Finite Group Databasebeta

← #11808793

Subgroups — #11808793

Order 1152.

1255 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63952C211yesmaximal, characteristic
2C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
3#10592660C211yesmaximal, characteristic
4C3×#4947C211yesmaximal, characteristic, complemented
5C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6#10591717C211yesmaximal, characteristic, complemented
7#10591712C211yesmaximal, characteristic
8Dic3×#217C211yesmaximal, characteristic, complemented
9#10591310C211yesmaximal, characteristic, complemented
10#10591239C211yesmaximal, characteristic, complemented
11#10591233C211yesmaximal, characteristic, complemented
12#10591233C211yesmaximal, characteristic, complemented
13#10591218C211yesmaximal, characteristic, complemented
14#10591211C211yesmaximal, characteristic, complemented
15#10591208C211yesmaximal, characteristic, complemented
16#76779—31nomaximal
17#73481—31nomaximal
18C22×#638C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63952—24no—
42Dic3×Dic6—24no—
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×Q8×Dic3—31no—
56C2×C4×#67—31no—
57C2×#67⋊C4—31no—
58C2×C4×Dic6—31no—
59C3×#393—31no—
60C3×C4×C22⋊C4—31no—
61#5231—31no—
62C4×#217—31no—
63#4961—31no—
64#4961—31no—
65#4961—31no—
66#4961—61no—
67#4959—31no—
68#4953—31no—
69#4952—31no—
70#4947D311yescharacteristic, complemented
71Dic3×C22⋊C4—31no—
72Dic3×C22⋊C4D311yescharacteristic, complemented
73C4×(C2×D3)⋊C4—31no—
74C4×(C2×D3)⋊C4—31no—
75#4932—31no—
76#4675—31no—
77#4674—31no—
78#4673—31no—
79#4666—31no—
80#4666—31no—
81#4660—31no—
82#4660—31no—
83#4660—31no—
84#4658—31no—
85#4648—31no—
86C24×C32C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C2×#638—22no—
91C2×#638—22no—
92C2×#638—22no—
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3×Dic3—22no—
97C22×C3×Dic3—22no—
98C22×C3×Dic3—22no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×Dic6—22no—
108C2×C3×Dic6—22no—
109C2×C3×Dic6—22no—
110C2×#624—22no—
111C2×#624—22no—
112C2×#624—22no—
113C32×C22⋊C4—22no—
114#3757—22no—
115#3752—22no—
116#3752—22no—
117C4⋊(C3⋊Dic3)—22no—
118C3×#217—22no—
119C3×#217—22no—
120C3×#217—22no—
121C3×C4×Dic3—22no—
122C3×C4×Dic3—22no—
123#3724—22no—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3—22no—
126#3722—22no—
127#3722—22no—
128#3722—22no—
129Dic32—22no—
130Dic32—22no—
131Dic32D414yes—
132#2398—91noSylow
133C22×C3×Q8—31no—
134C23×C3×C4—31no—
135C22×#67—31no—
136C22×#67—31no—
137C22×#67—61no—
138C23×Dic3C2×D311yescharacteristic
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C22×Dic6C2×D311yescharacteristic
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4C2×D311yescharacteristic
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×C3×C42—31no—
149C2×C3×C42—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—61no—
153C2×#217C2×D311yescharacteristic
154C2×#217C2×D311yescharacteristic
155C2×#217C2×D311yescharacteristic
156Q8×Dic3—64no—
157C4×#67—64no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—61no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3C2×D311yescharacteristic
186C2×C4×Dic3C2×D311yescharacteristic
187#67⋊C4—64no—
188C4×Dic6—64no—
189C3×#95—31no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—61no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32#4112yes—
221C23×C32C2411yescharacteristic
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4#4112yes—
235#638—28no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3C2×D412yes—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—44no—
265C2×C3×Dic3C2×D412yes—
266C2×C3×Dic3C2×D412yes—
267C2×C3×Dic3#4112yes—
268C2×C3×Dic3#4112yes—
269C2×C3×Dic3#4112yes—
270C3×Dic6—28no—
271#624—44no—
272C2×C4×Q8—91no—
273C2×C4×D4—91no—
274#400—91no—
275#400—91no—
276#397—91no—
277#397—91no—
278#394—91no—
279#394—91no—
280#393—31no—
281#393—91no—
282C4×C22⋊C4—31no—
283C4×C22⋊C4—91no—
284C4×C22⋊C4—91no—
285C4×C22⋊C4—91no—
286#376—91no—
287C24×C3—21no—
288C24×C3C22×D311yescharacteristic
289C24×C3C22×D311yescharacteristic
290C23×D3—31no—
291C23×D3—31no—
