Finite Group Databasebeta

← C2×#10596149 #11901259

Subgroups — C2×#10596149 #11901259

Order 1152.

4008 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#124C211yesmaximal, characteristic, complemented
2C2×#64156C211yesmaximal, characteristic, complemented
3C2×#64155C211yesmaximal, characteristic, complemented
4C2×#64148C211yesmaximal, characteristic, complemented
5C2×#64146C211yesmaximal, characteristic, complemented
6#10596149C2116yesmaximal, direct product factor
7C2×#64095C211yesmaximal, characteristic, complemented
8C2×#64093C211yesmaximal, characteristic, complemented
9C2×#64093C211yesmaximal, characteristic, complemented
10C2×#64092C211yesmaximal, characteristic, complemented
11C2×#64091C211yesmaximal, characteristic, complemented
12C2×#64090C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
14C2×#64088C211yesmaximal, characteristic, complemented
15C2×#64085C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
17C2×#5678—34nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic, complemented
20C22×C32×D4C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic
24C22×#638C2211yescharacteristic, complemented
25C23×C3⋊Dic3C2211yescharacteristic, complemented
26C22×C4⋊(C3⋊D3)C2211yescharacteristic
27C22×C4⋊(C3⋊D3)C2211yescharacteristic
28C22×C4×C3⋊D3C2211yescharacteristic
29C22×C4×C3⋊D3C2211yescharacteristic
30C22×C4×C3⋊D3C2211yescharacteristic, complemented
31C32×#124C2218yescomplemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic, complemented
35C2×C32×C22⋊C4C2211yescharacteristic, complemented
36C2×C32×C42C2211yescharacteristic, complemented
37C2×#3757C2211yescharacteristic
38C2×#3757C2211yescharacteristic
39#64156C2218yescomplemented
40#64155C2218yescomplemented
41#64148C2218yescomplemented
42#64146C2218yescomplemented
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×#3752C2211yescharacteristic
46C2×#3752C2211yescharacteristic
47C2×#3752C2211yescharacteristic
48C2×#3752C2211yescharacteristic
49C2×#3752C2211yescharacteristic, complemented
50C2×#3752C2211yescharacteristic, complemented
51C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53C2×#3750C2211yescharacteristic, complemented
54C2×#3750C2211yescharacteristic, complemented
55C2×#3750C2211yescharacteristic, complemented
56C2×#3750C2211yescharacteristic, complemented
57C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
58#64095C2218yescomplemented
59#64093C2218yescomplemented
60#64093C2218yescomplemented
61#64092C2218yescomplemented
62#64091C2218yescomplemented
63#64090C2218yescomplemented
64C22⋊C4×C3⋊D3C2218yescomplemented
65#64088C2218yescomplemented
66#64085C2218yescomplemented
67C4×C4⋊(C3⋊D3)C2218yescomplemented
68C2×C3×#124D314yescomplemented
69C2×#947—34no—
70C2×#946—34no—
71C2×#939—34no—
72C2×#937—34no—
73#5678—364no—
74C2×#886—34no—
75C2×#884—34no—
76C2×#884—34no—
77C2×#883—34no—
78C2×#882—34no—
79C2×#67⋊C4—34no—
80C2×D3×C22⋊C4—34no—
