Finite Group Databasebeta

← #11773335

Subgroups — #11773335

Order 1152.

1809 conjugacy classes of subgroups.

The subgroup lattice has 1187 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×#3722C211yesmaximal, characteristic
3C22×#3722C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#63579C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#69429—31nomaximal
9#69429—31nomaximal
10C24×C3⋊D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×#3752—22no—
18C2×#3752—22no—
19C2×#3752—22no—
20C2×#3722—22no—
21C2×#3722—22no—
22C2×#3722—22no—
23C2×#3722—22no—
24C2×#3722—22no—
25C2×#3722C414yescomplemented
26C3×C3⋊#95—22no—
27C3×C3⋊#95—22no—
28#63579—22no—
29#63579—22no—
30C22×(C2×D3)⋊C4—31no—
31C22×(C2×D3)⋊C4—31no—
32C22×(C2×D3)⋊C4—31no—
33C22×(C2×D3)⋊C4—31no—
34C22×(C2×D3)⋊C4—31no—
35C22×(C2×D3)⋊C4—31no—
36C22×(C2×D3)⋊C4—61no—
37C2×C3×#95—31no—
38C2×C3×#95—31no—
39C2×C3⋊#95—31no—
40C2×C3⋊#95—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95D311yescharacteristic, complemented
44C2×C3⋊#95D311yescharacteristic, complemented
45C24×C32C2311yescharacteristic
46C23×C3⋊D3—21no—
47C23×C3⋊D3—21no—
48C23×C3⋊D3—21no—
49C23×C3⋊D3—21no—
50C23×C3⋊D3—21no—
51C23×C3⋊D3—21no—
52C23×C3⋊D3—21no—
53C23×C3⋊D3—21no—
54C23×C3⋊D3—21no—
55C23×C3⋊D3—21no—
56C23×C3⋊D3—21no—
57C23×C3⋊D3—21no—
58C23×C3⋊D3C2×C412yes—
59C23×C3⋊D3D412yes—
60C23×C3⋊D3D412yes—
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4D412yes—
68C22×C3⋊Dic3—21no—
69C22×C3⋊Dic3—21no—
70C22×C3⋊Dic3—21no—
71C22×C3⋊Dic3—21no—
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3D412yes—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3C2×C412yes—
100C22×C3×Dic3C2×C412yes—
101C22×C3×Dic3D412yes—
102C22×C3×Dic3D412yes—
103#3752—28no—
104#3722—28no—
105#3722—28no—
106#1440—91noSylow
107C24×D3—31no—
108C24×D3—31no—
109C24×D3—61no—
110C23×C3×C4—21no—
111C23×C3×C4—31no—
112C23×C3×C4—31no—
113C23×C3×C4—31no—
114C23×C3×C4—31no—
115C23×C3×C4C2×D311yescharacteristic
116C23×C3×C4C2×D311yescharacteristic
117C23×Dic3—31no—
118C23×Dic3—31no—
119C23×Dic3—61no—
120C23×Dic3C2×D311yescharacteristic
121C23×Dic3C2×D311yescharacteristic
122C23×Dic3C2×D311yescharacteristic
123C23×Dic3C2×D311yescharacteristic
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—34no—
126C2×(C2×D3)⋊C4—62no—
127C2×(C2×D3)⋊C4—62no—
128C2×(C2×D3)⋊C4—62no—
129C2×(C2×D3)⋊C4—62no—
130C2×(C2×D3)⋊C4—62no—
131C2×(C2×D3)⋊C4—62no—
132C2×(C2×D3)⋊C4—62no—
133C2×(C2×D3)⋊C4—62no—
134C2×(C2×D3)⋊C4—62no—
135C2×(C2×D3)⋊C4—62no—
136C2×(C2×D3)⋊C4—62no—
137C2×(C2×D3)⋊C4—62no—
138C2×(C2×D3)⋊C4—64no—
139C2×(C2×D3)⋊C4—64no—
140C2×(C2×D3)⋊C4—64no—
141C2×(C2×D3)⋊C4—62no—
142C2×(C2×D3)⋊C4—62no—
143C2×(C2×D3)⋊C4—62no—
144C2×(C2×D3)⋊C4—62no—
145C3×#95—62no—
146C3×#95—62no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—62no—
150C3⋊#95—62no—
151C3⋊#95—62no—
152C3⋊#95—62no—
153C23×C32C22×C411yescharacteristic
154C23×C32C2×D411yescharacteristic
155C23×C32C2×D411yescharacteristic
156C23×C32C2×D411yescharacteristic
157C23×C32C2×D411yescharacteristic
