Finite Group Databasebeta

← C2×#10594661 #11910196

Subgroups — C2×#10594661 #11910196

Order 1152.

2859 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64103C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#895C211yesmaximal, characteristic, complemented
4C2×#63923C211yesmaximal, characteristic, complemented
5C2×#63922C211yesmaximal, characteristic, complemented
6C2×#63922C211yesmaximal, characteristic, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63912C211yesmaximal, characteristic, complemented
9C2×#63911C211yesmaximal, characteristic, complemented
10C2×#63906C211yesmaximal, characteristic, complemented
11C2×#63890C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63859C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594661C2116yesmaximal, direct product factor
17C2×#5711—31nomaximal
18C2×#5620—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic, complemented
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic, complemented
31C22×#626C2211yescharacteristic, complemented
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic, complemented
35C2×C32×C4⋊C4C2211yescharacteristic, complemented
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic, complemented
39C2×#3750C2211yescharacteristic, complemented
40#64103C2218yescomplemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×C4×Dic3C2211yescharacteristic, complemented
49C3×#898C2218yescomplemented
50C3×#895C2218yescomplemented
51C2×#3724C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×#3722C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57#63923C2218yescomplemented
58#63922C2218yescomplemented
59#63922C2218yescomplemented
60#63916C2218yescomplemented
61#63912C2218yescomplemented
62#63911C2218yescomplemented
63#63906C2218yescomplemented
64#63890C2218yescomplemented
65#63886C2218yescomplemented
66#63885C2218yescomplemented
67#63859C2218yescomplemented
68#63850C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#121—31no—
71C2×#940—31no—
72C2×#939—31no—
73C2×#939—31no—
74C2×#938—31no—
75C2×#937—31no—
76C2×#937—31no—
77C2×#930—31no—
78C2×#929—31no—
79#5711—316no—
80#5620—316no—
81C2×#898D311yescharacteristic, complemented
82C2×#895—31no—
83C2×#895—31no—
84C2×#895D311yescharacteristic, complemented
85C2×#894—31no—
86C2×#894—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#894—61no—
90C2×#886—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—31no—
99C2×#879—31no—
100C2×#876—31no—
101C2×#874—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C22×D32—42no—
109C22×D32—42no—
110C22×D32—42no—
111C22×D32C2314yes—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C2×C4⋊(C3⋊D3)—42no—
118C2×C4⋊(C3⋊D3)C2314yes—
119C2×C4×C3⋊D3—42no—
120C2×C4×C3⋊D3C2314yescomplemented
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×D12—42no—
126C2×C3×D12—42no—
127C2×C3×D12—42no—
128C2×C3×D12C2314yes—
129C2×C3×D12C2314yes—
130C2×C3×D12C2314yescomplemented
131C2×C3×C4×D3—42no—
132C2×C3×C4×D3C2314yescomplemented
133C2×#626—42no—
134C2×#626—42no—
135C2×#626—42no—
136C2×#626—42no—
137C2×#626—42no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×#626C2314yescomplemented
144C2×#626C2314yescomplemented
145C2×#625—42no—
146C2×#625—42no—
147C2×#625C2314yes—
148C2×#625C2314yes—
149C2×D3×Dic3—42no—
150C2×D3×Dic3C2314yescomplemented
151C32×C4⋊C4C2314yescomplemented
152#3752C2314yes—
153#3752C2314yes—
154#3752C2314yescomplemented
