Finite Group Databasebeta

← C2×#10594392 #11903255

Subgroups — C2×#10594392 #11903255

Order 1152.

2561 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64105C211yesmaximal, characteristic, complemented
2C2×C3×#896C211yesmaximal, characteristic, complemented
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×C4×#626C211yesmaximal, characteristic
5C2×#63896C211yesmaximal, characteristic, complemented
6C2×#63888C211yesmaximal, characteristic, complemented
7C2×#63888C211yesmaximal, characteristic, complemented
8C2×#63887C211yesmaximal, characteristic, complemented
9C2×#63883C211yesmaximal, characteristic, complemented
10C2×#63880C211yesmaximal, characteristic
11C2×#63880C211yesmaximal, characteristic
12C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13C2×#63867C211yesmaximal, characteristic, complemented
14C2×#63867C211yesmaximal, characteristic, complemented
15C2×#63866C211yesmaximal, characteristic, complemented
16#10594392C2116yesmaximal, direct product factor
17C2×#5636—31nomaximal
18C2×#5579—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34#64105C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#896C2218yescomplemented
45C3×#887C2218yescomplemented
46C2×#3724C2211yescharacteristic
47C2×#3724C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C4×#626C2218yes—
58#63896C2218yescomplemented
59#63888C2218yescomplemented
60#63888C2218yescomplemented
61#63887C2218yescomplemented
62#63883C2218yescomplemented
63#63880C2218yes—
64#63880C2218yes—
65D3×Dic3⋊C4C2218yescomplemented
66#63867C2218yescomplemented
67#63867C2218yescomplemented
68#63866C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C2×C3×C4×Q8—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×#946—31no—
74C2×#944—31no—
75C2×C4×#67—31no—
76C22×Dic3⋊C4—31no—
77#5636—316no—
78#5579—316no—
79C2×#896—31no—
80C2×#896—31no—
81C2×#896—31no—
82C2×#896—31no—
83C2×#896—31no—
84C2×#896—61no—
85C2×#896D311yescharacteristic, complemented
86C2×D3×C4⋊C4—31no—
87C2×D3×C4⋊C4—31no—
88C2×D3×C4⋊C4—31no—
89C2×#889—31no—
90C2×#889—31no—
91C2×#887D311yescharacteristic, complemented
92C2×#67⋊C4—31no—
93C2×#67⋊C4—31no—
94C2×#878—31no—
95C2×#878—31no—
96C2×C4×D12—31no—
97C2×C4×D12—31no—
98C2×C4×D12—31no—
99C2×#870—31no—
100C2×#870—31no—
101C2×#869—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C2×C4×C3⋊D3—42no—
111C2×C4×C3⋊D3C2314yes—
112C2×#634—42no—
113C2×#634C2314yes—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×C4×D3—42no—
122C2×C3×C4×D3C2314yes—
123C2×C3×Dic6—24no—
124C2×C3×Dic6—42no—
125C2×C3×Dic6C2314yes—
126C2×C3×Dic6C2314yes—
127C2×#626Q818yescomplemented
128C2×#626C2314yes—
129C2×#624—24no—
130C2×#624—42no—
131C2×#624C2314yes—
132C2×#624C2314yes—
133C2×D3×Dic3—24no—
134C2×D3×Dic3—42no—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2314yes—
137C32×C4⋊C4C2314yes—
138#3752C2314yes—
139#3752C2314yes—
140#3750C2314yes—
141#3750C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×C4×Dic3C2314yes—
149C3×C4×Dic3C2314yes—
150C3×C4×Dic3C2314yes—
151#3724C2314yes—
152#3724C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160#3722C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162C2×#554—91noSylow
163C22×C3×Q8—31no—
164C22×C3×Q8—31no—
165C23×C3×C4—31no—
166C22×#67—31no—
167C23×Dic3—31no—
168C23×Dic3—31no—
169C22×D12—31no—
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—61no—
179C22×C4×D3C2×D311yescharacteristic
180C22×Dic6—31no—
181C22×Dic6—31no—
182C22×Dic6—61no—
183C22×Dic6C2×D311yescharacteristic
184C22×Dic6C2×D311yescharacteristic
185C3×C22⋊Q8—38no—
186C3×C4×Q8—38no—
187C2×C3×C4⋊C4—21no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4C2×D311yescharacteristic
193C2×C3×C4⋊C4C2×D311yescharacteristic
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C42—31no—
197C2×C3×C42—31no—
198C2×C3×C42—31no—
199C2×#217—31no—
200#946—38no—