158C23×C32C2×D411yescharacteristic
159C23×C32C2×D411yescharacteristic
160C23×C32#4111yescharacteristic
161C23×C32#4111yescharacteristic
162C23×C32#4111yescharacteristic
163C23×C32#4111yescharacteristic
164C23×C32#4111yescharacteristic
165C23×C32#4111yescharacteristic
166C23×C32#4111yescharacteristic
167C23×C32#4111yescharacteristic
168C22×C3⋊D3—22no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3—22no—
175C22×C3⋊D3—22no—
176C22×C3⋊D3—22no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3—22no—
183C22×C3⋊D3—22no—
184C22×C3⋊D3—22no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3—41no—
187C22×C3⋊D3—41no—
188C22×C3⋊D3—41no—
189C22×C3⋊D3—41no—
190C22×C3⋊D3—41no—
191C22×C3⋊D3—41no—
192C22×C3⋊D3—41no—
193C22×C3⋊D3—41no—
194C22×C3⋊D3—41no—
195C22×C3⋊D3—41no—
196C22×C3⋊D3—41no—
197C22×C3⋊D3—41no—
198C22×C3⋊D3—41no—
199C22×C3⋊D3—41no—
200C22×C3⋊D3—41no—
201C22×C3⋊D3—41no—
202C22×C3⋊D3C22⋊C414yes—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4—41no—
207C2×C32×C4—41no—
208C2×C32×C4—41no—
209C2×C32×C4—41no—
210C2×C3⋊Dic3—22no—
211C2×C3⋊Dic3—22no—
212C2×C3⋊Dic3—22no—
213C2×C3⋊Dic3—41no—
214C2×C3⋊Dic3—41no—
215C2×C3⋊Dic3—41no—
216C2×C3⋊Dic3—41no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—41no—
230C2×C3×Dic3—41no—
231C2×C3×Dic3—41no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3—41no—
234C2×C3×Dic3—41no—
235C2×C3×Dic3—41no—
236C2×C3×Dic3—41no—
237C2×C3×Dic3—41no—
238C2×C3×Dic3—41no—
239C2×C3×Dic3—41no—
240C2×C3×Dic3—41no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—41no—
243C2×C3×Dic3—41no—
244C2×C3×Dic3—41no—
245C22×C22⋊C4—91no—
246C22×C22⋊C4—91no—
247C22×C22⋊C4—91no—
248C2×#95—31no—
249C2×#95—31no—
250C2×#95—91no—
251C2×#95—91no—
252C24×C3—21no—
253C24×C3C22×D311yescharacteristic
254C24×C3C22×D311yescharacteristic
255C23×D3—32no—
256C23×D3—32no—
257C23×D3—32no—
258C23×D3—32no—
259C23×D3—32no—
260C23×D3—32no—
261C23×D3—62no—
262C23×D3—62no—
263C23×D3—62no—
264C23×D3—62no—
265C23×D3—62no—
266C23×D3—62no—
267C23×D3—62no—
268C23×D3—61no—
269C23×D3—61no—
270C23×D3—61no—
271C23×D3—61no—
272C23×D3—61no—
273C23×D3—61no—
274C23×D3—61no—
275C23×D3—61no—
276C23×D3—61no—
277C23×D3—61no—
278C23×D3—61no—
279C23×D3—61no—
280C23×D3—61no—
281C23×D3—61no—
282C23×D3—61no—
283C23×D3—61no—
284C23×D3—61no—
285C23×D3—61no—
286C23×D3—61no—
287C23×D3—61no—
288C23×D3—61no—
289C23×D3—61no—
290C23×D3—61no—
291C23×D3—61no—
292C23×D3—121no—
293C23×D3—121no—
294C23×D3—121no—
295C23×D3—121no—
296C23×D3—121no—
297C23×D3—121no—
298C23×D3—121no—
299C23×D3—121no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—22no—
315C22×C3×C4—32no—
316C22×C3×C4—32no—
317C22×C3×C4—32no—
318C22×C3×C4—32no—
319C22×C3×C4—41no—
320C22×C3×C4—41no—
321C22×C3×C4—41no—
322C22×C3×C4—41no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4D1212yes—
348C22×C3×C4#6712yes—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—32no—
374C22×Dic3—32no—
375C22×Dic3—62no—
376C22×Dic3—62no—
377C22×Dic3—62no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—121no—
391C22×Dic3—121no—
