Finite Group Databasebeta

← C2×#10594663 #11910198

Subgroups — C2×#10594663 #11910198

Order 1152.

2901 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#894C211yesmaximal, characteristic, complemented
4C2×#63923C211yesmaximal, characteristic, complemented
5C2×#63923C211yesmaximal, characteristic, complemented
6C2×#63922C211yesmaximal, characteristic, complemented
7C2×#63912C211yesmaximal, characteristic, complemented
8C2×#63911C211yesmaximal, characteristic, complemented
9C2×#63910C211yesmaximal, characteristic, complemented
10C2×#63910C211yesmaximal, characteristic, complemented
11C2×#63909C211yesmaximal, characteristic, complemented
12C2×#63906C211yesmaximal, characteristic, complemented
13C2×#63868C211yesmaximal, characteristic, complemented
14C2×#63854C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594663C2116yesmaximal, direct product factor
17C2×#5711—31nomaximal
18C2×#5666—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic, complemented
32C22×#626C2211yescharacteristic, complemented
33C22×#625C2211yescharacteristic
34C22×#624C2211yescharacteristic, complemented
35C2×C32×C4⋊C4C2211yescharacteristic, complemented
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic, complemented
38#64104C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×C4×Dic3C2211yescharacteristic, complemented
49C3×#898C2218yescomplemented
50C3×#894C2218yescomplemented
51C2×#3724C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63923C2218yescomplemented
58#63923C2218yescomplemented
59#63922C2218yescomplemented
60#63912C2218yescomplemented
61#63911C2218yescomplemented
62#63910C2218yescomplemented
63#63910C2218yescomplemented
64#63909C2218yescomplemented
65#63906C2218yescomplemented
66#63868C2218yescomplemented
67#63854C2218yescomplemented
68#63853C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#123—31no—
71C2×#940—31no—
72C2×#937—31no—
73C2×#930—31no—
74C2×#930—31no—
75#5711—316no—
76#5666—316no—
77C2×#898—31no—
78C2×#898D311yescharacteristic, complemented
79C2×#895—31no—
80C2×#895—31no—
81C2×#895—31no—
82C2×#895—31no—
83C2×#895—31no—
84C2×#895—61no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#894D311yescharacteristic, complemented
88C2×#884—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—31no—
99C2×#882—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
116C2×C4⋊(C3⋊D3)—42no—
117C2×C4⋊(C3⋊D3)—42no—
118C2×C4⋊(C3⋊D3)—42no—
119C2×C4⋊(C3⋊D3)C2314yes—
120C2×C4⋊(C3⋊D3)C2314yes—
121C2×C4⋊(C3⋊D3)C2314yescomplemented
122C2×C4×C3⋊D3—42no—
123C2×C4×C3⋊D3C2314yescomplemented
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×D12—42no—
130C2×C3×D12C2314yes—
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×#626—42no—
140C2×#626C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#626C2314yescomplemented
146C2×#626C2314yescomplemented
147C2×#625—42no—
148C2×#625C2314yes—
149C2×#624—42no—
150C2×#624C2314yescomplemented
151C32×C4⋊C4C2314yescomplemented
152#3752C2314yes—
153#3752C2314yescomplemented
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yescomplemented
160C3×C4⋊Dic3C2314yescomplemented
161C3×Dic3⋊C4C2314yescomplemented
162C3×Dic3⋊C4C2314yescomplemented
163C3×C4×Dic3C2314yescomplemented
164#3724C2314yescomplemented