201#946—38no—
202#946—38no—
203#944—38no—
204C4×#67—38no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—61no—
213C2×(C2×D3)⋊C4—61no—
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—31no—
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—38no—
239C2×Dic3⋊C4—61no—
240C2×Dic3⋊C4—61no—
241C2×Dic3⋊C4C2×D311yescharacteristic
242C2×Dic3⋊C4C2×D311yescharacteristic
243C2×Dic3⋊C4C2×D311yescharacteristic
244C2×Dic3⋊C4C2×D311yescharacteristic
245C2×C4×Dic3C2×D311yescharacteristic
246C2×C4×Dic3C2×D311yescharacteristic
247C2×C4×Dic3C2×D311yescharacteristic
248#896—38no—
249#896—38no—
250#896—38no—
251#896—38no—
252#896—38no—
253#896—68no—
254#896C2×D318yescomplemented
255D3×C4⋊C4—38no—
256D3×C4⋊C4—38no—
257D3×C4⋊C4—38no—
258#889—38no—
259#889—38no—
260#887C2×D318yescomplemented
261#67⋊C4—38no—
262#67⋊C4—38no—
263#878—38no—
264#878—38no—
265C4×D12—38no—
266C4×D12—38no—
267C4×D12—38no—
268#870—38no—
269#870—38no—
270#869—38no—
271C23×C32C2411yescharacteristic
272C22×C3⋊D3—22no—
273C22×C3⋊D3—22no—
274C22×C3⋊D3C2×Q814yes—
275C22×C3⋊D3C2412yes—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3C2×Q814yes—
279C22×C3×D3C2412yes—
280C2×C32×C4—22no—
281C2×C32×C4—22no—
282C2×C32×C4—22no—
283C2×C32×C4C2412yes—
284C2×C32×C4C2412yes—
285C2×C32×C4C2412yes—
286C2×C3⋊Dic3—22no—
287C2×C3⋊Dic3—22no—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3C2412yes—
290C2×C3⋊Dic3C2412yes—
291C2×C3⋊Dic3C2412yes—
292C4×C3⋊D3—44no—
293#634—44no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3C2×Q814yes—
300C2×C3×Dic3#4114yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C3×C4×D3—44no—
309C3×Dic6—28no—
310C3×Dic6—44no—
311#626C2×Q8116yescomplemented
312#624—28no—
313#624—44no—
314D3×Dic3—28no—
315D3×Dic3—44no—
316#554—916no—
317C2×C4⋊Q8—91no—
318C2×#125—91no—
319C2×#125—91no—
320C2×C22⋊Q8—31no—
321C2×C22⋊Q8—91no—
322C2×C22⋊Q8—91no—
323C2×C22⋊Q8—91no—
324C2×C22⋊Q8—91no—
325C2×C22⋊Q8—91no—
326C2×C4×Q8—31no—
327C2×C4×D4—91no—
328C2×C4×D4—91no—
329C2×C4×D4—91no—
330C22×C4⋊C4—91no—
331C22×C4⋊C4—91no—
332C24×C3—31no—
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—61no—
336C23×D3C22×D311yescharacteristic
337C2×C3×Q8—34no—
338C2×C3×Q8—34no—
339C2×C3×Q8—64no—
340C2×C3×Q8—122no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—34no—
352C22×C3×C4—122no—
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—38no—
360C2×#67—34no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—34no—
368C22×Dic3—34no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—64no—
373C22×Dic3—122no—
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C2×D12—38no—
382C2×D12—34no—
383C2×C4×D3—34no—
384C2×C4×D3—34no—
385C2×C4×D3—34no—
386C2×C4×D3—34no—
387C2×C4×D3—34no—
388C2×C4×D3—34no—
389C2×C4×D3—34no—
390C2×C4×D3—34no—
391C2×C4×D3—42no—
392C2×C4×D3—64no—
393C2×C4×D3—64no—
394C2×C4×D3—64no—
395C2×C4×D3—64no—
396C2×C4×D3—122no—
397C2×C4×D3—122no—
398C2×C4×D3—122no—
399C2×C4×D3—122no—
400C2×C4×D3—124no—
401C2×C4×D3—122no—
402C2×C4×D3C22×D314yes—
403C2×Dic6—24no—
404C2×Dic6—34no—
405C2×Dic6—34no—
406C2×Dic6—42no—
407C2×Dic6—64no—
408C2×Dic6—122no—
409C2×Dic6—122no—
410C2×Dic6—124no—
411C2×Dic6C22×D314yes—
412C2×Dic6C22×D314yes—
413C3×C4⋊C4—24no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4—34no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4C22×D314yes—
419C3×C4⋊C4C22×D314yes—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—34no—
422C3×C42—34no—
423C3×C42—34no—
424C3×C42—34no—
425#217—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—64no—
434(C2×D3)⋊C4—64no—
435(C2×D3)⋊C4C22×D314yes—
436(C2×D3)⋊C4C22×D314yes—
437C4⋊Dic3—34no—
438C4⋊Dic3—34no—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—64no—
460Dic3⋊C4—64no—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463Dic3⋊C4C22×D314yes—
464Dic3⋊C4C22×D314yes—
465C4×Dic3C22×D314yes—