392C22×Dic3—121no—
393C22×Dic3—121no—
394C22×Dic3C4×D312yes—
395C22×Dic3C4×D312yes—
396C22×Dic3D1212yes—
397C22×Dic3#6712yes—
398(C2×D3)⋊C4—68no—
399(C2×D3)⋊C4—68no—
400(C2×D3)⋊C4—68no—
401(C2×D3)⋊C4—68no—
402(C2×D3)⋊C4—616no—
403(C2×D3)⋊C4—68no—
404(C2×D3)⋊C4—68no—
405C22×C32C2×C22⋊C411yescharacteristic
406C22×C32#11711yescharacteristic
407C22×C32#11711yescharacteristic
408C22×C32C4×D411yescharacteristic
409C22×C32C4×D411yescharacteristic
410C22×C32C4×D411yescharacteristic
411C22×C32C4×D411yescharacteristic
412C22×C32#12011yescharacteristic
413C22×C32#12011yescharacteristic
414C22×C32#12111yescharacteristic
415C22×C32#12111yescharacteristic
416C22×C32#12111yescharacteristic
417C22×C32#12111yescharacteristic
418C22×C32#12111yescharacteristic
419C22×C32#12111yescharacteristic
420C22×C32#12111yescharacteristic
421C22×C32#12111yescharacteristic
422C22×C32#12311yescharacteristic
423C22×C32#12311yescharacteristic
424C22×C32#12311yescharacteristic
425C22×C32#12311yescharacteristic
426C22×C32#12311yescharacteristic
427C22×C32#12311yescharacteristic
428C22×C32#12311yescharacteristic
429C22×C32#12311yescharacteristic
430C22×C32#12311yescharacteristic
431C22×C32#12311yescharacteristic
432C22×C32#12411yescharacteristic
433C22×C32#12411yescharacteristic
434C22×C32#12411yescharacteristic
435C22×C32#12411yescharacteristic
436C22×C32#12611yescharacteristic
437C22×C32#12611yescharacteristic
438C22×C32#12611yescharacteristic
439C22×C32#12611yescharacteristic
440C2×C3⋊D3—24no—
441C2×C3⋊D3—24no—
442C2×C3⋊D3—24no—
443C2×C3⋊D3—42no—
444C2×C3⋊D3—42no—
445C2×C3⋊D3—42no—
446C2×C3⋊D3—42no—
447C2×C3⋊D3—42no—
448C2×C3⋊D3—42no—
449C2×C3⋊D3—42no—
450C2×C3⋊D3—42no—
451C2×C3⋊D3—42no—
452C2×C3⋊D3—42no—
453C2×C3⋊D3—42no—
454C2×C3⋊D3—42no—
455C32×C4—42no—
456C3⋊Dic3—42no—
457C3×Dic3—42no—
458C3×Dic3—42no—
459C3×Dic3—42no—
460C3×Dic3—42no—
461C25—91no—
462C23×C4—31no—
463C23×C4—31no—
464C23×C4—31no—
465C23×C4—31no—
466C23×C4—91no—
467C23×C4D3211yescharacteristic
468C2×C22⋊C4—94no—
469C2×C22⋊C4—182no—
470C2×C22⋊C4—182no—
471C2×C22⋊C4—182no—
472C2×C22⋊C4—182no—
473C2×C22⋊C4—182no—
474C2×C22⋊C4—182no—
475C2×C22⋊C4—182no—
476C2×C22⋊C4—182no—
477#95—62no—
478#95—62no—
479#95—182no—
480#95—182no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3C2×C4×D311yescharacteristic
497C23×C3C2×C4×D311yescharacteristic
498C23×C3C2×D1211yescharacteristic
499C23×C3C2×D1211yescharacteristic
500C23×C3#23511yescharacteristic
501C23×C3#23511yescharacteristic
502C23×C3#23511yescharacteristic
503C23×C3#23511yescharacteristic
504C23×C3#23511yescharacteristic
505C23×C3#23511yescharacteristic
506C23×C3#23511yescharacteristic
507C23×C3#23511yescharacteristic
508C23×C3D3×D411yescharacteristic
509C23×C3D3×D411yescharacteristic
510C23×C3D3×D411yescharacteristic
511C23×C3D3×D411yescharacteristic
512C23×C3D3×D411yescharacteristic
513C23×C3D3×D411yescharacteristic
514C23×C3D3×D411yescharacteristic
515C23×C3D3×D411yescharacteristic
516C23×C3#23711yescharacteristic
517C23×C3#23711yescharacteristic
518C23×C3#23711yescharacteristic
