C3×C4—42no—
1072C3×C4—81no—
1073C3×C4—81no—
1074Dic3—42no—
1075Dic3—42no—
1076Dic3—42no—
1077Dic3—42no—
1078Dic3—81no—
1079Dic3—81no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—34no—
1099C23—34no—
1100C23—34no—
1101C23—34no—
1102C23—34no—
1103C23—34no—
1104C23—34no—
1105C23—34no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—632no—
1123C23—62no—
1124C23—62no—
1125C23—62no—
1126C23—62no—
1127C23—62no—
1128C23—62no—
1129C23—62no—
1130C23—62no—
1131C23—62no—
1132C23—62no—
1133C23—62no—
1134C23—62no—
1135C23—62no—
1136C23—62no—
1137C23—62no—
1138C23—62no—
1139C23—62no—
1140C23—62no—
1141C23—62no—
1142C23—62no—
1143C23—62no—
1144C23—62no—
1145C23—62no—
1146C23—62no—
1147C23—62no—
1148C23—62no—
1149C23—62no—
1150C23—62no—
1151C23—62no—
1152C23—62no—
1153C23—62no—
1154C23—62no—
1155C23—62no—
1156C23—62no—
1157C23—62no—
1158C23—62no—
1159C23—62no—
1160C23—62no—
1161C23—62no—
1162C23—62no—
1163C23—62no—
1164C23—62no—
1165C23—62no—
1166C23—62no—
1167C23—62no—
1168C23—62no—
1169C23—1216no—
1170C23—1216no—
1171C23—1216no—
1172C23—1216no—
1173C23—1216no—
1174C23—1216no—
1175C23—1216no—
1176C23—1216no—
1177C23—1216no—
1178C23—1216no—
1179C23—1216no—
1180C23—1216no—
1181C23—1216no—
1182C23—1216no—
1183C23—121no—
1184C23—121no—
1185C23—121no—
1186C23—121no—
1187C23—121no—
1188C23—121no—
1189C23—121no—
1190C23—121no—
1191C23—121no—
1192C23—121no—
1193C23—121no—
1194C23—121no—
1195C23—121no—
1196C23—121no—
1197C23—121no—
1198C23—121no—
1199C23#94614yes—
1200C23C2×D3×D411yescharacteristic
1201C23C2×D3×D411yescharacteristic
1202C23C2×D3×D411yescharacteristic
1203C23C2×D3×D411yescharacteristic
1204C23#100411yescharacteristic
1205C23#100411yescharacteristic
1206C23C2×D3×Q811yescharacteristic
1207C23C2×#23911yescharacteristic
1208C23D3×#4111yescharacteristic
1209C23D3×#4111yescharacteristic
1210C23D3×#4111yescharacteristic
1211C23D3×#4111yescharacteristic
1212C23#100911yescharacteristic
1213C23#100911yescharacteristic
1214C23C22×#6711yescharacteristic
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—62no—
1257C2×C4—62no—
1258C2×C4—62no—
1259C2×C4—62no—
1260C2×C4—62no—
1261C2×C4—62no—
1262C2×C4—62no—
1263C2×C4—62no—
1264C2×C4—62no—
1265C2×C4—62no—
1266C2×C4—62no—
1267C2×C4—62no—
1268C2×C4—1216no—
1269C2×C4—1216no—
1270C2×C4—121no—
1271C2×C4—121no—
1272C2×C4—121no—
1273C2×C4—121no—
1274C2×C4—121no—
1275C2×C4—121no—
1276C2×C4—121no—
1277C2×C4—121no—
1278C2×C4—121no—
1279C2×C4—121no—
1280C2×C4—121no—
1281C2×C4—121no—
1282C2×C4—121no—
1283C2×C4—121no—
1284C2×C4—121no—
1285C2×C4—121no—
1286C2×C4—121no—
1287C2×C4—121no—
1288C2×C4—121no—
1289C2×C4—121no—
1290C2×C4—121no—
1291C2×C4—121no—
1292C2×C4—121no—
1293C2×C4—121no—
1294C2×C4—121no—
1295C2×C4—121no—
1296C2×C4—121no—
1297C2×C4—121no—
1298C2×C4—121no—
1299C2×C4—121no—
1300C2×C4#93714yes—
1301C2×C3—44no—
1302C2×C3C2×#39611yescharacteristic
1303C2×C3#240811yescharacteristic
1304C2×C3#241011yescharacteristic
1305C2×C3#241111yescharacteristic
1306C2×C3#242411yescharacteristic
1307C2×C3#242411yescharacteristic
1308C2×C3#243711yescharacteristic
1309C2×C3#243711yescharacteristic
1310C2×C3#243711yescharacteristic
1311C2×C3#243711yescharacteristic
1312C2×C3#248011yescharacteristic
1313C2×C3#248011yescharacteristic
1314C2×C3#253411yescharacteristic
1315C2×C3#262611yescharacteristic
1316C2×C3#284811yescharacteristic
1317D3—28no—
1318D3—44no—
1319C22—24no—
1320C22—24no—
1321C22—24no—
1322C22—38no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—64no—
1336C22—64no—
1337C22—64no—
1338C22—64no—
1339C22—64no—