165Dic3⋊Dic3C2314yescomplemented
166#3722C2314yes—
167#3722C2314yes—
168#3722C2314yescomplemented
169(C2×D3)⋊Dic3C2314yes—
170C2×#560—91noSylow
171C24×D3—31no—
172C24×D3—31no—
173C22×C3×D4—31no—
174C23×C3×C4—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—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—31no—
197C22×D12—61no—
198C22×D12—61no—
199C22×D12—61no—
200C22×D12C2×D311yescharacteristic
201C22×C4×D3—31no—
202C22×C4×D3—31no—
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—61no—
206C22×C4×D3C2×D311yescharacteristic, complemented
207C3×#126—38no—
208C3×#123—38no—
209C2×C3×C4⋊C4—21no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4—31no—
212C2×C3×C4⋊C4—31no—
213C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
214C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C22⋊C4—31no—
218C2×C3×C22⋊C4—31no—
219C2×C3×C22⋊C4—31no—
220C2×C3×C22⋊C4—31no—
221C2×C3×C42—31no—
222C2×#217—31no—
223#940—38no—
224#937—38no—
225#930—38no—
226#930—38no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
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—61no—
239C2×(C2×D3)⋊C4—61no—
240C2×(C2×D3)⋊C4C2×D311yescharacteristic
241C2×(C2×D3)⋊C4C2×D311yescharacteristic
242C2×(C2×D3)⋊C4C2×D311yescharacteristic
243C2×(C2×D3)⋊C4C2×D311yescharacteristic
244C2×(C2×D3)⋊C4C2×D311yescharacteristic
245C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3C2×D311yescharacteristic, complemented
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4C2×D311yescharacteristic, complemented
252C2×Dic3⋊C4C2×D311yescharacteristic, complemented
253C2×C4×Dic3C2×D311yescharacteristic, complemented
254#898—38no—
255#898C2×D318yescomplemented
256#895—38no—
257#895—38no—
258#895—38no—
259#895—38no—
260#895—38no—
261#895—68no—
262#894—38no—
263#894—38no—
264#894C2×D318yescomplemented
265#884—38no—
266#884—38no—
267#884—38no—
268#884—38no—
269#884—38no—
270#883—38no—
271#883—38no—
272#882—38no—
273#882—38no—
274#882—38no—
275#882—38no—
276#882—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⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—22no—
289C22×C3⋊D3C2412yes—
290C22×C3⋊D3C2412yes—
291C22×C3⋊D3C2412yes—
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×D3—22no—
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⋊Dic3C2412yes—
316C4⋊(C3⋊D3)—44no—
317C4⋊(C3⋊D3)—44no—
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×Dic3—22no—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
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#626—44no—
339#625—44no—
340#624—44no—
341#560—916no—
342C2×#127—91no—
343C2×#126—31no—
344C2×#126—91no—
345C2×#123—31no—
346C2×#123—91no—
347C2×#123—91no—
348C2×#121—91no—
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—
360C23×D3—31no—
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—31no—
365C23×D3—31no—
366C23×D3—34no—
367C23×D3—34no—
368C23×D3—61no—
369C23×D3—61no—
370C23×D3—61no—
371C23×D3—122no—
372C23×D3—122no—
373C23×D3—122no—
374C23×D3—122no—
375C23×D3—122no—
376C23×D3—122no—
377C23×D3C22×D311yescharacteristic
378C23×D3C22×D311yescharacteristic
379C23×D3C22×D311yescharacteristic
380C2×C3×D4—34no—
381C2×C3×D4—122no—
382C22×C3×C4—21no—
383C22×C3×C4—21no—
384C22×C3×C4—21no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—34no—