81C2×#879—34no—
82C2×#876—34no—
83C2×C4×D12—34no—
84C24×C32C2311yescharacteristic
85C24×C32C2311yescharacteristic
86C23×C3⋊D3—24no—
87C23×C3⋊D3—42no—
88C23×C3⋊D3—42no—
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3⋊D3C2311yescharacteristic
92C23×C3⋊D3C2314yes—
93C2×C32×Q8—42no—
94C2×C32×Q8C2314yescomplemented
95C2×C32×D4—42no—
96C2×C32×D4C2314yes—
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C2×#638—24no—
103C2×#638—42no—
104C2×#638—42no—
105C2×#638—42no—
106C2×#638C2314yes—
107C2×#638C2314yes—
108C2×#638C2314yes—
109C2×#638C2314yescomplemented
110C22×C3⋊Dic3—42no—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2314yescomplemented
117C2×C4⋊(C3⋊D3)—24no—
118C2×C4⋊(C3⋊D3)—42no—
119C2×C4⋊(C3⋊D3)C2314yes—
120C2×C4⋊(C3⋊D3)C2314yes—
121C2×C4×C3⋊D3—42no—
122C2×C4×C3⋊D3—42no—
123C2×C4×C3⋊D3—42no—
124C2×C4×C3⋊D3C2314yes—
125C2×C4×C3⋊D3C2314yes—
126C2×C4×C3⋊D3C2314yescomplemented
127C32×C22⋊C4C2314yes—
128C32×C22⋊C4C2314yes—
129C32×C22⋊C4C2314yescomplemented
130C32×C22⋊C4C2314yescomplemented
131C32×C42C2314yescomplemented
132#3757C2314yes—
133#3757C2314yes—
134#3752C2314yes—
135#3752C2314yes—
136#3752C2314yes—
137#3752C2314yes—
138#3752C2314yes—
139#3752C2314yes—
140#3752C2314yescomplemented
141#3752C2314yescomplemented
142C4⋊(C3⋊Dic3)C2314yescomplemented
143C4⋊(C3⋊Dic3)C2314yescomplemented
144#3750C2314yescomplemented
145#3750C2314yescomplemented
146#3750C2314yescomplemented
147#3750C2314yescomplemented
148C4×C3⋊Dic3C2314yescomplemented
149C2×#538—91noSylow
150C24×D3—34no—
151C22×C3×Q8C2×D314yescomplemented
152C22×C3×D4C2×D314yes—
153C22×#67—34no—
154C22×#67—34no—
155C22×#67—34no—
156C22×#67—34no—
157C23×Dic3—34no—
158C22×D12—34no—
159C22×D12—34no—
160C22×C4×D3—34no—
161C22×C4×D3—34no—
162C22×C4×D3—34no—
163C3×#124C2×D3132yescomplemented
164C2×C3×C22⋊C4C2×D314yes—
165C2×C3×C22⋊C4C2×D314yes—
166C2×C3×C22⋊C4C2×D314yescomplemented
167C2×C3×C22⋊C4C2×D314yescomplemented
168C2×C3×C42C2×D314yescomplemented
169C2×#217—34no—
170C2×#217—34no—
171#947—332no—
172#946—332no—
173#939—332no—
174#937—332no—
175C2×(C2×D3)⋊C4—34no—
176C2×(C2×D3)⋊C4—34no—
177C2×(C2×D3)⋊C4—34no—
178C2×(C2×D3)⋊C4—34no—
179C2×(C2×D3)⋊C4—34no—
180C2×(C2×D3)⋊C4—34no—
181C2×(C2×D3)⋊C4—34no—
182C2×(C2×D3)⋊C4—34no—
183C2×C4⋊Dic3—34no—
184C2×C4⋊Dic3—34no—
185C2×Dic3⋊C4—34no—
186C2×Dic3⋊C4—34no—
187C2×Dic3⋊C4—34no—
188C2×Dic3⋊C4—34no—
189C2×C4×Dic3—34no—
190#886—332no—
191#884—332no—
192#884—332no—
193#883—332no—
194#882—332no—
195#67⋊C4—332no—
196D3×C22⋊C4—332no—
197#879—332no—
198#876—332no—
199C4×D12—332no—
200C23×C32—22no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32C2412yes—
207C23×C32C2412yes—
208C23×C32C2411yescharacteristic
209C22×C3⋊D3—22no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3—22no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3—22no—
215C22×C3⋊D3—22no—
216C22×C3⋊D3—22no—
217C22×C3⋊D3—28no—
218C22×C3⋊D3—44no—
219C22×C3⋊D3—44no—