155#3750C2314yescomplemented
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yescomplemented
161C3×C4⋊Dic3C2314yescomplemented
162C3×Dic3⋊C4C2314yescomplemented
163C3×C4×Dic3C2314yescomplemented
164#3724C2314yescomplemented
165Dic3⋊Dic3C2314yescomplemented
166#3722C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yescomplemented
170C2×#560—91noSylow
171C24×D3—31no—
172C24×D3—31no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C23×C3×C4—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C23×Dic3—31no—
188C22×D12—31no—
189C22×D12—31no—
190C22×D12—31no—
191C22×D12—31no—
192C22×D12—31no—
193C22×D12—31no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—61no—
197C22×D12C2×D311yescharacteristic
198C22×D12C2×D311yescharacteristic
199C22×D12C2×D311yescharacteristic, complemented
200C22×C4×D3—31no—
201C22×C4×D3—31no—
202C22×C4×D3—31no—
203C22×C4×D3—61no—
204C22×C4×D3C2×D311yescharacteristic, complemented
205C3×#126—38no—
206C3×#121—38no—
207C2×C3×C4⋊C4—21no—
208C2×C3×C4⋊C4—31no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
211C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
212C2×C3×C22⋊C4—31no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C42—31no—
218C2×#217—31no—
219C2×#217—31no—
220C2×#217—31no—
221#940—38no—
222#939—38no—
223#939—38no—
224#938—38no—
225#937—38no—
226#937—38no—
227#930—38no—
228#929—38no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—61no—
241C2×(C2×D3)⋊C4—61no—
242C2×(C2×D3)⋊C4—61no—
243C2×(C2×D3)⋊C4C2×D311yescharacteristic
244C2×(C2×D3)⋊C4C2×D311yescharacteristic
245C2×(C2×D3)⋊C4C2×D311yescharacteristic
246C2×(C2×D3)⋊C4C2×D311yescharacteristic
247C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
248C2×C4⋊Dic3—31no—
249C2×C4⋊Dic3C2×D311yescharacteristic, complemented
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—61no—
256C2×Dic3⋊C4C2×D311yescharacteristic, complemented
257C2×C4×Dic3C2×D311yescharacteristic, complemented
258#898C2×D318yescomplemented
259#895—38no—
260#895—38no—
261#895C2×D318yescomplemented
262#894—38no—
263#894—38no—
264#894—38no—
265#894—38no—
266#894—68no—
267#886—38no—
268#884—38no—
269#884—38no—
270#884—38no—
271#884—38no—
272#882—38no—
273#882—38no—
274#882—38no—
275#882—38no—
276#879—38no—
277#876—38no—
278#874—38no—
279C23×C32C2411yescharacteristic
280C22×C3⋊D3—22no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3C2412yes—
287C22×C3⋊D3C2412yes—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3C2412yes—
301C22×C3×D3C2412yes—
302C22×C3×D3C2412yes—
303C22×C3×D3C2412yes—
304C2×D32—44no—
305C2×D32—44no—
306C2×D32—44no—
307C2×D32—416no—
308C2×C32×C4—22no—
309C2×C32×C4—22no—
310C2×C32×C4—22no—
311C2×C32×C4C2412yes—
312C2×C32×C4C2412yes—
313C2×C32×C4C2412yes—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3C2412yes—
317C2×C3⋊Dic3C2412yes—
318C4⋊(C3⋊D3)—44no—
319C4×C3⋊D3—44no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C3×D12—44no—
329C3×D12—44no—
330C3×D12—44no—
331C3×C4×D3—44no—
332#626—44no—
333#626—44no—
334#626—44no—
335#626—44no—
336#626—44no—
337#626—44no—
338#625—44no—
339#625—44no—
340D3×Dic3—44no—
341#560—916no—
342C2×#127—91no—
343C2×#126—31no—
344C2×#126—91no—
345C2×#123—91no—
346C2×#123—91no—
347C2×#123—91no—
348C2×#121—31no—
349C2×#121—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×#121—91no—
353C2×#121—91no—
354C2×#120—91no—
355C2×#120—91no—
356C2×#120—91no—
357C24×C3—31no—