519C23×C3#23711yescharacteristic
520C23×C3#23911yescharacteristic
521C23×C3#23911yescharacteristic
522C23×C3#23911yescharacteristic
523C23×C3#23911yescharacteristic
524C23×C3C2×#6711yescharacteristic
525C23×C3C2×#6711yescharacteristic
526C22×D3—34no—
527C22×D3—34no—
528C22×D3—64no—
529C22×D3—64no—
530C22×D3—64no—
531C22×D3—64no—
532C22×D3—64no—
533C22×D3—64no—
534C22×D3—64no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—62no—
551C22×D3—62no—
552C22×D3—62no—
553C22×D3—62no—
554C22×D3—62no—
555C22×D3—62no—
556C22×D3—62no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3—62no—
568C22×D3—62no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—122no—
572C22×D3—122no—
573C22×D3—122no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3—122no—
580C22×D3—122no—
581C22×D3—122no—
582C22×D3—122no—
583C22×D3—122no—
584C22×D3—122no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3—122no—
588C22×D3—122no—
589C22×D3—122no—
590C22×D3—122no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—122no—
595C22×D3—122no—
596C22×D3—122no—
597C22×D3—122no—
598C22×D3—122no—
599C22×D3—121no—
600C22×D3—121no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—121no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—121no—
619C22×D3—121no—
620C22×D3—121no—
621C22×D3—121no—
622C22×D3—121no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C2×C3×C4—24no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—42no—
639C2×C3×C4—42no—
640C2×C3×C4—42no—
641C2×C3×C4—42no—
642C2×C3×C4—42no—
643C2×C3×C4—42no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4—62no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—121no—
665C2×C3×C4—121no—
666C2×C3×C4—121no—
667C2×C3×C4—121no—
668C2×C3×C4—121no—
669C2×C3×C4—121no—
670C2×C3×C4—121no—
671C2×C3×C4—121no—
672C2×C3×C4—121no—
673C2×C3×C4—121no—
674C2×C3×C4—121no—
675C2×C3×C4—121no—
676C2×C3×C4—121no—
677C2×C3×C4—121no—
678C2×C3×C4—121no—
679C2×C3×C4—121no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—41no—
693C2×Dic3—41no—
694C2×Dic3—41no—
695C2×Dic3—41no—
696C2×Dic3—41no—
697C2×Dic3—41no—
698C2×Dic3—41no—
699C2×Dic3—41no—
700C2×Dic3—41no—
701C2×Dic3—41no—
702C2×Dic3—41no—
703C2×Dic3—41no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—64no—
709C2×Dic3—62no—
710C2×Dic3—62no—
711C2×Dic3—62no—
712C2×Dic3—62no—
713C2×Dic3—62no—
714C2×Dic3—62no—
715C2×Dic3—122no—
716C2×Dic3—122no—
717C2×Dic3—122no—
718C2×Dic3—122no—
719C2×Dic3—122no—
720C2×Dic3—122no—
721C2×Dic3—121no—
722C2×Dic3—121no—
723C2×Dic3—121no—
724C2×Dic3—121no—
725C2×Dic3—121no—
726C2×Dic3—121no—
727C2×Dic3—121no—
728C2×Dic3—121no—
729C2×C32#38111yescharacteristic
730C2×C32#38611yescharacteristic
731C2×C32#38611yescharacteristic
732C2×C32#38811yescharacteristic
733C2×C32#38811yescharacteristic
734C2×C32#38811yescharacteristic
735C2×C32#38811yescharacteristic
736C2×C32#39411yescharacteristic
737C2×C32#39411yescharacteristic
738C2×C32#39411yescharacteristic
739C2×C32#39411yescharacteristic
740C2×C32#39711yescharacteristic
741C2×C32#39711yescharacteristic