391C22×C3×C4—122no—
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C2×#67—34no—
399C2×#67—34no—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—122no—
408C2×#67—122no—
409C2×#67—122no—
410C2×#67—122no—
411C2×#67—122no—
412C2×#67—122no—
413C2×#67—122no—
414C2×#67—122no—
415C2×#67—122no—
416C22×Dic3—31no—
417C22×Dic3—31no—
418C22×Dic3—61no—
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C2×D12—34no—
425C2×D12—34no—
426C2×D12—34no—
427C2×D12—34no—
428C2×D12—34no—
429C2×D12—34no—
430C2×D12—34no—
431C2×D12—34no—
432C2×D12—34no—
433C2×D12—34no—
434C2×D12—34no—
435C2×D12—34no—
436C2×D12—34no—
437C2×D12—42no—
438C2×D12—64no—
439C2×D12—64no—
440C2×D12—64no—
441C2×D12—122no—
442C2×D12—122no—
443C2×D12—122no—
444C2×D12—122no—
445C2×D12—122no—
446C2×D12—122no—
447C2×D12—124no—
448C2×D12—124no—
449C2×D12—124no—
450C2×D12—122no—
451C2×D12—122no—
452C2×D12—122no—
453C2×D12—122no—
454C2×D12—122no—
455C2×D12—122no—
456C2×D12—122no—
457C2×D12C22×D314yes—
458C2×C4×D3—34no—
459C2×C4×D3—34no—
460C2×C4×D3—34no—
461C2×C4×D3—34no—
462C2×C4×D3—42no—
463C2×C4×D3—64no—
464C2×C4×D3—122no—
465C2×C4×D3—122no—
466C2×C4×D3—122no—
467C2×C4×D3—122no—
468C2×C4×D3—124no—
469C2×C4×D3C22×D314yescomplemented
470C3×C4⋊C4—24no—
471C3×C4⋊C4—34no—
472C3×C4⋊C4—34no—
473C3×C4⋊C4—34no—
474C3×C4⋊C4C22×D314yescomplemented
475C3×C4⋊C4C22×D314yescomplemented
476C3×C22⋊C4—34no—
477C3×C22⋊C4—34no—
478C3×C22⋊C4—34no—
479C3×C22⋊C4—34no—
480C3×C22⋊C4—34no—
481C3×C22⋊C4—34no—
482C3×C42—34no—
483#217—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—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—64no—
496(C2×D3)⋊C4—64no—
497(C2×D3)⋊C4C22×D314yes—
498(C2×D3)⋊C4C22×D314yes—
499(C2×D3)⋊C4C22×D314yes—
500(C2×D3)⋊C4C22×D314yes—
501(C2×D3)⋊C4C22×D314yes—
502(C2×D3)⋊C4C22×D314yescomplemented
503C4⋊Dic3—34no—
504C4⋊Dic3C22×D314yescomplemented
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4C22×D314yescomplemented
509Dic3⋊C4C22×D314yescomplemented
510C4×Dic3C22×D314yescomplemented
511C22×C32H(5,𝔽2)12yes—
512C22×C32H(5,𝔽2)12yes—
513C22×C32H(5,𝔽2)12yes—
514C22×C32C2511yescharacteristic
515C2×C3⋊D3—22no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—22no—
518C2×C3⋊D3—22no—
519C2×C3⋊D3—22no—
520C2×C3⋊D3—22no—
521C2×C3⋊D3—22no—
522C2×C3⋊D3—22no—
523C2×C3⋊D3—22no—
524C2×C3⋊D3—44no—
525C2×C3⋊D3—44no—
526C2×C3⋊D3—44no—
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—22no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—44no—
537C2×C3×D3—44no—
538C2×C3×D3—44no—
539D32—416no—
540C32×C4—22no—
541C32×C4—22no—
542C32×C4—22no—
543C3⋊Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C25—91no—
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—
560C22×D4—91no—
561C22×D4—91no—
562C23×C4—31no—
563C23×C4—91no—
564C23×C4—91no—
565#127—98no—
566#126—38no—
567#126—98no—
568#123—38no—
569#123—98no—
570#123—98no—
571#121—98no—
572#121—98no—
573#121—98no—
574#121—98no—
575#121—98no—
576#121—98no—
577#120—98no—
578#120—98no—
579#120—98no—
580C2×C4⋊C4—31no—
581C2×C4⋊C4—31no—
582C2×C4⋊C4—31no—
583C2×C4⋊C4—91no—
584C2×C4⋊C4—91no—
585C2×C4⋊C4D3211yescharacteristic, complemented
586C2×C22⋊C4—31no—
587C2×C22⋊C4—31no—
588C2×C22⋊C4—31no—
589C2×C22⋊C4—31no—
