Finite Group Databasebeta

← #11810296

Subgroups — #11810296

Order 1152.

2400 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#64162C211yesmaximal, characteristic
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×#64092C211yesmaximal, characteristic, complemented
5#10592946C211yesmaximal, characteristic, complemented
6#10592912C211yesmaximal, characteristic, complemented
7#10592911C211yesmaximal, characteristic, complemented
8#10592909C211yesmaximal, characteristic, complemented
9#10592660C211yesmaximal, characteristic, complemented
10#10592658C211yesmaximal, characteristic, complemented
11#10592655C211yesmaximal, characteristic, complemented
12#10592651C211yesmaximal, characteristic, complemented
13#10592650C211yesmaximal, characteristic, complemented
14#10592648C211yesmaximal, characteristic, complemented
15#10592644C211yesmaximal, characteristic, complemented
16#82128—34nomaximal
17C25×C32C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C32×C22⋊C4—24no—
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29#64162—24no—
30C2×#3757C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3757C2211yescharacteristic
35C2×#3757C2211yescharacteristic
36C2×#3757C2211yescharacteristic
37C2×#3757C2211yescharacteristic
38C2×#3757C2211yescharacteristic
39C4×#638—24no—
40C2×#3752C2211yescharacteristic, complemented
41C2×#3752C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic, complemented
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47C2×#3750C2211yescharacteristic, complemented
48C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
49#64092—24no—
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56C22×C3×C22⋊C4D314yescomplemented
57C2×#953—34no—
58C2×C4×#67—34no—
59C2×#883—34no—
60#5247—34no—
61#5213—34no—
62#5212—34no—
63#5210—34no—
64#4961—34no—
65#4959—34no—
66#4956—34no—
67#4952—34no—
68#4951—34no—
69#4949—34no—
70#4945—34no—
71C24×C32—22no—
72C24×C32—22no—
73C24×C32—22no—
74C24×C32—22no—
75C24×C32—22no—
76C24×C32—41no—
77C24×C32—41no—
78C24×C32C2311yescharacteristic
79C24×C32C2311yescharacteristic
80C24×C32C2311yescharacteristic
81C23×C3⋊D3C2311yescharacteristic
82C22×C32×C4—22no—
83C22×C32×C4—22no—
84C22×C32×C4—22no—
85C22×C32×C4—22no—
86C22×C32×C4—41no—
87C22×C32×C4—41no—
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638—22no—
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—22no—
98C2×#638—41no—
99C2×#638—41no—
100C2×#638D414yes—
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—22no—
110C2×C4×C3⋊D3—41no—
111C32×C22⋊C4—22no—
112C32×C22⋊C4—22no—
113C32×C22⋊C4—22no—
114C32×C22⋊C4D414yescomplemented
115#3757—22no—
116#3757—22no—
117#3757—22no—
118#3757—22no—
119#3757—22no—
120#3757—22no—
121#3757—22no—
122#3757—41no—
123#3757—41no—
124#3752—22no—
125#3752—22no—
126#3752—41no—
127C4⋊(C3⋊Dic3)—22no—
128C4⋊(C3⋊Dic3)—41no—
129#3750—22no—
130#3750—22no—
131#3750—41no—
132C4×C3⋊Dic3—22no—
133#2418—91noSylow
134C25×C3C2×D314yes—
135C23×C3×C4C2×D314yes—
136C23×C3×C4C2×D314yes—
137C22×#67—34no—
138C22×#67—34no—
139C22×#67—34no—
140C22×C4×D3—34no—
141C2×C3×C22⋊C4—216no—
142C2×C3×C22⋊C4C2×D314yes—
143C2×C3×C22⋊C4C2×D314yes—
144C2×C3×C22⋊C4C2×D314yes—
145C2×C3×C22⋊C4C2×D314yes—
146#953—616no—
147C2×#217—34no—
148C2×#217—34no—
149C2×#217—34no—
150C2×#217—34no—
151C2×#217—34no—
152C2×#217—34no—
153C2×#217—34no—
154C2×#217—34no—
155C2×#217—34no—
156C4×#67—616no—
157C2×(C2×D3)⋊C4—34no—