742C2×C32#39711yescharacteristic
743C2×C32#39711yescharacteristic
744C3⋊D3—44no—
745C24—92no—
746C24—92no—
747C24—92no—
748C24—181no—
749C24—181no—
750C24—181no—
751C24—181no—
752C24—181no—
753C24—181no—
754C24—181no—
755C24—181no—
756C24—181no—
757C24—181no—
758C24—181no—
759C24—181no—
760C24C2×D3211yescharacteristic
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—32no—
768C22×C4—32no—
769C22×C4—32no—
770C22×C4—32no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—92no—
796C22×C4—181no—
797C22×C4—181no—
798C22×C4—181no—
799C22×C4—181no—
800C22×C4—181no—
801C22×C4—181no—
802C22×C4#62612yes—
803C22⋊C4—188no—
804C22⋊C4—188no—
805C22⋊C4—188no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3#87211yescharacteristic
842C22×C3#87211yescharacteristic
843C22×C3C4×D1211yescharacteristic
844C22×C3C4×D1211yescharacteristic
845C22×C3#87511yescharacteristic
846C22×C3#87511yescharacteristic
847C22×C3#87611yescharacteristic
848C22×C3#87611yescharacteristic
849C22×C3D3×C22⋊C411yescharacteristic
850C22×C3D3×C22⋊C411yescharacteristic
851C22×C3#67⋊C411yescharacteristic
852C22×C3#67⋊C411yescharacteristic
853C22×C3#88211yescharacteristic
854C22×C3#88211yescharacteristic
855C22×C3#88311yescharacteristic
856C22×C3#88311yescharacteristic
857C22×C3#88311yescharacteristic
858C22×C3#88311yescharacteristic
859C22×C3#88311yescharacteristic
860C22×C3#88311yescharacteristic
861C22×C3#88411yescharacteristic
862C22×C3#88411yescharacteristic
863C22×C3#88411yescharacteristic
864C22×C3#88411yescharacteristic
865C22×C3#88411yescharacteristic
866C22×C3#88411yescharacteristic
867C22×C3#88511yescharacteristic
868C22×C3#88511yescharacteristic
869C22×C3#88511yescharacteristic
870C22×C3#88511yescharacteristic
871C22×C3#88611yescharacteristic
872C22×C3#88611yescharacteristic
873C22×C3#89211yescharacteristic
874C22×C3#89211yescharacteristic
875C22×C3#89311yescharacteristic
876C22×C3#89311yescharacteristic
877C22×C3#89411yescharacteristic
878C22×C3#89411yescharacteristic
879C22×C3#89411yescharacteristic
880C22×C3#89411yescharacteristic
881C22×C3#89411yescharacteristic
882C22×C3#89411yescharacteristic
883C22×C3#89411yescharacteristic
884C22×C3#89411yescharacteristic
885C22×C3#89411yescharacteristic
886C22×C3#89411yescharacteristic
887C22×C3#89511yescharacteristic
888C22×C3#89511yescharacteristic
889C22×C3#89511yescharacteristic
890C22×C3#89511yescharacteristic
891C22×C3#89811yescharacteristic
892C22×C3#89811yescharacteristic
893C22×C3#89811yescharacteristic
894C22×C3#89811yescharacteristic
895C22×C3#89811yescharacteristic
896C22×C3#89811yescharacteristic
897C22×C3C4×#6711yescharacteristic
898C22×C3C4×#6711yescharacteristic
899C22×C3#92911yescharacteristic
900C22×C3#92911yescharacteristic
901C22×C3#93011yescharacteristic
902C22×C3#93011yescharacteristic
903C22×C3#93711yescharacteristic
904C22×C3#93711yescharacteristic
905C22×C3#93811yescharacteristic
906C22×C3#93811yescharacteristic
907C22×C3#93911yescharacteristic
908C22×C3#93911yescharacteristic
909C22×C3#94711yescharacteristic