590C2×C22⋊C4—31no—
591C2×C22⋊C4—31no—
592C2×C22⋊C4—91no—
593C2×C22⋊C4—91no—
594C2×C22⋊C4—91no—
595C2×C22⋊C4—91no—
596C2×C22⋊C4—91no—
597C2×C22⋊C4—91no—
598C2×C42—31no—
599C23×C3—21no—
600C23×C3—32no—
601C23×C3—32no—
602C23×C3—32no—
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×C3C23×D311yescharacteristic
613C23×C3C23×D311yescharacteristic
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—32no—
624C22×D3—32no—
625C22×D3—32no—
626C22×D3—32no—
627C22×D3—32no—
628C22×D3—32no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—64no—
633C22×D3—62no—
634C22×D3—62no—
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—62no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—62no—
651C22×D3—122no—
652C22×D3—122no—
653C22×D3—122no—
654C22×D3—122no—
655C22×D3—122no—
656C22×D3—122no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3—124no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—124no—
663C22×D3—124no—
664C22×D3—124no—
665C22×D3—1216no—
666C22×D3—1216no—
667C22×D3C23×D312yes—
668C22×D3C23×D312yes—
669C22×D3C23×D312yes—
670C3×D4—124no—
671C2×C3×C4—24no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—42no—
687C2×C3×C4—42no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4—62no—
692C2×C3×C4—62no—
693C2×C3×C4—124no—
694C2×C3×C4C23×D312yes—
695C2×C3×C4C23×D312yes—
696C2×C3×C4C23×D312yes—
697C2×C3×C4C23×D312yes—
698C2×C3×C4C23×D312yes—
699C2×C3×C4C23×D312yes—
700#67—124no—
701#67—124no—
702#67—124no—
703#67—124no—
704#67—124no—
705#67—124no—
706#67—124no—
707#67—124no—
708#67—124no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—62no—
719C2×Dic3—122no—
720C2×Dic3C23×D312yes—
721C2×Dic3C23×D312yes—
722C2×Dic3C23×D312yes—
723C2×Dic3C23×D312yes—
724C2×Dic3C23×D312yes—
725D12—44no—
726D12—124no—
727D12—124no—
728D12—124no—
729D12—124no—
730D12—124no—
731D12—124no—
732D12—128no—
733D12—128no—
734D12—128no—
735D12—124no—
736D12—124no—
737D12—124no—
738D12—124no—
739D12—124no—
740D12—124no—
741D12—124no—
742C4×D3—44no—
743C4×D3—124no—
744C4×D3—124no—
745C4×D3—124no—
746C4×D3—124no—
747C4×D3—128no—
748C2×C32#56014yescomplemented
749C2×C32C2×H(5,𝔽2)11yescharacteristic
750C2×C32C2×H(5,𝔽2)11yescharacteristic
751C2×C32C2×H(5,𝔽2)11yescharacteristic
752C3⋊D3—42no—
753C3⋊D3—42no—
754C3⋊D3—42no—
755C3×D3—42no—
756C3×D3—42no—
757C3×D3—42no—
758C24—31no—
759C24—31no—
760C24—31no—
761C24—94no—
762C24—91no—
763C24—91no—
764C24—91no—
765C24—362no—
766C24—362no—
767C24—362no—
768C2×D4—34no—
769C2×D4—94no—
770C2×D4—94no—
771C2×D4—94no—
772C2×D4—94no—
773C2×D4—94no—
774C2×D4—94no—
775C2×D4—94no—
776C2×D4—94no—
777C2×D4—94no—
778C2×D4—94no—
779C2×D4—94no—
780C2×D4—122no—
781C2×D4—362no—
782C2×D4—362no—
783C2×D4—362no—
784C2×D4—362no—
785C2×D4—362no—
786C2×D4—362no—
787C2×D4—362no—
788C2×D4—362no—
789C2×D4—362no—
790C2×D4—362no—
791C2×D4—362no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—34no—
798C22×C4—94no—
799C22×C4—91no—
800C22×C4—94no—
801C22×C4—122no—
802C22×C4—362no—
803C22×C4—362no—
804C22×C4C2×D3211yescharacteristic
805C22×C4C2×D3211yescharacteristic
806C22×C4C2×D3211yescharacteristic
807C4⋊C4—34no—
808C4⋊C4—34no—
809C4⋊C4—34no—
810C4⋊C4—94no—
811C4⋊C4—94no—
812C4⋊C4C2×D3214yescomplemented
813C22⋊C4—34no—
814C22⋊C4—34no—
815C22⋊C4—34no—