158C2×(C2×D3)⋊C4—34no—
159C2×(C2×D3)⋊C4—34no—
160C2×C4⋊Dic3—34no—
161C2×C4⋊Dic3—34no—
162C2×Dic3⋊C4—34no—
163C2×Dic3⋊C4—34no—
164C2×Dic3⋊C4—34no—
165C2×C4×Dic3—34no—
166#883—616no—
167C3⋊#95—34no—
168C3⋊#95—34no—
169C3⋊#95—34no—
170C3⋊#95—34no—
171C3⋊#95—34no—
172C3⋊#95—34no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—28no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—21no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—21no—
189C23×C32—21no—
190C23×C32—44no—
191C23×C32—44no—
192C23×C32—44no—
193C23×C32—44no—
194C23×C32—44no—
195C23×C32—44no—
196C23×C32C2×D412yes—
197C23×C32C2×D412yes—
198C23×C32#4112yes—
199C23×C32#4112yes—
200C23×C32#4112yes—
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3—21no—
206C22×C3⋊D3—21no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3C2×D412yes—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—44no—
220C2×C32×C4—44no—
221C2×C32×C4C2×D412yes—
222C2×C32×C4C2×D412yes—
223#638—28no—
224#638—44no—
225#638—44no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
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⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D412yes—
247C4×C3⋊D3—44no—
248C2×#123—91no—
249C2×#120—91no—
250C2×C4×D4—91no—
251C22×C22⋊C4C3⋊D311yescharacteristic, complemented
252#399—91no—
253#397—91no—
254#394—91no—
255#394—91no—
256#388—91no—
257#388—91no—
258#386—91no—
259#386—91no—
260#385—91no—
261#380—91no—
262#379—91no—
263C24×C3—28no—
264C24×C3—28no—
265C24×C3—28no—
266C24×C3—28no—
267C24×C3—28no—
268C24×C3—44no—
269C24×C3—44no—
270C24×C3C22×D314yes—
271C24×C3C22×D314yes—
272C24×C3C22×D314yes—
273C23×D3—34no—
274C22×C3×C4—28no—
275C22×C3×C4—28no—
276C22×C3×C4—28no—
277C22×C3×C4—28no—
278C22×C3×C4—44no—
279C22×C3×C4—44no—
280C22×C3×C4C22×D314yes—
281C22×C3×C4C22×D314yes—
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D314yes—
284C2×#67—316no—
285C2×#67—68no—
286C2×#67—68no—
287C2×#67—68no—
288C2×#67—68no—
289C2×#67—68no—
290C2×#67—68no—
291C2×#67—124no—
292C2×#67—124no—
293C22×Dic3—34no—
294C22×Dic3—34no—
295C22×Dic3—34no—
296C22×Dic3—34no—
297C22×Dic3—34no—
298C22×Dic3—34no—
299C22×Dic3—34no—
300C2×C4×D3—68no—
301C2×C4×D3—68no—
302C2×C4×D3—124no—
303C3×C22⋊C4—28no—
304C3×C22⋊C4—28no—
305C3×C22⋊C4—28no—
306C3×C22⋊C4#67116yescomplemented
307#217—68no—
308#217—68no—
309#217—68no—
310#217—68no—
311#217—68no—
312#217—68no—
313#217—68no—
314#217—124no—
315#217—124no—
316(C2×D3)⋊C4—68no—
317(C2×D3)⋊C4—68no—
318(C2×D3)⋊C4—124no—
319C4⋊Dic3—68no—
320C4⋊Dic3—124no—
321Dic3⋊C4—68no—
322Dic3⋊C4—68no—
323Dic3⋊C4—124no—
324C4×Dic3—68no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—22no—
337C22×C32—416no—
338C22×C32—41no—
339C22×C32—41no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32—41no—
345C22×C32—41no—
346C22×C32#12314yescomplemented
347C22×C32C22×D411yescharacteristic
348C22×C32C22×D411yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32H(5,𝔽2)11yescharacteristic
353C22×C32H(5,𝔽2)11yescharacteristic
354C2×C3⋊D3—22no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—41no—
358C2×C3⋊D3—41no—
359C2×C3⋊D3—41no—
360C2×C3⋊D3—41no—
361C32×C4—22no—
362C32×C4—22no—
363C32×C4—41no—
364C32×C4—41no—
365C3⋊Dic3—22no—
366C3⋊Dic3—41no—
367C3⋊Dic3—41no—
368C3⋊Dic3—41no—
369C3⋊Dic3—41no—
370C3⋊Dic3—41no—
371C3⋊Dic3—41no—
372C25C2×C3⋊D311yescharacteristic
373C22×D4—91no—
374C22×D4—91no—
375C22×D4—91no—
376C23×C4—91no—
377C23×C4C2×C3⋊D311yescharacteristic