220C22×C3⋊D3—416no—
221C22×C3⋊D3#4114yes—
222C22×C3⋊D3C2412yes—
223C22×C3⋊D3C2412yes—
224C22×C3⋊D3C2412yes—
225C32×Q8—44no—
226C32×D4—44no—
227C2×C32×C4—22no—
228C2×C32×C4—22no—
229C2×C32×C4—22no—
230C2×C32×C4—22no—
231C2×C32×C4—22no—
232C2×C32×C4C2412yes—
233C2×C32×C4C2412yes—
234C2×C32×C4C2412yes—
235C2×C32×C4C2412yes—
236C2×C32×C4C2412yes—
237#638—28no—
238#638—44no—
239#638—44no—
240#638—44no—
241C2×C3⋊Dic3—22no—
242C2×C3⋊Dic3—22no—
243C2×C3⋊Dic3—22no—
244C2×C3⋊Dic3—22no—
245C2×C3⋊Dic3—22no—
246C2×C3⋊Dic3—44no—
247C2×C3⋊Dic3C2412yes—
248C2×C3⋊Dic3C2412yes—
249C2×C3⋊Dic3C2412yes—
250C2×C3⋊Dic3C2412yes—
251C2×C3⋊Dic3C2412yes—
252C4⋊(C3⋊D3)—28no—
253C4⋊(C3⋊D3)—44no—
254C4×C3⋊D3—44no—
255C4×C3⋊D3—44no—
256C4×C3⋊D3—44no—
257#538—916no—
258C2×#126—91no—
259C2×#126—91no—
260C2×#124—91no—
261C2×#124C3⋊D311yescharacteristic, complemented
262C2×#123—91no—
263C2×#123—91no—
264C2×C22⋊Q8—91no—
265C2×#121—91no—
266C2×#121—91no—
267C2×#121—91no—
268C2×#120—91no—
269C2×#120—91no—
270C2×C4×D4—91no—
271C2×C4×D4—91no—
272C22×C22⋊C4—91no—
273C24×C3C22×D314yes—
274C24×C3C22×D314yes—
275C23×D3—34no—
276C23×D3—34no—
277C23×D3—34no—
278C23×D3—316no—
279C23×D3—616no—
280C23×D3—128no—
281C23×D3—128no—
282C2×C3×Q8—48no—
283C2×C3×Q8C22×D3116yescomplemented
284C2×C3×D4—48no—
285C2×C3×D4C22×D3116yes—
286C22×C3×C4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C22×C3×C4C22×D314yes—
289C22×C3×C4C22×D314yes—
290C22×C3×C4C22×D314yes—
291C2×#67—316no—
292C2×#67—316no—
293C2×#67—316no—
294C2×#67—316no—
295C2×#67—616no—
296C2×#67—128no—
297C2×#67—128no—
298C2×#67—128no—
299C22×Dic3—34no—
300C22×Dic3—34no—
301C22×Dic3—34no—
302C22×Dic3—34no—
303C22×Dic3—34no—
304C22×Dic3—316no—
305C22×Dic3—128no—
306C2×D12—316no—
307C2×D12—316no—
308C2×D12—616no—
309C2×D12—128no—
310C2×C4×D3—316no—
311C2×C4×D3—316no—
312C2×C4×D3—316no—
313C2×C4×D3—128no—
314C2×C4×D3—128no—
315C2×C4×D3—128no—
316C3×C22⋊C4C22×D3116yes—
317C3×C22⋊C4C22×D3116yes—
318C3×C22⋊C4C22×D3116yescomplemented
319C3×C22⋊C4C22×D3116yescomplemented
320C3×C42C22×D3116yescomplemented
321#217—316no—
322#217—316no—
323(C2×D3)⋊C4—316no—
324(C2×D3)⋊C4—316no—
325(C2×D3)⋊C4—316no—
326(C2×D3)⋊C4—316no—
327(C2×D3)⋊C4—316no—
328(C2×D3)⋊C4—316no—
329(C2×D3)⋊C4—316no—
330(C2×D3)⋊C4—316no—
331C4⋊Dic3—316no—
332C4⋊Dic3—316no—
333Dic3⋊C4—316no—
334Dic3⋊C4—316no—
335Dic3⋊C4—316no—
336Dic3⋊C4—316no—
337C4×Dic3—316no—
338C22×C32—22no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—44no—
345C22×C32—44no—
346C22×C32C2×#4112yes—
347C22×C32H(5,𝔽2)12yes—
348C22×C32H(5,𝔽2)12yes—
349C22×C32C2511yescharacteristic
350C2×C3⋊D3—28no—
351C2×C3⋊D3—22no—
352C2×C3⋊D3—22no—
353C2×C3⋊D3—22no—
354C2×C3⋊D3—22no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—416no—
360C2×C3⋊D3—44no—
361C2×C3⋊D3—44no—
362C2×C3⋊D3C2×#4114yes—
363C32×C4—22no—
364C32×C4—22no—
365C32×C4—22no—
366C32×C4—22no—
367C32×C4—22no—
368C3⋊Dic3—22no—
369C3⋊Dic3—22no—
370C3⋊Dic3—22no—