292C23×D3—61no—
293C2×C3×Q8—62no—
294C2×C3×Q8—62no—
295C2×C3×Q8—62no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—62no—
307C22×C3×C4—62no—
308C22×C3×C4—62no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C2×#67—62no—
314C2×#67—62no—
315C2×#67—62no—
316C2×#67—62no—
317C2×#67—62no—
318C2×#67—62no—
319C2×#67—122no—
320C2×#67—122no—
321C2×#67—122no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C2×C4×D3—62no—
343C2×C4×D3—62no—
344C2×C4×D3—62no—
345C2×C4×D3—62no—
346C2×C4×D3—62no—
347C2×C4×D3—62no—
348C2×Dic6—22no—
349C2×Dic6—22no—
350C2×Dic6—22no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—42no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—62no—
356C3×C22⋊C4—62no—
357C3×C42—62no—
358C3×C42—62no—
359#217—22no—
360#217—22no—
361#217—22no—
362#217—62no—
363#217—62no—
364#217—122no—
365(C2×D3)⋊C4—62no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—62no—
369(C2×D3)⋊C4—62no—
370(C2×D3)⋊C4—62no—
371(C2×D3)⋊C4—62no—
372(C2×D3)⋊C4—62no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—122no—
376(C2×D3)⋊C4—122no—
377C4⋊Dic3—62no—
378C4⋊Dic3—62no—
379C4⋊Dic3—62no—
380C4⋊Dic3—62no—
381C4⋊Dic3—122no—
382Dic3⋊C4—62no—
383Dic3⋊C4—62no—
384Dic3⋊C4—62no—
385Dic3⋊C4—62no—
386C4×Dic3—22no—
387C4×Dic3—22no—
388C4×Dic3—34no—
389C4×Dic3—34no—
390C4×Dic3—62no—
391C4×Dic3—62no—
392C4×Dic3—62no—
393C4×Dic3—62no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C22×C32C2×#4111yescharacteristic
405C22×C32C2×#4111yescharacteristic
406C22×C32C2×#4111yescharacteristic
407C22×C32C2×#4111yescharacteristic
408C2×C3⋊D3—22no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3—22no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C32×C4—22no—
416C32×C4—41no—
417C3⋊Dic3—22no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3#12414yes—
428C22×Q8—31no—
429C22×D4—91no—
430C23×C4—31no—
431C23×C4—91no—
432C4×Q8—184no—
433C4×D4—184no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C22⋊C4D3211yescharacteristic
448C2×C42—31no—
449C2×C42—31no—
450C2×C42—91no—
451C2×C42—91no—
452C2×C42—91no—
453#95—31no—
454#95—31no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463#95—91no—
464#95—91no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—22no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3#23512yes—
486C23×C3#23912yes—
487C23×C3C23×D311yescharacteristic
488C23×C3C23×D311yescharacteristic
489C22×D3—32no—
490C22×D3—32no—
491C22×D3—62no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—121no—
507C22×D3—121no—
508C22×D3—121no—
509C22×D3—121no—
510C3×Q8—68no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—22no—
522C2×C3×C4—32no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—124no—
552C2×C3×C4#23512yes—
553C2×C3×C4#23712yes—
554#67—68no—
555#67—68no—
556#67—128no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—32no—
577C2×Dic3—32no—
578C2×Dic3—44no—
579C2×Dic3—62no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3#23512yes—
605C2×Dic3D3×D412yes—
606C2×Dic3D3×D412yes—
607C2×Dic3#23712yes—
608C2×Dic3#23712yes—
609C4×D3—124no—
610C4×D3—124no—
611Dic6—28no—
612C2×C32—42no—
613C2×C32#52511yescharacteristic
614C2×C32#52511yescharacteristic
615C2×C32C2×#12411yescharacteristic
616C2×C32#52911yescharacteristic
617C2×C32#52911yescharacteristic
618C2×C32#52911yescharacteristic
619C2×C32#52911yescharacteristic
620C3⋊D3—42no—
621C24—91no—
622C24C2×D3211yescharacteristic
623C2×Q8—62no—
624C2×Q8—62no—
625C2×Q8—62no—
626C2×D4—182no—
627C2×D4—182no—
628C2×D4—182no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—91no—
641C22×C4—91no—
642C22×C4—91no—
643C22×C4—182no—
644C22×C4—182no—
645C22×C4—182no—
646C22×C4C2×D3211yescharacteristic
647C22×C4C2×D3211yescharacteristic
648C4⋊C4—182no—
649C4⋊C4—182no—
650C4⋊C4—182no—
651C4⋊C4—182no—
652C22⋊C4—22no—
653C22⋊C4—62no—
654C22⋊C4—62no—
655C22⋊C4—62no—
656C22⋊C4—182no—
657C22⋊C4—182no—
658C22⋊C4—182no—
659C22⋊C4—182no—
660C22⋊C4—182no—
661C22⋊C4—182no—
662C42—62no—
663C42—62no—
664C42—94no—
665C42—182no—
666C42—182no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3C2×#23511yescharacteristic
