Finite Group Databasebeta

← C2×#10593914 #11901407

Subgroups — C2×#10593914 #11901407

Order 1152.

2401 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64079C211yesmaximal, characteristic, complemented
2C2×C3×#876C211yesmaximal, characteristic, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C2×#63905C211yesmaximal, characteristic, complemented
5C2×#63899C211yesmaximal, characteristic, complemented
6C2×#63893C211yesmaximal, characteristic, complemented
7C2×#63891C211yesmaximal, characteristic, complemented
8C2×#63891C211yesmaximal, characteristic, complemented
9C2×#63885C211yesmaximal, characteristic
10C2×#63884C211yesmaximal, characteristic, complemented
11C2×#63879C211yesmaximal, characteristic, complemented
12C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13C2×#63861C211yesmaximal, characteristic, complemented
14C2×#63851C211yesmaximal, characteristic, complemented
15C2×#63846C211yesmaximal, characteristic, complemented
16#10593914C2116yesmaximal, direct product factor
17C2×#5707—31nomaximal
18C2×#5564—31nomaximal
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C42C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35#64079C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C3×#876C2218yescomplemented
46C3×C4×D12C2218yescomplemented
47C2×#3724C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63905C2218yescomplemented
58#63899C2218yescomplemented
59#63893C2218yescomplemented
60#63891C2218yescomplemented
61#63891C2218yescomplemented
62#63885C2218yes—
63#63884C2218yescomplemented
64#63879C2218yescomplemented
65D3×Dic3⋊C4C2218yescomplemented
66#63861C2218yescomplemented
67#63851C2218yescomplemented
68#63846C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#935—31no—
73C2×#929—31no—
74C2×C4×#67—31no—
75C2×#924—31no—
76C22×Dic3⋊C4—31no—
77#5707—316no—
78#5564—316no—
79C2×#898—31no—
80C2×#897—31no—
81C2×#896—31no—
82C2×#896—31no—
83C2×#894—31no—
84C2×D3×C4⋊C4—31no—
85C2×#890—31no—
86C2×#889—31no—
87C2×#886—31no—
88C2×#886—31no—
89C2×#884—31no—
90C2×#883—31no—
91C2×#883—31no—
92C2×#883—31no—
93C2×#67⋊C4—31no—
94C2×#879—31no—
95C2×#878—31no—
96C2×#878—31no—
97C2×#876D311yescharacteristic, complemented
98C2×C4×D12D311yescharacteristic, complemented
99C2×#870—31no—
100C2×#870—31no—
101C2×#870—61no—
102C23×C3×D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×D12—24no—
118C2×C3×D12C2314yes—
119C2×C3×C4×D3—42no—
120C2×C3×C4×D3—42no—
121C2×C3×C4×D3C2314yes—
122C2×C3×C4×D3C2314yes—
123C2×#627—42no—
124C2×#627C2314yes—
125C2×#625—24no—
126C2×#625—42no—
127C2×#625C2314yes—
128C2×#625C2314yes—
129C2×D3×Dic3—24no—
130C2×D3×Dic3—42no—
131C2×D3×Dic3—42no—
132C2×D3×Dic3C2314yes—
133C2×D3×Dic3C2314yes—
134C2×D3×Dic3C2314yes—
135C32×C42C2314yes—
136C4⋊(C3⋊Dic3)C2314yes—
137C4⋊(C3⋊Dic3)C2314yes—
138#3750C2314yes—
139#3750C2314yes—
140#3750C2314yes—
141#3750C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×C4⋊Dic3C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×Dic3⋊C4C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160Dic32C2314yes—
161C2×#539—91noSylow
162C22×C3×D4—31no—
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—31no—
169C23×Dic3—31no—
170C23×Dic3—31no—
171C23×Dic3—31no—
172C22×D12C2×D311yescharacteristic
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3C2×D311yescharacteristic
177C22×C4×D3C2×D311yescharacteristic
178C22×Dic6—31no—
179C22×Dic6—31no—
180C3×#126—38no—
181C3×C4×D4—38no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C42—21no—