910C22×C3#94711yescharacteristic
911C2×D3—68no—
912C2×D3—64no—
913C2×D3—64no—
914C2×D3—64no—
915C2×D3—64no—
916C2×D3—64no—
917C2×D3—64no—
918C2×D3—124no—
919C2×D3—124no—
920C2×D3—124no—
921C2×D3—124no—
922C2×D3—124no—
923C2×D3—124no—
924C2×D3—124no—
925C2×D3—124no—
926C2×D3—124no—
927C2×D3—124no—
928C2×D3—124no—
929C2×D3—124no—
930C2×D3—124no—
931C2×D3—124no—
932C2×D3—122no—
933C2×D3—122no—
934C2×D3—122no—
935C2×D3—122no—
936C2×D3—122no—
937C2×D3—122no—
938C2×D3—122no—
939C2×D3—122no—
940C2×D3—122no—
941C2×D3—122no—
942C2×D3—122no—
943C2×D3—122no—
944C2×D3—122no—
945C2×D3—122no—
946C2×D3—122no—
947C2×D3—122no—
948C2×D3—122no—
949C2×D3—122no—
950C2×D3—122no—
951C2×D3—122no—
952C2×D3—122no—
953C2×D3—122no—
954C2×D3—122no—
955C2×D3—122no—
956C3×C4—44no—
957C3×C4—42no—
958C3×C4—42no—
959C3×C4—122no—
960C3×C4—122no—
961C3×C4—122no—
962C3×C4—122no—
963Dic3—42no—
964Dic3—42no—
965Dic3—42no—
966Dic3—42no—
967Dic3—124no—
968Dic3—122no—
969Dic3—122no—
970C32#144011yescharacteristic, complemented, Sylow
971C23—94no—
972C23—182no—
973C23—182no—
974C23—182no—
975C23—182no—
976C23—182no—
977C23—182no—
978C23—182no—
979C23—182no—
980C23—182no—
981C23—182no—
982C23—182no—
983C23—182no—
984C23—182no—
985C23—182no—
986C23—182no—
987C23—182no—
988C23—182no—
989C23—182no—
990C23—361no—
991C23—361no—
992C23—361no—
993C23—361no—
994C23—361no—
995C23—361no—
996C23—361no—
997C23—361no—
998C23—361no—
999C23—361no—
1000C23—361no—
1001C23—361no—
1002C23—361no—
1003C23—361no—
1004C23—361no—
1005C23—361no—
1006C23#379611yescharacteristic
1007C23#379811yescharacteristic
1008C23#379911yescharacteristic
1009C23#379911yescharacteristic
1010C23#379911yescharacteristic
1011C23C4×D3211yescharacteristic
1012C23D3×D1211yescharacteristic
1013C23#380211yescharacteristic
1014C23#380411yescharacteristic
1015C23#380411yescharacteristic
1016C23#380411yescharacteristic
1017C23C2×#62611yescharacteristic
1018C23D3×#6711yescharacteristic
1019C23#381111yescharacteristic
1020C23#381111yescharacteristic
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—182no—
1057C2×C4—182no—
1058C2×C4—182no—
1059C2×C4—361no—
1060C2×C4—361no—
1061C2×C4—361no—
1062C2×C4—361no—
1063C2×C3—21no—
1064C2×C3—21no—
1065C2×C3—21no—
1066C2×C3—21no—
1067C2×C3—21no—
1068C2×C3—21no—
1069C2×C3—21no—
1070C2×C3—21no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3#466411yescharacteristic
1079C2×C3#466411yescharacteristic
1080C2×C3#466511yescharacteristic
1081C2×C3#466511yescharacteristic
1082C2×C3#466911yescharacteristic
1083C2×C3#466911yescharacteristic
1084C2×C3#467011yescharacteristic
1085C2×C3#467011yescharacteristic
1086C2×C3#467211yescharacteristic
1087C2×C3#467211yescharacteristic
1088C2×C3#467411yescharacteristic
1089C2×C3#467411yescharacteristic
1090C2×C3#467511yescharacteristic
1091C2×C3#467511yescharacteristic
1092C2×C3#467511yescharacteristic
1093C2×C3#467511yescharacteristic
1094C2×C3#494011yescharacteristic
1095C2×C3#494011yescharacteristic
1096C2×C3#495611yescharacteristic
1097C2×C3#495611yescharacteristic