358C24×C3—31no—
359C24×C3—31no—
360C24×C3—31no—
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—31no—
365C23×D3—34no—
366C23×D3—34no—
367C23×D3—61no—
368C23×D3—61no—
369C23×D3—122no—
370C23×D3—122no—
371C23×D3—122no—
372C23×D3—122no—
373C23×D3—122no—
374C23×D3—122no—
375C23×D3C22×D311yescharacteristic
376C23×D3C22×D311yescharacteristic
377C23×D3C22×D311yescharacteristic
378C23×D3C22×D311yescharacteristic
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—122no—
383C2×C3×D4—122no—
384C2×C3×D4—122no—
385C22×C3×C4—21no—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—34no—
393C22×C3×C4—122no—
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—122no—
411C2×#67—122no—
412C2×#67—122no—
413C2×#67—122no—
414C2×#67—122no—
415C2×#67—122no—
416C2×#67—122no—
417C2×#67—122no—
418C2×#67—122no—
419C2×#67—122no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—31no—
423C22×Dic3—31no—
424C22×Dic3—34no—
425C22×Dic3—61no—
426C22×Dic3—61no—
427C22×Dic3—122no—
428C22×Dic3C22×D311yescharacteristic
429C22×Dic3C22×D311yescharacteristic
430C22×Dic3C22×D311yescharacteristic
431C22×Dic3C22×D311yescharacteristic
432C2×D12—34no—
433C2×D12—34no—
434C2×D12—34no—
435C2×D12—34no—
436C2×D12—34no—
437C2×D12—34no—
438C2×D12—34no—
439C2×D12—34no—
440C2×D12—42no—
441C2×D12—42no—
442C2×D12—42no—
443C2×D12—64no—
444C2×D12—122no—
445C2×D12—122no—
446C2×D12—124no—
447C2×D12—122no—
448C2×D12—122no—
449C2×D12—122no—
450C2×D12—122no—
451C2×D12—122no—
452C2×D12—122no—
453C2×D12C22×D314yes—
454C2×D12C22×D314yes—
455C2×D12C22×D314yescomplemented
456C2×C4×D3—34no—
457C2×C4×D3—34no—
458C2×C4×D3—34no—
459C2×C4×D3—42no—
460C2×C4×D3—64no—
461C2×C4×D3—122no—
462C2×C4×D3—122no—
463C2×C4×D3—122no—
464C2×C4×D3—124no—
465C2×C4×D3C22×D314yescomplemented
466C3×C4⋊C4—24no—
467C3×C4⋊C4—34no—
468C3×C4⋊C4—34no—
469C3×C4⋊C4C22×D314yescomplemented
470C3×C4⋊C4C22×D314yescomplemented
471C3×C22⋊C4—34no—
472C3×C22⋊C4—34no—
473C3×C22⋊C4—34no—
474C3×C22⋊C4—34no—
475C3×C22⋊C4—34no—
476C3×C42—34no—
477#217—34no—
478#217—34no—
479#217—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—64no—
492(C2×D3)⋊C4—64no—
493(C2×D3)⋊C4—64no—
494(C2×D3)⋊C4C22×D314yes—
495(C2×D3)⋊C4C22×D314yes—
496(C2×D3)⋊C4C22×D314yes—
497(C2×D3)⋊C4C22×D314yes—
498(C2×D3)⋊C4C22×D314yescomplemented
499C4⋊Dic3—34no—
500C4⋊Dic3C22×D314yescomplemented
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—64no—
507Dic3⋊C4C22×D314yescomplemented
508C4×Dic3C22×D314yescomplemented
509C22×C32H(5,𝔽2)12yes—
510C22×C32H(5,𝔽2)12yes—
511C22×C32H(5,𝔽2)12yes—
512C22×C32C2511yescharacteristic
513C2×C3⋊D3—22no—
514C2×C3⋊D3—22no—
515C2×C3⋊D3—22no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—22no—
518C2×C3⋊D3—22no—
519C2×C3⋊D3—44no—
520C2×C3⋊D3—44no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—22no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—44no—
534C2×C3×D3—44no—
535C2×C3×D3—44no—
536C2×C3×D3—44no—
537D32—416no—
538C32×C4—22no—
539C32×C4—22no—
540C32×C4—22no—
541C3⋊Dic3—22no—
542C3⋊Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C25—91no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4—31no—
551C22×D4—91no—
552C22×D4—91no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C22×D4—91no—
559C22×D4—91no—
560C23×C4—31no—
561C23×C4—91no—
562C23×C4—91no—
563#127—98no—
564#126—38no—
565#126—98no—
566#123—98no—
567#123—98no—
568#123—98no—
569#121—38no—
570#121—98no—