192C2×C3×C42C2×D311yescharacteristic
193C2×C3×C42C2×D311yescharacteristic
194C2×#217—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199#939—38no—
200#935—38no—
201#929—38no—
202C4×#67—38no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×(C2×D3)⋊C4C2×D311yescharacteristic
211C2×(C2×D3)⋊C4C2×D311yescharacteristic
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—31no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—61no—
221C2×C4⋊Dic3—61no—
222C2×C4⋊Dic3C2×D311yescharacteristic
223#924—38no—
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—38no—
238C2×Dic3⋊C4—61no—
239C2×Dic3⋊C4—61no—
240C2×Dic3⋊C4—61no—
241C2×Dic3⋊C4—61no—
242C2×Dic3⋊C4C2×D311yescharacteristic
243C2×Dic3⋊C4C2×D311yescharacteristic
244C2×Dic3⋊C4C2×D311yescharacteristic
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247#898—38no—
248#897—38no—
249#896—38no—
250#896—38no—
251#894—38no—
252D3×C4⋊C4—38no—
253#890—38no—
254#889—38no—
255#886—38no—
256#886—38no—
257#884—38no—
258#883—38no—
259#883—38no—
260#883—38no—
261#67⋊C4—38no—
262#879—38no—
263#878—38no—
264#878—38no—
265#876C2×D318yescomplemented
266C4×D12C2×D318yescomplemented
267#870—38no—
268#870—38no—
269#870—68no—
270C23×C32C2411yescharacteristic
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3#4114yes—
280C22×C3×D3C2412yes—
281C22×C3×D3C2412yes—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4—22no—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C2×C32×C4C2412yes—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3—22no—
292C2×C3⋊Dic3—22no—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C2×C3⋊Dic3C2412yes—
296C2×C3⋊Dic3C2412yes—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C3×D12—28no—
308C3×C4×D3—44no—
309C3×C4×D3—44no—
310#627—44no—
311#625—28no—
312#625—44no—
313D3×Dic3—28no—
314D3×Dic3—44no—
315D3×Dic3—44no—
316#539—916no—
317C2×#126—31no—
318C2×#126—91no—
319C2×#125—91no—
320C2×#125—91no—
321C2×#123—91no—
322C2×#123—91no—
323C2×#123—91no—
324C2×#123—91no—
325C2×C22⋊Q8—91no—
326C2×C22⋊Q8—91no—
327C2×C22⋊Q8—91no—
328C2×#121—91no—
329C2×C4×D4—31no—
330C2×C4×D4—91no—
331C22×C4⋊C4—91no—
332C24×C3—31no—
333C24×C3—31no—
334C24×C3—31no—
335C23×D3C22×D311yescharacteristic
336C23×D3C22×D311yescharacteristic
337C23×D3C22×D311yescharacteristic
338C2×C3×D4—34no—
339C2×C3×D4—64no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—34no—
349C22×C3×C4—34no—
350C22×C3×C4—122no—
351C22×C3×C4—122no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—64no—
363C2×#67—64no—
364C2×#67—122no—
365C2×#67—122no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—34no—
375C22×Dic3—34no—
376C22×Dic3—34no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—64no—
382C22×Dic3—122no—
383C22×Dic3—122no—
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C2×D12—24no—
390C2×D12C22×D314yes—
391C2×C4×D3—34no—
392C2×C4×D3—34no—
393C2×C4×D3—34no—
394C2×C4×D3—42no—
395C2×C4×D3—42no—
396C2×C4×D3—64no—
397C2×C4×D3—122no—
398C2×C4×D3—122no—
399C2×C4×D3C22×D314yes—
400C2×C4×D3C22×D314yes—
401C2×Dic6—34no—
402C2×Dic6—34no—
403C2×Dic6—122no—
404C2×Dic6—122no—
405C3×C4⋊C4—34no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C42—24no—
415C3×C42C22×D314yes—
416C3×C42C22×D314yes—
417#217—34no—
418#217—34no—
419#217—34no—
420#217—34no—
421#217—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4C22×D314yes—
428(C2×D3)⋊C4C22×D314yes—
429(C2×D3)⋊C4C22×D314yes—
430(C2×D3)⋊C4C22×D314yes—
431(C2×D3)⋊C4C22×D314yes—
432C4⋊Dic3—34no—
433C4⋊Dic3—34no—