378C23×C4C2×C3⋊D311yescharacteristic
379#123—184no—
380#120—184no—
381C4×D4—184no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4—91no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4—91no—
391C2×C22⋊C4—91no—
392C2×C22⋊C4—91no—
393C2×C22⋊C4—91no—
394C2×C22⋊C4—91no—
395C2×C22⋊C4—91no—
396C2×C22⋊C4—91no—
397C2×C22⋊C4—91no—
398C2×C22⋊C4—91no—
399C2×C22⋊C4—91no—
400C2×C22⋊C4C2×C3⋊D311yescharacteristic
401C2×C22⋊C4C2×C3⋊D311yescharacteristic
402C2×C22⋊C4C2×C3⋊D311yescharacteristic
403C2×C22⋊C4C2×C3⋊D311yescharacteristic
404C2×C42—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95—91no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—232no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—416no—
429C23×C3—416no—
430C23×C3—416no—
431C23×C3—416no—
432C23×C3—416no—
433C23×C3—416no—
434C23×C3#23518yes—
435C23×C3#23518yes—
436C23×C3D3×D418yes—
437C23×C3#23718yes—
438C23×C3C2×#6718yes—
439C23×C3C23×D314yes—
440C22×D3—38no—
441C22×D3—64no—
442C22×D3—64no—
443C22×D3—64no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—64no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—416no—
458C2×C3×C4—416no—
459C2×C3×C4C2×#6718yes—
460C2×C3×C4C2×#6718yes—
461#67—632no—
462#67—1216no—
463#67—1216no—
464C2×Dic3—38no—
465C2×Dic3—64no—
466C2×Dic3—64no—
467C2×Dic3—64no—
468C2×Dic3—64no—
469C2×Dic3—64no—
470C2×Dic3—64no—
471C2×Dic3—64no—
472C2×Dic3—64no—
473C2×Dic3—64no—
474C2×Dic3—64no—
475C2×Dic3—64no—
476C2×Dic3—64no—
477C2×Dic3—64no—
478C2×Dic3—64no—
479C2×Dic3—64no—
480C2×Dic3—64no—
481C2×Dic3—64no—
482C2×Dic3—64no—
483C2×Dic3—64no—
484C2×Dic3—64no—
485C4×D3—1216no—
486C2×C32—24no—
487C2×C32—42no—
488C2×C32—42no—
489C2×C32C2×#12311yescharacteristic
490C2×C32#52511yescharacteristic
491C2×C32#53811yescharacteristic
492C2×C32D4211yescharacteristic
493C2×C32#54611yescharacteristic
494C2×C32#54611yescharacteristic
495C2×C32#55111yescharacteristic
496C3⋊D3—42no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—41no—
503C24—41no—
504C24—91no—
505C24C22×C3⋊D311yescharacteristic
506C24C22×C3⋊D311yescharacteristic
507C24C22×C3⋊D311yescharacteristic
508C2×D4—94no—
509C2×D4—182no—
510C2×D4—182no—
511C2×D4—182no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—182no—
515C2×D4—361no—
516C2×D4—361no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—91no—
529C22×C4—91no—
530C22×C4—182no—
531C22×C4—182no—
532C22×C4—361no—
533C22×C4C22×C3⋊D311yescharacteristic
534C22×C4C22×C3⋊D311yescharacteristic
535C22×C4C22×C3⋊D311yescharacteristic
536C22×C4C22×C3⋊D311yescharacteristic
537C4⋊C4—182no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C4⋊C4—361no—
541C4⋊C4—361no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—182no—
546C22⋊C4—182no—
547C22⋊C4—182no—
548C22⋊C4—182no—
549C22⋊C4—182no—
550C22⋊C4—182no—
551C22⋊C4—182no—
552C22⋊C4—182no—
553C22⋊C4—182no—
554C22⋊C4—361no—
555C22⋊C4—361no—
556C22⋊C4—361no—
557C22⋊C4#63814yescomplemented
558C42—182no—
559C22×C3—28no—
560C22×C3—28no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—28no—
565C22×C3—28no—
566C22×C3—28no—
567C22×C3—28no—
568C22×C3—28no—
569C22×C3—28no—
570C22×C3—28no—
571C22×C3—464no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3#883116yescomplemented
581C22×C3C2×#23514yes—
582C22×C3C2×#23514yes—
583C22×C3C2×D3×D414yes—
584C22×C3C2×#23714yes—
585C22×C3#100414yes—
586C22×C3#100414yes—
587C22×C3C22×#6714yes—
588C2×D3—68no—
589C2×D3—68no—