571#121—98no—
572#121—98no—
573#121—98no—
574#121—98no—
575#120—98no—
576#120—98no—
577#120—98no—
578C2×C4⋊C4—31no—
579C2×C4⋊C4—31no—
580C2×C4⋊C4—91no—
581C2×C4⋊C4—91no—
582C2×C4⋊C4—91no—
583C2×C4⋊C4D3211yescharacteristic, complemented
584C2×C22⋊C4—31no—
585C2×C22⋊C4—31no—
586C2×C22⋊C4—31no—
587C2×C22⋊C4—31no—
588C2×C22⋊C4—31no—
589C2×C22⋊C4—91no—
590C2×C22⋊C4—91no—
591C2×C22⋊C4—91no—
592C2×C22⋊C4—91no—
593C2×C22⋊C4—91no—
594C2×C22⋊C4—91no—
595C2×C22⋊C4—91no—
596C2×C42—31no—
597C23×C3—21no—
598C23×C3—32no—
599C23×C3—32no—
600C23×C3—32no—
601C23×C3—32no—
602C23×C3—62no—
603C23×C3—62no—
604C23×C3—62no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3—62no—
611C23×C3—62no—
612C23×C3—62no—
613C23×C3—62no—
614C23×C3C23×D311yescharacteristic
615C23×C3C23×D311yescharacteristic
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—32no—
629C22×D3—32no—
630C22×D3—32no—
631C22×D3—32no—
632C22×D3—62no—
633C22×D3—62no—
634C22×D3—64no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—62no—
641C22×D3—62no—
642C22×D3—62no—
643C22×D3—62no—
644C22×D3—62no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—122no—
648C22×D3—122no—
649C22×D3—122no—
650C22×D3—122no—
651C22×D3—122no—
652C22×D3—124no—
653C22×D3—124no—
654C22×D3—124no—
655C22×D3—124no—
656C22×D3—124no—
657C22×D3—124no—
658C22×D3—1216no—
659C22×D3—1216no—
660C22×D3C23×D312yes—
661C22×D3C23×D312yes—
662C22×D3C23×D312yes—
663C22×D3C23×D312yes—
664C3×D4—124no—
665C3×D4—124no—
666C3×D4—124no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—32no—
677C2×C3×C4—32no—
678C2×C3×C4—32no—
679C2×C3×C4—32no—
680C2×C3×C4—42no—
681C2×C3×C4—42no—
682C2×C3×C4—42no—
683C2×C3×C4—62no—
684C2×C3×C4—62no—
685C2×C3×C4—62no—
686C2×C3×C4—62no—
687C2×C3×C4—124no—
688C2×C3×C4C23×D312yes—
689C2×C3×C4C23×D312yes—
690C2×C3×C4C23×D312yes—
691C2×C3×C4C23×D312yes—
692C2×C3×C4C23×D312yes—
693C2×C3×C4C23×D312yes—
694#67—124no—
695#67—124no—
696#67—124no—
697#67—124no—
698#67—124no—
699#67—124no—
700#67—124no—
701#67—124no—
702#67—124no—
703#67—124no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—32no—
709C2×Dic3—32no—
710C2×Dic3—32no—
711C2×Dic3—32no—
712C2×Dic3—62no—
713C2×Dic3—62no—
714C2×Dic3—62no—
715C2×Dic3—62no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—122no—
719C2×Dic3—122no—
720C2×Dic3—124no—
721C2×Dic3C23×D312yes—
722C2×Dic3C23×D312yes—
723C2×Dic3C23×D312yes—
724C2×Dic3C23×D312yes—
725D12—44no—
726D12—44no—
727D12—44no—
728D12—124no—
729D12—124no—
730D12—128no—
731D12—124no—
732D12—124no—
733D12—124no—
734D12—124no—
735D12—124no—
736D12—124no—
737C4×D3—44no—
738C4×D3—124no—
739C4×D3—124no—
740C4×D3—124no—
741C4×D3—128no—
742C2×C32#56014yescomplemented
743C2×C32C2×H(5,𝔽2)11yescharacteristic
744C2×C32C2×H(5,𝔽2)11yescharacteristic
745C2×C32C2×H(5,𝔽2)11yescharacteristic
746C3⋊D3—42no—
747C3⋊D3—42no—
748C3×D3—42no—
749C3×D3—42no—
750C3×D3—42no—
751C3×D3—42no—
752C24—31no—
753C24—31no—
754C24—31no—
755C24—31no—
756C24—94no—
757C24—91no—
758C24—91no—
759C24—362no—
760C24—362no—
761C24—362no—
762C2×D4—34no—
763C2×D4—34no—
764C2×D4—34no—
765C2×D4—94no—
766C2×D4—94no—
767C2×D4—94no—
768C2×D4—94no—
769C2×D4—94no—
770C2×D4—94no—
771C2×D4—94no—
772C2×D4—94no—
773C2×D4—94no—
774C2×D4—122no—
775C2×D4—122no—
776C2×D4—122no—
777C2×D4—362no—
778C2×D4—362no—
779C2×D4—362no—
780C2×D4—362no—
781C2×D4—362no—
782C2×D4—362no—
783C2×D4—362no—
784C2×D4—362no—
785C2×D4—362no—