434C4⋊Dic3—34no—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3—34no—
439C4⋊Dic3—64no—
440C4⋊Dic3—64no—
441C4⋊Dic3C22×D314yes—
442Dic3⋊C4—34no—
443Dic3⋊C4—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—64no—
456Dic3⋊C4—64no—
457Dic3⋊C4—64no—
458Dic3⋊C4—64no—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D314yes—
461Dic3⋊C4C22×D314yes—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C22×C32C2×#4112yes—
465C22×C32H(5,𝔽2)12yes—
466C22×C322−1+412yes—
467C22×C32C2511yescharacteristic
468C2×C3×D3—28no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—44no—
478C2×C3×D3—44no—
479C2×C3×D3C2×#4114yes—
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×Dic3—22no—
492C22×Q8—91no—
493C22×D4—31no—
494C22×D4—91no—
495C22×D4—91no—
496C23×C4—31no—
497C23×C4—31no—
498C23×C4—91no—
499C23×C4—91no—
500C23×C4—91no—
501#126—38no—
502#126—98no—
503#125—98no—
504#125—98no—
505#123—98no—
506#123—98no—
507#123—98no—
508#123—98no—
509C22⋊Q8—98no—
510C22⋊Q8—98no—
511C22⋊Q8—98no—
512#121—98no—
513C4×D4—38no—
514C4×D4—98no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—98no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
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×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C42—91no—
541C2×C42D3211yescharacteristic
542C23×C3—21no—
543C23×C3—34no—
544C23×C3—32no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—62no—
548C23×C3—62no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3—62no—
552C23×C3—62no—
553C23×C3—62no—
554C23×C3—62no—
555C23×C3C23×D311yescharacteristic
556C23×C3C23×D311yescharacteristic
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3#23514yes—
566C22×D3C23×D312yes—
567C22×D3C23×D312yes—
568C22×D3C23×D312yes—
569C3×D4—68no—
570C2×C3×C4—24no—
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—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—42no—
586C2×C3×C4—42no—
587C2×C3×C4—62no—
588C2×C3×C4—62no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4—124no—
593C2×C3×C4—124no—
594C2×C3×C4C23×D312yes—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D312yes—
599C2×C3×C4C23×D312yes—
600#67—68no—
601#67—68no—
602#67—124no—
603#67—124no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—68no—
622C2×Dic3—62no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—122no—
631C2×Dic3—122no—
632C2×Dic3—122no—
633C2×Dic3—122no—
634C2×Dic3—124no—
635C2×Dic3—124no—
636C2×Dic3C23×D312yes—
637C2×Dic3C23×D312yes—
638C2×Dic3C23×D312yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641D12—28no—
642C4×D3—44no—
643C4×D3—44no—
644C4×D3—68no—
645C4×D3—124no—
646C4×D3—124no—
647Dic6—124no—
648Dic6—124no—
649C2×C32#53914yescomplemented
650C2×C32C22×#4111yescharacteristic
651C2×C32C2×H(5,𝔽2)11yescharacteristic
652C2×C32C2×2−1+411yescharacteristic
653C3×D3—24no—
654C3×D3—42no—
655C3×D3—42no—
656C24—31no—
657C24—31no—
658C24—31no—
659C2×Q8—94no—
660C2×Q8—362no—
661C2×D4—34no—
662C2×D4—64no—
663C2×D4—94no—
664C2×D4—94no—
665C2×D4—184no—
666C2×D4—362no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—34no—
673C22×C4—34no—
674C22×C4—94no—
675C22×C4—94no—
676C22×C4—94no—
677C22×C4—91no—
678C22×C4—91no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—122no—
682C22×C4—122no—
683C22×C4—184no—
684C22×C4—362no—
685C22×C4—362no—
686C22×C4C2×D3211yescharacteristic
687C22×C4C2×D3211yescharacteristic
688C22×C4C2×D3211yescharacteristic
689C4⋊C4—34no—
690C4⋊C4—34no—
691C4⋊C4—34no—
692C4⋊C4—34no—
693C4⋊C4—94no—
694C4⋊C4—94no—
695C4⋊C4—94no—