590C2×D3—68no—
591C2×D3—124no—
592C2×D3—124no—
593C2×D3—124no—
594C2×D3—124no—
595C3×C4—28no—
596C3×C4—28no—
597C3×C4—44no—
598C3×C4—44no—
599Dic3—68no—
600Dic3—124no—
601Dic3—124no—
602Dic3—124no—
603Dic3—124no—
604Dic3—124no—
605Dic3—124no—
606C32#241811yescharacteristic, complemented, Sylow
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—28no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—92no—
631C23—181no—
632C23—181no—
633C23—181no—
634C23—181no—
635C23—181no—
636C23—181no—
637C23#382812yes—
638C23#382812yes—
639C23D4×C3⋊D312yes—
640C23#383012yes—
641C23C2×#63812yes—
642C23C23×C3⋊D311yescharacteristic
643D4—188no—
644D4—364no—
645D4—364no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—92no—
659C2×C4—181no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—181no—
672C2×C4—181no—
673C2×C4—181no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—181no—
678C2×C4—181no—
679C2×C4—364no—
680C2×C4C2×#63812yes—
681C2×C4C2×#63812yes—
682C2×C3—216no—
683C2×C3—48no—
684C2×C3—48no—
685C2×C3C2×#88314yes—
686C2×C3#549014yes—
687C2×C3#549414yes—
688C2×C3#549514yes—
689C2×C3#579114yes—
690C2×C3D4×#6714yes—
691C2×C3#580614yes—
692D3—128no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—416no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—182no—
715C22—182no—
716C22—182no—
717C22—361no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22#6409214yescomplemented
722C22C2×#382811yescharacteristic
723C22C2×#382811yescharacteristic
724C22C2×D4×C3⋊D311yescharacteristic
725C22C2×#383011yescharacteristic
726C22#6436111yescharacteristic
727C22#6436111yescharacteristic
728C22C22×#63811yescharacteristic
729C4—22no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—182no—
734C4—361no—
735C4—361no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#8212814yescomplemented
741C2—24no—
742C2—42no—
743C2—42no—
744C2—362no—
745C2C2×#6409211yescharacteristic
746C2#1059596111yescharacteristic
747C2#1059596511yescharacteristic
748C2#1059596611yescharacteristic
749C2#1059626211yescharacteristic
750C2D4×#63811yescharacteristic
751C2#1059627711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC22×C32×C22⋊C4C2
prime radicalC2×#64162C2
hypercenterC22×C22⋊C4C3⋊D3
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C22⋊C4C2semidirect
3. C2×C4×#638C2semidirect
4. C2×#64092C2semidirect
5. #10592946C2semidirect
6. #10592912C2semidirect
7. #10592911C2semidirect
8. #10592909C2semidirect
9. #10592660C2semidirect
10. #10592658C2semidirect
11. #10592655C2semidirect
12. #10592651C2semidirect
13. #10592650C2semidirect
14. #10592648C2semidirect
15. #10592644C2semidirect
23. C22×C4×C3⋊D3C22semidirect
40. C2×#3752C22semidirect
41. C2×#3752C22semidirect
42. C2×#3752C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. C2×#3750C22semidirect
46. C2×#3750C22semidirect
47. C2×#3750C22semidirect
48. C2×C4×C3⋊Dic3C22semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
56. C22×C3×C22⋊C4D3semidirect
114. C32×C22⋊C4D4semidirect
251. C22×C22⋊C4C3⋊D3semidirect
306. C3×C22⋊C4#67semidirect
346. C22×C32#123semidirect
557. C22⋊C4#638semidirect
580. C22×C3#883semidirect
606. C32#2418semidirect
721. C22#64092semidirect
740. C3#82128semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊C42
C2×#641622
C2×C4×#6382
C2×#640922
#105929462
#105929122
#105929112
#105929092
#105926602
#105926582
#105926552
#105926512
#105926502
#105926482
#105926442
#821283