786C22×C4—31no—
787C22×C4—31no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—34no—
791C22×C4—94no—
792C22×C4—91no—
793C22×C4—91no—
794C22×C4—94no—
795C22×C4—122no—
796C22×C4—362no—
797C22×C4—362no—
798C22×C4C2×D3211yescharacteristic
799C22×C4C2×D3211yescharacteristic
800C22×C4C2×D3211yescharacteristic
801C4⋊C4—34no—
802C4⋊C4—34no—
803C4⋊C4—94no—
804C4⋊C4—94no—
805C4⋊C4—94no—
806C4⋊C4C2×D3214yescomplemented
807C22⋊C4—34no—
808C22⋊C4—34no—
809C22⋊C4—34no—
810C22⋊C4—34no—
811C22⋊C4—34no—
812C22⋊C4—94no—
813C22⋊C4—94no—
814C22⋊C4—94no—
815C22⋊C4—94no—
816C22⋊C4—94no—
817C22⋊C4—94no—
818C22⋊C4—94no—
819C42—34no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—21no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—124no—
837C22×C3—124no—
838C22×C3—124no—
839C22×C3—124no—
840C22×C3#100412yes—
841C22×C3#100412yes—
842C22×C3#100912yes—
843C22×C3#100912yes—
844C22×C3#100912yes—
845C22×C3#100912yes—
846C22×C3C24×D311yescharacteristic
847C22×C3C24×D311yescharacteristic
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—22no—
858C2×D3—22no—
859C2×D3—22no—
860C2×D3—44no—
861C2×D3—44no—
862C2×D3—44no—
863C2×D3—44no—
864C2×D3—64no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—122no—
878C2×D3—122no—
879C2×D3—122no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3—1216no—
883C2×D3—1216no—
884C2×D3—128no—
885C2×D3—124no—
886C2×D3—124no—
887C2×D3—124no—
888C2×D3—124no—
889C2×D3—244no—
890C3×C4—22no—
891C3×C4—22no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—22no—
896C3×C4—42no—
897C3×C4—42no—
898C3×C4—42no—
899C3×C4—62no—
900C3×C4—62no—
901C3×C4—62no—
902C3×C4—62no—
903Dic3—22no—
904Dic3—22no—
905Dic3—22no—
906Dic3—22no—
907Dic3—62no—
908Dic3—62no—
909Dic3—62no—
910Dic3—62no—
911Dic3—122no—
912Dic3—122no—
913C32C2×#56011yescharacteristic, complemented, Sylow
914C23—32no—
915C23—32no—
916C23—32no—
917C23—32no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—92no—
931C23—92no—
932C23—182no—
933C23—182no—
934C23—182no—
935C23—182no—
936C23—182no—
937C23—182no—
938C23—364no—
939C23—364no—
940C23—364no—
941C23—3616no—
942C23C22×D3211yescharacteristic
943D4—124no—
944D4—124no—
945D4—124no—
946D4—364no—
947D4—364no—
948D4—364no—
949D4—364no—
950D4—364no—
951D4—364no—
952D4—364no—
953D4—364no—
954D4—364no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—32no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—92no—
967C2×C4—92no—
968C2×C4—124no—
969C2×C4—182no—
970C2×C4—182no—
971C2×C4—364no—
972C2×C4—364no—
973C2×C4C22×D3212yes—
974C2×C4C22×D3212yes—
975C2×C4C22×D3212yes—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—24no—
980C2×C3—122no—
981C2×C3—122no—
982C2×C3—122no—
983C2×C3—122no—
984C2×C3#562014yescomplemented
985C2×C3#571114yescomplemented
986C2×C3C2×#100411yescharacteristic
987C2×C3C2×#100411yescharacteristic
988C2×C3C2×#100911yescharacteristic
989C2×C3C2×#100911yescharacteristic
990C2×C3C2×#100911yescharacteristic
991C2×C3C2×#100911yescharacteristic
992D3—42no—
993D3—42no—
994D3—42no—
995D3—42no—
996D3—124no—
997D3—122no—
998D3—122no—
999D3—122no—
1000D3—122no—
1001D3—242no—
1002C22—62no—
1003C22—62no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—62no—
1008C22—62no—
1009C22—62no—
1010C22—62no—
1011C22—62no—
1012C22—62no—
1013C22—62no—
1014C22—124no—
1015C22—124no—
1016C22—124no—
1017C22—124no—
1018C22—182no—
1019C22—182no—
1020C22—182no—
1021C22—182no—
1022C22—182no—