1340C22—64no—
1341C22—64no—
1342C22—64no—
1343C22—64no—
1344C22—64no—
1345C22—64no—
1346C22—64no—
1347C22—64no—
1348C22—64no—
1349C22—64no—
1350C22—64no—
1351C22—64no—
1352C22—1264no—
1353C22—122no—
1354C22—122no—
1355C22—122no—
1356C22—122no—
1357C22—122no—
1358C22—122no—
1359C22—122no—
1360C22—122no—
1361C22—122no—
1362C22—122no—
1363C22—122no—
1364C22—122no—
1365C22D3×#12111yescharacteristic
1366C22D3×#12111yescharacteristic
1367C22D3×#12111yescharacteristic
1368C22#560511yescharacteristic
1369C22#560711yescharacteristic
1370C22#560911yescharacteristic
1371C22#560911yescharacteristic
1372C22#561011yescharacteristic
1373C22#561011yescharacteristic
1374C22#561211yescharacteristic
1375C22#561211yescharacteristic
1376C22#561311yescharacteristic
1377C22D3×C22⋊Q811yescharacteristic
1378C22D3×C22⋊Q811yescharacteristic
1379C22D3×C22⋊Q811yescharacteristic
1380C22D3×C22⋊Q811yescharacteristic
1381C22#562711yescharacteristic
1382C22#562711yescharacteristic
1383C22#563011yescharacteristic
1384C22#563011yescharacteristic
1385C22#563411yescharacteristic
1386C22#563411yescharacteristic
1387C22#563711yescharacteristic
1388C22#563711yescharacteristic
1389C22D3×#12611yescharacteristic
1390C22#570411yescharacteristic
1391C22#570511yescharacteristic
1392C22#570511yescharacteristic
1393C22C2×#93711yescharacteristic
1394C22D4×#6711yescharacteristic
1395C22D4×#6711yescharacteristic
1396C22C2×#94611yescharacteristic
1397C22#582811yescharacteristic
1398C22#582911yescharacteristic
1399C22#582911yescharacteristic
1400C4—24no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—81no—
1405C4—81no—
1406C4—122no—
1407C4—122no—
1408C4—122no—
1409C4—122no—
1410C4—241no—
1411C4—241no—
1412C3#1472611yescharacteristic, complemented, Sylow
1413C2—44no—
1414C2—68no—
1415C2—124no—
1416C2#7730311yescharacteristic
1417C2D3×#39611yescharacteristic
1418C2#7741411yescharacteristic
1419C2#7741611yescharacteristic
1420C2#7741811yescharacteristic
1421C2#7741811yescharacteristic
1422C2#7742111yescharacteristic
1423C2#7742411yescharacteristic
1424C2#8264011yescharacteristic
1425C2#8270211yescharacteristic
1426C2#8270711yescharacteristic
1427C2#8281611yescharacteristic
1428C2#8281611yescharacteristic
1429C2#8283411yescharacteristic
1430C2#8308111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#396C2
prime radicalC25×D3C22
hypercenterC2×#396D3
hypocenterC3#14726
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C2×C3×#396C2semidirect
3. C2×#4994C2semidirect
4. C2×#4989C2semidirect
5. C2×#4989C2semidirect
6. C2×#4987C2semidirect
9. #71570C2semidirect
10. #71570C2semidirect
11. #71547C2semidirect
12. #71547C2semidirect
13. #71546C2semidirect
14. #69428C2semidirect
15. (C2×D3)⋊#95C2semidirect
20. C22×C3×C4⋊C4C22semidirect
21. C22×C3×C4⋊C4C22semidirect
22. C22×C3×C4⋊C4C22semidirect
39. C22×C4⋊Dic3C22semidirect
40. C22×Dic3⋊C4C22semidirect
41. C22×Dic3⋊C4C22semidirect
46. C2×C3×#95C22semidirect
47. C2×C3⋊#95C22semidirect
48. C2×C3⋊#95C22semidirect
49. C2×C3⋊#95C22semidirect
50. C2×C3⋊#95C22semidirect
51. C2×C3⋊#95C22semidirect
52. C2×C3⋊#95C22semidirect
53. C2×C3⋊#95C22semidirect
54. C2×C3⋊#95C22semidirect
55. C2×C3⋊#95C22semidirect
64. C2×#396D3semidirect
204. C22×C4⋊C4C2×D3semidirect
205. C22×C4⋊C4C2×D3semidirect
206. C22×C4⋊C4C2×D3semidirect
242. C2×#95C2×D3semidirect
1067. C2×D3#396semidirect
1412. C3#14726semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊C42
C2×C3×#3962
C2×#49942
C2×#49892
C2×#49872
C2×#49552
#715702
#715472
#715462
#694282
(C2×D3)⋊#952
#147263