371C3⋊Dic3—22no—
372C3⋊Dic3—22no—
373C25—91no—
374C22×Q8C2×C3⋊D311yescharacteristic, complemented
375C22×D4—91no—
376C22×D4—91no—
377C22×D4—91no—
378C22×D4—91no—
379C22×D4—91no—
380C22×D4—91no—
381C22×D4C2×C3⋊D311yescharacteristic
382C23×C4—91no—
383C23×C4—91no—
384C23×C4—91no—
385C23×C4—91no—
386#126—98no—
387#126—98no—
388#124—98no—
389#124C2×C3⋊D318yescomplemented
390#123—98no—
391#123—98no—
392C22⋊Q8—98no—
393#121—98no—
394#121—98no—
395#121—98no—
396#120—98no—
397#120—98no—
398C4×D4—98no—
399C4×D4—98no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—91no—
403C2×C4⋊C4—91no—
404C2×C4⋊C4—91no—
405C2×C4⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C22⋊C4—91no—
410C2×C22⋊C4—91no—
411C2×C22⋊C4—91no—
412C2×C22⋊C4—91no—
413C2×C22⋊C4—91no—
414C2×C22⋊C4—91no—
415C2×C22⋊C4—91no—
416C2×C22⋊C4—98no—
417C2×C22⋊C4C2×C3⋊D311yescharacteristic
418C2×C22⋊C4C2×C3⋊D311yescharacteristic
419C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
420C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
421C2×C42—91no—
422C2×C42C2×C3⋊D311yescharacteristic, complemented
423C23×C3—28no—
424C23×C3—28no—
425C23×C3—28no—
426C23×C3—28no—
427C23×C3—28no—
428C23×C3—28no—
429C23×C3C23×D318yes—
430C23×C3C23×D318yes—
431C23×C3C23×D314yes—
432C22×D3—316no—
433C22×D3—38no—
434C22×D3—38no—
435C22×D3—38no—
436C22×D3—632no—
437C22×D3—68no—
438C22×D3—68no—
439C22×D3—68no—
440C22×D3—68no—
441C22×D3—68no—
442C22×D3—68no—
443C22×D3—68no—
444C22×D3—68no—
445C22×D3—1216no—
446C22×D3—1216no—
447C22×D3—1264no—
448C3×Q8—416no—
449C3×D4—416no—
450C2×C3×C4—28no—
451C2×C3×C4—28no—
452C2×C3×C4—28no—
453C2×C3×C4—28no—
454C2×C3×C4—28no—
455C2×C3×C4C23×D318yes—
456C2×C3×C4C23×D318yes—
457C2×C3×C4C23×D318yes—
458C2×C3×C4C23×D318yes—
459C2×C3×C4C23×D318yes—
460#67—632no—
461#67—1216no—
462#67—1216no—
463#67—1216no—
464C2×Dic3—38no—
465C2×Dic3—38no—
466C2×Dic3—38no—
467C2×Dic3—38no—
468C2×Dic3—38no—
469C2×Dic3—68no—
470C2×Dic3—68no—
471C2×Dic3—68no—
472C2×Dic3—68no—
473C2×Dic3—68no—
474C2×Dic3—1216no—
475D12—632no—
476D12—1216no—
477C4×D3—1216no—
478C4×D3—1216no—
479C4×D3—1216no—
480C2×C32—42no—
481C2×C32—42no—
482C2×C32#53814yescomplemented
483C2×C32C22×#4111yescharacteristic
484C2×C32C2×H(5,𝔽2)11yescharacteristic
485C2×C32C2×H(5,𝔽2)11yescharacteristic
486C3⋊D3—24no—
487C3⋊D3—42no—
488C3⋊D3—42no—
489C24—91no—
490C24—91no—
491C24—91no—
492C24—94no—
493C24—184no—
494C24—362no—
495C24—362no—
496C24C22×C3⋊D311yescharacteristic
497C24C22×C3⋊D311yescharacteristic
498C2×Q8—42no—
499C2×Q8C22×C3⋊D314yescomplemented
500C2×D4—42no—
501C2×D4—94no—
502C2×D4—94no—
503C2×D4—94no—
504C2×D4—94no—
505C2×D4—94no—
506C2×D4—94no—
507C2×D4—184no—
508C2×D4—184no—
509C2×D4—362no—
510C2×D4—362no—
511C2×D4—362no—
512C2×D4—362no—
513C2×D4C22×C3⋊D314yes—
514C22×C4—91no—
515C22×C4—91no—
516C22×C4—91no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—94no—
520C22×C4—94no—
521C22×C4—94no—
522C22×C4—94no—