1023C22—182no—
1024C22—3616no—
1025C22—364no—
1026C22—364no—
1027C22#6430712yes—
1028C22#6431412yes—
1029C22#6432012yes—
1030C22C23×D3211yescharacteristic
1031C4—22no—
1032C4—22no—
1033C4—22no—
1034C4—62no—
1035C4—62no—
1036C4—62no—
1037C4—62no—
1038C4—182no—
1039C4—182no—
1040C3—21no—
1041C3C2×#562011yescharacteristic, complemented
1042C3C2×#571111yescharacteristic, complemented
1043C2—122no—
1044C2—122no—
1045C2—122no—
1046C2—122no—
1047C2—362no—
1048C2—362no—
1049C2#1059466114yesdirect product factor
1050C2C2×#6430711yescharacteristic
1051C2C2×#6431411yescharacteristic
1052C2C2×#6432011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64103C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#895C2semidirect
4. C2×#63923C2semidirect
5. C2×#63922C2semidirect
6. C2×#63922C2semidirect
7. C2×#63916C2semidirect
8. C2×#63912C2semidirect
9. C2×#63911C2semidirect
10. C2×#63906C2semidirect
11. C2×#63890C2semidirect
12. C2×#63886C2semidirect
13. C2×#63885C2semidirect
14. C2×#63859C2semidirect
15. C2×#63850C2semidirect
16. #10594661C2direct (N × H)
21. C22×C4×C3⋊D3C22semidirect
24. C22×C3×D12C22semidirect
25. C22×C3×C4×D3C22semidirect
30. C22×#626C22semidirect
31. C22×#626C22semidirect
34. C22×D3×Dic3C22semidirect
35. C2×C32×C4⋊C4C22semidirect
38. C2×#3752C22semidirect
39. C2×#3750C22semidirect
40. #64103C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×C4⋊Dic3C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×C4×Dic3C22semidirect
49. C3×#898C22semidirect
50. C3×#895C22semidirect
51. C2×#3724C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. #63923C22semidirect
58. #63922C22semidirect
59. #63922C22semidirect
60. #63916C22semidirect
61. #63912C22semidirect
62. #63911C22semidirect
63. #63906C22semidirect
64. #63890C22semidirect
65. #63886C22semidirect
66. #63885C22semidirect
67. #63859C22semidirect
68. #63850C22semidirect
81. C2×#898D3semidirect
84. C2×#895D3semidirect
120. C2×C4×C3⋊D3C23semidirect
130. C2×C3×D12C23semidirect
132. C2×C3×C4×D3C23semidirect
143. C2×#626C23semidirect
144. C2×#626C23semidirect
150. C2×D3×Dic3C23semidirect
151. C32×C4⋊C4C23semidirect
154. #3752C23semidirect
155. #3750C23semidirect
160. C3×(C2×D3)⋊C4C23semidirect
161. C3×C4⋊Dic3C23semidirect
162. C3×Dic3⋊C4C23semidirect
163. C3×C4×Dic3C23semidirect
164. #3724C23semidirect
165. Dic3⋊Dic3C23semidirect
169. (C2×D3)⋊Dic3C23semidirect
199. C22×D12C2×D3semidirect
204. C22×C4×D3C2×D3semidirect
210. C2×C3×C4⋊C4C2×D3semidirect
211. C2×C3×C4⋊C4C2×D3semidirect
247. C2×(C2×D3)⋊C4C2×D3semidirect
249. C2×C4⋊Dic3C2×D3semidirect
256. C2×Dic3⋊C4C2×D3semidirect
257. C2×C4×Dic3C2×D3semidirect
258. #898C2×D3semidirect
261. #895C2×D3semidirect
455. C2×D12C22×D3semidirect
465. C2×C4×D3C22×D3semidirect
469. C3×C4⋊C4C22×D3semidirect
470. C3×C4⋊C4C22×D3semidirect
498. (C2×D3)⋊C4C22×D3semidirect
500. C4⋊Dic3C22×D3semidirect
507. Dic3⋊C4C22×D3semidirect
508. C4×Dic3C22×D3semidirect
583. C2×C4⋊C4D32semidirect
742. C2×C32#560semidirect
806. C4⋊C4C2×D32semidirect
913. C32C2×#560semidirect
984. C2×C3#5620semidirect
985. C2×C3#5711semidirect
1041. C3C2×#5620semidirect
1042. C3C2×#5711semidirect
1049. C2#10594661direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641032
C2×C3×#8982
C2×C3×#8952
C2×#639232
C2×#639222
C2×#639162
C2×#639122
C2×#639112
C2×#639062
C2×#638902
C2×#638862
C2×#638852
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