466C4×Dic3C22×D314yes—
467C4×Dic3C22×D314yes—
468C22×C32C22×Q812yes—
469C22×C32C2×#4112yes—
470C22×C32H(5,𝔽2)12yes—
471C22×C32C2511yescharacteristic
472C2×C3⋊D3—28no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3C22×Q814yes—
476C2×C3×D3—28no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3C22×Q814yes—
480C32×C4—22no—
481C32×C4—22no—
482C32×C4—22no—
483C3⋊Dic3—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3C22×Q814yes—
492C3×Dic3C2×#4114yes—
493C22×Q8—31no—
494C22×Q8—31no—
495C22×Q8—91no—
496C22×D4—91no—
497C23×C4—31no—
498C23×C4—91no—
499C23×C4—91no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4—91no—
503C4⋊Q8—98no—
504#125—98no—
505#125—98no—
506C22⋊Q8—38no—
507C22⋊Q8—98no—
508C22⋊Q8—98no—
509C22⋊Q8—98no—
510C22⋊Q8—98no—
511C22⋊Q8—98no—
512C4×Q8—38no—
513C4×D4—98no—
514C4×D4—98no—
515C4×D4—98no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—98no—
521C2×C4⋊C4—98no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—91no—
532C2×C4⋊C4—91no—
533C2×C4⋊C4D3211yescharacteristic
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C42—31no—
541C2×C42—31no—
542C2×C42—31no—
543C23×C3—21no—
544C23×C3—34no—
545C23×C3—32no—
546C23×C3—62no—
547C23×C3—62no—
548C23×C3C23×D311yescharacteristic
549C23×C3C23×D311yescharacteristic
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—34no—
553C22×D3—34no—
554C22×D3—32no—
555C22×D3—32no—
556C22×D3—64no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3—62no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3D3×Q814yes—
565C22×D3C23×D312yes—
566C3×Q8—68no—
567C3×Q8—124no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—34no—
578C2×C3×C4—34no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—42no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4—62no—
593C2×C3×C4—62no—
594C2×C3×C4—124no—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D312yes—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D312yes—
601#67—316no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—32no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3—62no—
616C2×Dic3—64no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—62no—
623C2×Dic3—68no—
624C2×Dic3—122no—
625C2×Dic3—122no—
626C2×Dic3—124no—
627C2×Dic3#23514yes—
628C2×Dic3D3×Q814yes—
629C2×Dic3C23×D312yes—
630C2×Dic3C23×D312yes—
631C2×Dic3C23×D312yes—
632C2×Dic3C23×D312yes—
633C2×Dic3C23×D312yes—
634C2×Dic3C23×D312yes—
635C2×Dic3C23×D312yes—
636D12—316no—
637C4×D3—44no—
638C4×D3—68no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—124no—
642C4×D3—124no—
643C4×D3—124no—
644C4×D3—124no—
645C4×D3—128no—
646C4×D3—124no—
647Dic6—28no—
648Dic6—44no—
649Dic6—124no—
650Dic6—124no—
651Dic6—128no—
652C2×C32#55414yescomplemented
653C2×C32C23×Q811yescharacteristic
654C2×C32C22×#4111yescharacteristic
655C2×C32C2×H(5,𝔽2)11yescharacteristic
656C3⋊D3—24no—
657C3×D3—24no—
658C24—31no—
659C24—91no—
660C2×Q8—34no—
661C2×Q8—34no—
662C2×Q8—64no—
663C2×Q8—94no—
664C2×Q8—122no—
665C2×Q8—362no—
666C2×D4—94no—
667C2×D4—98no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—34no—
676C22×C4—94no—
677C22×C4—94no—
678C22×C4—94no—
679C22×C4—94no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—94no—
684C22×C4—122no—
685C22×C4—184no—
686C22×C4—184no—
687C22×C4—362no—
688C22×C4—362no—
689C22×C4—362no—
690C22×C4C2×D3211yescharacteristic
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3211yescharacteristic
693C4⋊C4—34no—
694C4⋊C4—34no—
695C4⋊C4—34no—
696C4⋊C4—34no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4C2×D3214yes—
709C22⋊C4—34no—
710C22⋊C4—34no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C42—34no—
716C42—34no—
717C42—34no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—21no—
722C22×C3—34no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—68no—
726C22×C3C2×#23512yes—
727C22×C3#100412yes—