696C22×C3C2×#23511yescharacteristic
697C22×C3C2×#23511yescharacteristic
698C22×C3C2×D3×D411yescharacteristic
699C22×C3C2×D3×D411yescharacteristic
700C22×C3C2×#23711yescharacteristic
701C22×C3C2×#23711yescharacteristic
702C22×C3C2×#23711yescharacteristic
703C22×C3C2×#23911yescharacteristic
704C22×C3D3×#4111yescharacteristic
705C22×C3D3×#4111yescharacteristic
706C22×C3D3×#4111yescharacteristic
707C22×C3D3×#4111yescharacteristic
708C22×C3D3×#4111yescharacteristic
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—62no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—122no—
716C2×D3—122no—
717C2×D3—122no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—241no—
727C2×D3—241no—
728C2×D3—241no—
729C2×D3—241no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—34no—
733C3×C4—42no—
734C3×C4—41no—
735C3×C4—41no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—81no—
739C3×C4—121no—
740C3×C4—121no—
741C3×C4—121no—
742C3×C4—121no—
743C3×C4—121no—
744Dic3—22no—
745Dic3—22no—
746Dic3—41no—
747Dic3—41no—
748Dic3—41no—
749Dic3—41no—
750Dic3—41no—
751Dic3—62no—
752Dic3—62no—
753Dic3—122no—
754Dic3—121no—
755Dic3—121no—
756Dic3—121no—
757Dic3—121no—
758Dic3—241no—
759Dic3—241no—
760Dic3#88514yes—
761C32#239811yescharacteristic, complemented, Sylow
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—92no—
769C23—181no—
770C23—181no—
771C23—181no—
772C23—181no—
773C23—181no—
774C23—181no—
775C23#379912yes—
776C23C22×D3211yescharacteristic
777Q8—68no—
778D4—188no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—32no—
787C2×C4—32no—
788C2×C4—32no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—92no—
809C2×C4—124no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4—181no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—364no—
819C2×C4#380412yes—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—42no—
828C2×C3—42no—
829C2×C3—82no—
830C2×C3#547911yescharacteristic
831C2×C3C2×#88511yescharacteristic
832C2×C3#552811yescharacteristic
833C2×C3#553811yescharacteristic
834C2×C3#554711yescharacteristic
835C2×C3#554711yescharacteristic
836C2×C3#555711yescharacteristic
837C2×C3#558611yescharacteristic
838C2×C3#562411yescharacteristic
839C2×C3#562411yescharacteristic
840C2×C3#562711yescharacteristic
841C2×C3D3×#12411yescharacteristic
842C2×C3#568011yescharacteristic
843C2×C3#568011yescharacteristic
844D3—122no—
845D3—122no—
846D3—242no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—182no—
855C22—182no—
856C22—182no—
857C22—361no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22C2×#379911yescharacteristic
862C22D3×#23511yescharacteristic
863C22D32×D411yescharacteristic
864C22D3×#23711yescharacteristic
865C22D3×#23711yescharacteristic
866C22#6431211yescharacteristic
867C22C2×#380411yescharacteristic
868C4—22no—
869C4—34no—
870C4—41no—
871C4—62no—
872C4—62no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—121no—
877C4—121no—
878C4—182no—
879C4—361no—
880C4—361no—
881C3—21no—
882C3#7348111yescharacteristic, complemented
883C3#7677911yescharacteristic, complemented
884C2—42no—
885C2—362no—
886C2#1059406611yescharacteristic
887C2#1059409911yescharacteristic
888C2#1059421611yescharacteristic
889C2D3×#88511yescharacteristic
890C2#1059495511yescharacteristic
891C2#1059512911yescharacteristic
892C2#1059519111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×Dic6C2semidirect
4. C3×#4947C2semidirect
5. C3×Dic3×C22⋊C4C2semidirect
6. #10591717C2semidirect
8. Dic3×#217C2semidirect
9. #10591310C2semidirect
10. #10591239C2semidirect
11. #10591233C2semidirect
12. #10591233C2semidirect
13. #10591218C2semidirect
14. #10591211C2semidirect
15. #10591208C2semidirect
70. #4947D3semidirect
72. Dic3×C22⋊C4D3semidirect
761. C32#2398semidirect
882. C3#73481semidirect
883. C3#76779semidirect

Maximal subgroups

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

subgroupindex
C2×#639522
C2×Dic3×Dic62
#105926602
C3×#49472
C3×Dic3×C22⋊C42
#105917172
#105917122
Dic3×#2172
#105913102
#105912392
#105912332
#105912182
#105912112
#105912082
#767793
#734813