1098C2×C3#495911yescharacteristic
1099C2×C3#495911yescharacteristic
1100C2×C3#496111yescharacteristic
1101C2×C3#496111yescharacteristic
1102C2×C3#499011yescharacteristic
1103C2×C3#499011yescharacteristic
1104C2×C3#499111yescharacteristic
1105C2×C3#499111yescharacteristic
1106C2×C3#499211yescharacteristic
1107C2×C3#499211yescharacteristic
1108D3—128no—
1109D3—124no—
1110D3—124no—
1111C22—184no—
1112C22—184no—
1113C22—184no—
1114C22—362no—
1115C22—362no—
1116C22—362no—
1117C22—362no—
1118C22—362no—
1119C22—362no—
1120C22—362no—
1121C22—362no—
1122C22—362no—
1123C22—362no—
1124C22—362no—
1125C22—362no—
1126C22#6383611yescharacteristic
1127C22#6383611yescharacteristic
1128C22#6384811yescharacteristic
1129C22#6384811yescharacteristic
1130C22#6385011yescharacteristic
1131C22#6385211yescharacteristic
1132C22#6385311yescharacteristic
1133C22#6385411yescharacteristic
1134C22#6385411yescharacteristic
1135C22#6385411yescharacteristic
1136C22#6386411yescharacteristic
1137C22#6386811yescharacteristic
1138C22#6386811yescharacteristic
1139C22#6388011yescharacteristic
1140C22#6388111yescharacteristic
1141C22#6389011yescharacteristic
1142C22#6389711yescharacteristic
1143C22#6389711yescharacteristic
1144C22C4×#62611yescharacteristic
1145C22#6390411yescharacteristic
1146C22#6390711yescharacteristic
1147C22#6390911yescharacteristic
1148C22#6391011yescharacteristic
1149C22#6391011yescharacteristic
1150C22#6391211yescharacteristic
1151C22#6391611yescharacteristic
1152C22#6392111yescharacteristic
1153C22#6392211yescharacteristic
1154C22#6395311yescharacteristic
1155C22#6395811yescharacteristic
1156C22#6396611yescharacteristic
1157C22#6397111yescharacteristic
1158C22#6397511yescharacteristic
1159C22#6397811yescharacteristic
1160C22#6398111yescharacteristic
1161C4—42no—
1162C4—122no—
1163C4—122no—
1164C4—122no—
1165C4—122no—
1166C4—362no—
1167C3—21no—
1168C3#6942911yescharacteristic, complemented
1169C3#6942911yescharacteristic, complemented
1170C2—364no—
1171C2#1059119411yescharacteristic
1172C2#1059120411yescharacteristic
1173C2#1059120811yescharacteristic
1174C2#1059121611yescharacteristic
1175C2#1059125811yescharacteristic
1176C2#1059125911yescharacteristic
1177C2#1059127511yescharacteristic
1178C2#1059128911yescharacteristic
1179C2#1059129211yescharacteristic
1180C2#1059132111yescharacteristic
1181C2#1059132611yescharacteristic
1182C2#1059137111yescharacteristic
1183C2#1059138711yescharacteristic
1184C2#1059139211yescharacteristic
1185C2#1059171211yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, cosocleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32#1440
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×C3×C3⋊#95C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C2×#63579C2semidirect
7. C2×#63579C2semidirect
25. C2×#3722C4semidirect
43. C2×C3⋊#95D3semidirect
44. C2×C3⋊#95D3semidirect
970. C32#1440semidirect
1168. C3#69429semidirect
1169. C3#69429semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C22×#37222
C2×C3×C3⋊#952
C2×#635792
#694293