728C22×C3C2×D3×Q812yes—
729C22×C3C2×D3×Q812yes—
730C22×C3D3×#4112yes—
731C22×C3#100912yes—
732C22×C3C24×D311yescharacteristic
733C22×C3C24×D311yescharacteristic
734C2×D3—28no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—34no—
738C2×D3—34no—
739C2×D3—64no—
740C2×D3—68no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—68no—
746C2×D3—122no—
747C2×D3—122no—
748C2×D3—128no—
749C2×D3C2×D3×Q814yes—
750C3×C4—22no—
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—22no—
755C3×C4—22no—
756C3×C4—34no—
757C3×C4—34no—
758C3×C4—42no—
759C3×C4—42no—
760C3×C4—42no—
761C3×C4—62no—
762C3×C4—62no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4—62no—
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—22no—
770Dic3—22no—
771Dic3—64no—
772Dic3—62no—
773Dic3—62no—
774Dic3—62no—
775Dic3—62no—
776Dic3—62no—
777Dic3—62no—
778Dic3—122no—
779Dic3—122no—
780Dic3C2×#23514yes—
781Dic3C2×D3×Q814yes—
782C32C2×#55411yescharacteristic, complemented, Sylow
783C23—34no—
784C23—32no—
785C23—62no—
786C23—62no—
787C23—94no—
788C23—92no—
789C23—182no—
790C23—182no—
791C23C22×D3211yescharacteristic
792Q8—68no—
793Q8—124no—
794Q8—364no—
795D4—916no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—34no—
800C2×C4—34no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—92no—
814C2×C4—92no—
815C2×C4—92no—
816C2×C4—124no—
817C2×C4—188no—
818C2×C4—188no—
819C2×C4—182no—
820C2×C4—182no—
821C2×C4—182no—
822C2×C4—364no—
823C2×C4—364no—
824C2×C4—364no—
825C2×C4C22×D3212yes—
826C2×C4C22×D3212yes—
827C2×C4C22×D3212yes—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—24no—
832C2×C3—64no—
833C2×C3#557914yescomplemented
834C2×C3#563614yescomplemented
835C2×C3C22×#23511yescharacteristic
836C2×C3C2×#100411yescharacteristic
837C2×C3C22×D3×Q811yescharacteristic
838C2×C3C22×D3×Q811yescharacteristic
839C2×C3C2×D3×#4111yescharacteristic
840C2×C3C2×#100911yescharacteristic
841D3—24no—
842D3—64no—
843D3—64no—
844D3—124no—
845C22—34no—
846C22—62no—
847C22—62no—
848C22—68no—
849C22—94no—
850C22—182no—
851C22—182no—
852C22—188no—
853C22D3×#23512yes—
854C22#6431412yes—
855C22D32×Q812yes—
856C22C23×D3211yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—34no—
861C4—34no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—62no—
867C4—182no—
868C4—182no—
869C4—182no—
870C3—21no—
871C3C2×#557911yescharacteristic, complemented
872C3C2×#563611yescharacteristic, complemented
873C2—64no—
874C2—184no—
875C2#1059439214yesdirect product factor
876C2C2×D3×#23511yescharacteristic
877C2C2×#6431411yescharacteristic
878C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#554
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×#64105C2semidirect
2. C2×C3×#896C2semidirect
3. C2×C3×#887C2semidirect
5. C2×#63896C2semidirect
6. C2×#63888C2semidirect
7. C2×#63888C2semidirect
8. C2×#63887C2semidirect
9. C2×#63883C2semidirect
12. C2×D3×Dic3⋊C4C2semidirect
13. C2×#63867C2semidirect
14. C2×#63867C2semidirect
15. C2×#63866C2semidirect
16. #10594392C2direct (N × H)
34. #64105C22semidirect
44. C3×#896C22semidirect
45. C3×#887C22semidirect
58. #63896C22semidirect
59. #63888C22semidirect
60. #63888C22semidirect
61. #63887C22semidirect
62. #63883C22semidirect
65. D3×Dic3⋊C4C22semidirect
66. #63867C22semidirect
67. #63867C22semidirect
68. #63866C22semidirect
85. C2×#896D3semidirect
91. C2×#887D3semidirect
127. C2×#626Q8semidirect
254. #896C2×D3semidirect
260. #887C2×D3semidirect
311. #626C2×Q8semidirect
652. C2×C32#554semidirect
782. C32C2×#554semidirect
833. C2×C3#5579semidirect
834. C2×C3#5636semidirect
871. C3C2×#5579semidirect
872. C3C2×#5636semidirect
875. C2#10594392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641052
C2×C3×#8962
C2×C3×#8872
C2×C4×#6262
C2×#638962
C2×#638882
C2×#638872
C2×#638832
C2×#638802
C2×D3×Dic3⋊C42
C2×#638672
C2×#638662
#105943922
C2×#56363
C2×#55793