523C22×C4—362no—
524C22×C4—362no—
525C22×C4—362no—
526C22×C4—362no—
527C22×C4C22×C3⋊D311yescharacteristic
528C22×C4C22×C3⋊D311yescharacteristic
529C22×C4C22×C3⋊D311yescharacteristic
530C22×C4C22×C3⋊D311yescharacteristic
531C22×C4C22×C3⋊D311yescharacteristic
532C4⋊C4—94no—
533C4⋊C4—94no—
534C4⋊C4—94no—
535C4⋊C4—94no—
536C4⋊C4—94no—
537C4⋊C4—94no—
538C22⋊C4—94no—
539C22⋊C4—94no—
540C22⋊C4—94no—
541C22⋊C4—94no—
542C22⋊C4—94no—
543C22⋊C4—94no—
544C22⋊C4—94no—
545C22⋊C4—94no—
546C22⋊C4—94no—
547C22⋊C4—94no—
548C22⋊C4C22×C3⋊D314yes—
549C22⋊C4C22×C3⋊D314yes—
550C22⋊C4C22×C3⋊D314yescomplemented
551C22⋊C4C22×C3⋊D314yescomplemented
552C42—94no—
553C42C22×C3⋊D314yescomplemented
554C22×C3—28no—
555C22×C3—28no—
556C22×C3—28no—
557C22×C3—28no—
558C22×C3—28no—
559C22×C3—28no—
560C22×C3—416no—
561C22×C3—416no—
562C22×C3#100418yes—
563C22×C3D3×#4118yes—
564C22×C3#100918yes—
565C22×C3C24×D314yes—
566C2×D3—316no—
567C2×D3—632no—
568C2×D3—68no—
569C2×D3—68no—
570C2×D3—68no—
571C2×D3—68no—
572C2×D3—68no—
573C2×D3—68no—
574C2×D3—68no—
575C2×D3—68no—
576C2×D3—1264no—
577C2×D3—1216no—
578C2×D3—1216no—
579C3×C4—28no—
580C3×C4—28no—
581C3×C4—28no—
582C3×C4—28no—
583C3×C4—28no—
584Dic3—68no—
585Dic3—68no—
586Dic3—68no—
587Dic3—68no—
588Dic3—68no—
589C32C2×#53811yescharacteristic, complemented, Sylow
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—94no—
597C23—92no—
598C23—92no—
599C23—92no—
600C23—188no—
601C23—182no—
602C23—182no—
603C23—182no—
604C23—182no—
605C23—182no—
606C23—182no—
607C23—182no—
608C23—182no—
609C23—364no—
610C23—364no—
611C23—3616no—
612C23C23×C3⋊D312yes—
613C23C23×C3⋊D312yes—
614C23C23×C3⋊D311yescharacteristic
615Q8—44no—
616D4—44no—
617D4—188no—
618D4—188no—
619D4—364no—
620D4—364no—
621D4—364no—
622D4—364no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—92no—
629C2×C4—92no—
630C2×C4—92no—
631C2×C4—92no—
632C2×C4—92no—
633C2×C4—182no—
634C2×C4—182no—
635C2×C4—182no—
636C2×C4—182no—
637C2×C4—182no—
638C2×C4—364no—
639C2×C4—364no—
640C2×C4—364no—
641C2×C4—364no—
642C2×C4C23×C3⋊D312yes—
643C2×C4C23×C3⋊D312yes—
644C2×C4C23×C3⋊D312yes—
645C2×C4C23×C3⋊D312yes—
646C2×C4C23×C3⋊D312yes—
647C2×C3—48no—
648C2×C3—48no—
649C2×C3#5678116yescomplemented
650C2×C3C2×#100414yes—
651C2×C3C2×D3×#4114yes—
652C2×C3C2×#100914yes—
653D3—616no—
654D3—128no—
655D3—128no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—44no—
663C22—44no—
664C22—94no—
665C22—188no—
666C22—182no—
667C22—182no—
668C22—182no—
669C22—182no—
670C22—182no—
671C22—182no—
672C22—182no—
673C22—182no—
674C22—3616no—
675C22—364no—
676C22—364no—
677C22#6436112yes—
678C22#41×C3⋊D312yes—
679C22#6436612yes—
680C22C24×C3⋊D311yescharacteristic
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—182no—
687C4—182no—
688C4—182no—
689C4—182no—
690C4—182no—
691C3C2×#567814yescomplemented
692C2—42no—
693C2—42no—
694C2—184no—
695C2—362no—
696C2—362no—
697C2#1059614914yesdirect product factor