816C22⋊C4—34no—
817C22⋊C4—34no—
818C22⋊C4—34no—
819C22⋊C4—94no—
820C22⋊C4—94no—
821C22⋊C4—94no—
822C22⋊C4—94no—
823C22⋊C4—94no—
824C22⋊C4—94no—
825C42—34no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—21no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—124no—
840C22×C3—124no—
841C22×C3—124no—
842C22×C3#100412yes—
843C22×C3#100912yes—
844C22×C3#100912yes—
845C22×C3#100912yes—
846C22×C3#100912yes—
847C22×C3#100912yes—
848C22×C3C24×D311yescharacteristic
849C22×C3C24×D311yescharacteristic
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—44no—
860C2×D3—44no—
861C2×D3—44no—
862C2×D3—64no—
863C2×D3—62no—
864C2×D3—62no—
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—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—122no—
882C2×D3—122no—
883C2×D3—122no—
884C2×D3—122no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3—122no—
888C2×D3—122no—
889C2×D3—1216no—
890C2×D3—1216no—
891C2×D3—128no—
892C2×D3—124no—
893C2×D3—124no—
894C2×D3—124no—
895C2×D3—124no—
896C2×D3—124no—
897C2×D3—124no—
898C2×D3—244no—
899C2×D3—244no—
900C3×C4—24no—
901C3×C4—22no—
902C3×C4—22no—
903C3×C4—22no—
904C3×C4—22no—
905C3×C4—22no—
906C3×C4—22no—
907C3×C4—42no—
908C3×C4—42no—
909C3×C4—62no—
910C3×C4—62no—
911C3×C4—62no—
912C3×C4—62no—
913C3×C4—62no—
914Dic3—22no—
915Dic3—22no—
916Dic3—22no—
917Dic3—22no—
918Dic3—22no—
919Dic3—62no—
920Dic3—62no—
921Dic3—122no—
922C32C2×#56011yescharacteristic, complemented, Sylow
923C23—32no—
924C23—32no—
925C23—32no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—92no—
936C23—92no—
937C23—92no—
938C23—182no—
939C23—182no—
940C23—182no—
941C23—182no—
942C23—182no—
943C23—182no—
944C23—182no—
945C23—182no—
946C23—182no—
947C23—364no—
948C23—364no—
949C23—364no—
950C23—3616no—
951C23C22×D3211yescharacteristic
952D4—124no—
953D4—364no—
954D4—364no—
955D4—364no—
956D4—364no—
957D4—364no—
958D4—364no—
959D4—364no—
960D4—364no—
961D4—364no—
962D4—364no—
963D4—364no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—32no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—32no—
971C2×C4—32no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—92no—
978C2×C4—124no—
979C2×C4—182no—
980C2×C4—364no—
981C2×C4—364no—
982C2×C4C22×D3212yes—
983C2×C4C22×D3212yes—
984C2×C4C22×D3212yes—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—24no—
989C2×C3—122no—
990C2×C3—122no—
991C2×C3—122no—
992C2×C3#566614yescomplemented
993C2×C3#571114yescomplemented
994C2×C3C2×#100411yescharacteristic
995C2×C3C2×#100911yescharacteristic
996C2×C3C2×#100911yescharacteristic
997C2×C3C2×#100911yescharacteristic
998C2×C3C2×#100911yescharacteristic
999C2×C3C2×#100911yescharacteristic
1000D3—42no—
1001D3—42no—
1002D3—42no—
1003D3—124no—
1004D3—122no—
1005D3—122no—
1006D3—122no—
1007D3—122no—
1008D3—122no—
1009D3—122no—
1010D3—242no—
1011D3—242no—
1012C22—62no—
1013C22—62no—
1014C22—62no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—124no—
1022C22—124no—
1023C22—124no—
1024C22—182no—
1025C22—182no—
1026C22—182no—
1027C22—182no—
1028C22—182no—
1029C22—182no—
1030C22—182no—
1031C22—182no—
1032C22—182no—
1033C22—3616no—
1034C22—364no—
1035C22—364no—
1036C22—364no—
1037C22#6430812yes—
1038C22#6431412yes—
1039C22#6432012yes—
1040C22C23×D3211yescharacteristic