698C2C2×#6436111yescharacteristic
699C2C2×#41×C3⋊D311yescharacteristic
700C2C2×#6436611yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#124C2
socleC23×C32C24
hypercenterC2×#124C3⋊D3
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C32×#124C2semidirect
2. C2×#64156C2semidirect
3. C2×#64155C2semidirect
4. C2×#64148C2semidirect
5. C2×#64146C2semidirect
6. #10596149C2direct (N × H)
7. C2×#64095C2semidirect
8. C2×#64093C2semidirect
9. C2×#64093C2semidirect
10. C2×#64092C2semidirect
11. C2×#64091C2semidirect
12. C2×#64090C2semidirect
13. C2×C22⋊C4×C3⋊D3C2semidirect
14. C2×#64088C2semidirect
15. C2×#64085C2semidirect
16. C2×C4×C4⋊(C3⋊D3)C2semidirect
19. C22×C32×Q8C22semidirect
24. C22×#638C22semidirect
25. C23×C3⋊Dic3C22semidirect
30. C22×C4×C3⋊D3C22semidirect
31. C32×#124C22semidirect
34. C2×C32×C22⋊C4C22semidirect
35. C2×C32×C22⋊C4C22semidirect
36. C2×C32×C42C22semidirect
39. #64156C22semidirect
40. #64155C22semidirect
41. #64148C22semidirect
42. #64146C22semidirect
49. C2×#3752C22semidirect
50. C2×#3752C22semidirect
51. C2×C4⋊(C3⋊Dic3)C22semidirect
52. C2×C4⋊(C3⋊Dic3)C22semidirect
53. C2×#3750C22semidirect
54. C2×#3750C22semidirect
55. C2×#3750C22semidirect
56. C2×#3750C22semidirect
57. C2×C4×C3⋊Dic3C22semidirect
58. #64095C22semidirect
59. #64093C22semidirect
60. #64093C22semidirect
61. #64092C22semidirect
62. #64091C22semidirect
63. #64090C22semidirect
64. C22⋊C4×C3⋊D3C22semidirect
65. #64088C22semidirect
66. #64085C22semidirect
67. C4×C4⋊(C3⋊D3)C22semidirect
68. C2×C3×#124D3semidirect
94. C2×C32×Q8C23semidirect
109. C2×#638C23semidirect
116. C22×C3⋊Dic3C23semidirect
126. C2×C4×C3⋊D3C23semidirect
129. C32×C22⋊C4C23semidirect
130. C32×C22⋊C4C23semidirect
131. C32×C42C23semidirect
140. #3752C23semidirect
141. #3752C23semidirect
142. C4⋊(C3⋊Dic3)C23semidirect
143. C4⋊(C3⋊Dic3)C23semidirect
144. #3750C23semidirect
145. #3750C23semidirect
146. #3750C23semidirect
147. #3750C23semidirect
148. C4×C3⋊Dic3C23semidirect
151. C22×C3×Q8C2×D3semidirect
163. C3×#124C2×D3semidirect
166. C2×C3×C22⋊C4C2×D3semidirect
167. C2×C3×C22⋊C4C2×D3semidirect
168. C2×C3×C42C2×D3semidirect
261. C2×#124C3⋊D3semidirect
283. C2×C3×Q8C22×D3semidirect
318. C3×C22⋊C4C22×D3semidirect
319. C3×C22⋊C4C22×D3semidirect
320. C3×C42C22×D3semidirect
374. C22×Q8C2×C3⋊D3semidirect
389. #124C2×C3⋊D3semidirect
419. C2×C22⋊C4C2×C3⋊D3semidirect
420. C2×C22⋊C4C2×C3⋊D3semidirect
422. C2×C42C2×C3⋊D3semidirect
482. C2×C32#538semidirect
499. C2×Q8C22×C3⋊D3semidirect
550. C22⋊C4C22×C3⋊D3semidirect
551. C22⋊C4C22×C3⋊D3semidirect
553. C42C22×C3⋊D3semidirect
589. C32C2×#538semidirect
649. C2×C3#5678semidirect
691. C3C2×#5678semidirect
697. C2#10596149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1242
C2×#641562
C2×#641552
C2×#641482
C2×#641462
#105961492
C2×#640952
C2×#640932
C2×#640922
C2×#640912
C2×#640902
C2×C22⋊C4×C3⋊D32
C2×#640882
C2×#640852
C2×C4×C4⋊(C3⋊D3)2
C2×#56783