1041C4—22no—
1042C4—22no—
1043C4—22no—
1044C4—62no—
1045C4—62no—
1046C4—62no—
1047C4—62no—
1048C4—62no—
1049C4—182no—
1050C3—21no—
1051C3C2×#566611yescharacteristic, complemented
1052C3C2×#571111yescharacteristic, complemented
1053C2—122no—
1054C2—122no—
1055C2—122no—
1056C2—362no—
1057C2—362no—
1058C2—362no—
1059C2#1059466314yesdirect product factor
1060C2C2×#6430811yescharacteristic
1061C2C2×#6431411yescharacteristic
1062C2C2×#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×#64104C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#894C2semidirect
4. C2×#63923C2semidirect
5. C2×#63923C2semidirect
6. C2×#63922C2semidirect
7. C2×#63912C2semidirect
8. C2×#63911C2semidirect
9. C2×#63910C2semidirect
10. C2×#63910C2semidirect
11. C2×#63909C2semidirect
12. C2×#63906C2semidirect
13. C2×#63868C2semidirect
14. C2×#63854C2semidirect
15. C2×#63853C2semidirect
16. #10594663C2direct (N × H)
22. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C4×C3⋊D3C22semidirect
25. C22×C3×C4×D3C22semidirect
31. C22×#626C22semidirect
32. C22×#626C22semidirect
34. C22×#624C22semidirect
35. C2×C32×C4⋊C4C22semidirect
37. C2×#3752C22semidirect
38. #64104C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×C4⋊Dic3C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×C4×Dic3C22semidirect
49. C3×#898C22semidirect
50. C3×#894C22semidirect
51. C2×#3724C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
55. C2×#3722C22semidirect
57. #63923C22semidirect
58. #63923C22semidirect
59. #63922C22semidirect
60. #63912C22semidirect
61. #63911C22semidirect
62. #63910C22semidirect
63. #63910C22semidirect
64. #63909C22semidirect
65. #63906C22semidirect
66. #63868C22semidirect
67. #63854C22semidirect
68. #63853C22semidirect
78. C2×#898D3semidirect
87. C2×#894D3semidirect
121. C2×C4⋊(C3⋊D3)C23semidirect
123. C2×C4×C3⋊D3C23semidirect
132. C2×C3×C4×D3C23semidirect
145. C2×#626C23semidirect
146. C2×#626C23semidirect
150. C2×#624C23semidirect
151. C32×C4⋊C4C23semidirect
153. #3752C23semidirect
159. C3×(C2×D3)⋊C4C23semidirect
160. C3×C4⋊Dic3C23semidirect
161. C3×Dic3⋊C4C23semidirect
162. C3×Dic3⋊C4C23semidirect
163. C3×C4×Dic3C23semidirect
164. #3724C23semidirect
165. Dic3⋊Dic3C23semidirect
168. #3722C23semidirect
206. C22×C4×D3C2×D3semidirect
213. C2×C3×C4⋊C4C2×D3semidirect
214. C2×C3×C4⋊C4C2×D3semidirect
245. C2×(C2×D3)⋊C4C2×D3semidirect
247. C2×C4⋊Dic3C2×D3semidirect
251. C2×Dic3⋊C4C2×D3semidirect
252. C2×Dic3⋊C4C2×D3semidirect
253. C2×C4×Dic3C2×D3semidirect
255. #898C2×D3semidirect
264. #894C2×D3semidirect
469. C2×C4×D3C22×D3semidirect
474. C3×C4⋊C4C22×D3semidirect
475. C3×C4⋊C4C22×D3semidirect
502. (C2×D3)⋊C4C22×D3semidirect
504. C4⋊Dic3C22×D3semidirect
508. Dic3⋊C4C22×D3semidirect
509. Dic3⋊C4C22×D3semidirect
510. C4×Dic3C22×D3semidirect
585. C2×C4⋊C4D32semidirect
748. C2×C32#560semidirect
812. C4⋊C4C2×D32semidirect
922. C32C2×#560semidirect
992. C2×C3#5666semidirect
993. C2×C3#5711semidirect
1051. C3C2×#5666semidirect
1052. C3C2×#5711semidirect
1059. C2#10594663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C3×#8982
C2×C3×#8942
C2×#639232
C2×#639222
C2×#639122
C2×#639112
C2×#639102
C2×#639092
C2×#639062
C2×#638682
C2×#638542
C2×#638532
#105946632
C2×#57113
C2×#56663