696C4⋊C4—94no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—94no—
703C22⋊C4—34no—
704C22⋊C4—34no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—94no—
709C22⋊C4—94no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C42—94no—
714C42C2×D3214yes—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—21no—
719C22×C3—34no—
720C22×C3—62no—
721C22×C3—68no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—124no—
730C22×C3—124no—
731C22×C3C2×#23512yes—
732C22×C3#100412yes—
733C22×C3D3×#4112yes—
734C22×C3#100912yes—
735C22×C3#101012yes—
736C22×C3#101012yes—
737C22×C3C24×D311yescharacteristic
738C22×C3C24×D311yescharacteristic
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—28no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—44no—
749C2×D3—44no—
750C2×D3C2×#23514yes—
751C3×C4—24no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—22no—
755C3×C4—22no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—42no—
759C3×C4—42no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—62no—
763C3×C4—62no—
764C3×C4—62no—
765Dic3—22no—
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—22no—
770Dic3—62no—
771Dic3—62no—
772Dic3—62no—
773Dic3—62no—
774Dic3—62no—
775Dic3—62no—
776Dic3—62no—
777Dic3—62no—
778Dic3—122no—
779Dic3—122no—
780Dic3—122no—
781Dic3—122no—
782C32C2×#53911yescharacteristic, complemented, Sylow
783C23—34no—
784C23—32no—
785C23—32no—
786C23—32no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23C22×D3211yescharacteristic
796Q8—364no—
797D4—68no—
798D4—188no—
799D4—364no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
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—92no—
817C2×C4—124no—
818C2×C4—124no—
819C2×C4—188no—
820C2×C4—182no—
821C2×C4—182no—
822C2×C4—182no—
823C2×C4—182no—
824C2×C4—364no—
825C2×C4—364no—
826C2×C4C22×D3212yes—
827C2×C4C22×D3212yes—
828C2×C4C22×D3212yes—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—24no—
833C2×C3—64no—
834C2×C3—122no—
835C2×C3—122no—
836C2×C3#556414yescomplemented
837C2×C3#570714yescomplemented
838C2×C3C22×#23511yescharacteristic
839C2×C3C2×#100411yescharacteristic
840C2×C3C2×D3×#4111yescharacteristic
841C2×C3C2×#100911yescharacteristic
842C2×C3C2×#101011yescharacteristic
843C2×C3C2×#101011yescharacteristic
844D3—24no—
845D3—42no—
846D3—42no—
847C22—34no—
848C22—62no—
849C22—62no—
850C22—68no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—62no—
856C22—62no—
857C22—124no—
858C22—124no—
859C22#6429812yes—
860C22D3×#23512yes—
861C22#6430712yes—
862C22C23×D3211yescharacteristic
863C4—22no—
864C4—22no—
865C4—22no—
866C4—62no—
867C4—62no—
868C4—62no—
869C4—62no—
870C4—62no—
871C4—182no—
872C4—182no—
873C4—182no—
874C4—182no—
875C3—21no—
876C3C2×#556411yescharacteristic, complemented
877C3C2×#570711yescharacteristic, complemented
878C2—64no—
879C2—122no—
880C2—122no—
881C2#1059391414yesdirect product factor
882C2C2×#6429811yescharacteristic
883C2C2×D3×#23511yescharacteristic
884C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC2×#63885C2
hypercenterC2×C42D32
hypocenterC32C2×#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64079C2semidirect
2. C2×C3×#876C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C2×#63905C2semidirect
5. C2×#63899C2semidirect
6. C2×#63893C2semidirect
7. C2×#63891C2semidirect
8. C2×#63891C2semidirect
10. C2×#63884C2semidirect
11. C2×#63879C2semidirect
12. C2×D3×Dic3⋊C4C2semidirect
13. C2×#63861C2semidirect
14. C2×#63851C2semidirect
15. C2×#63846C2semidirect
16. #10593914C2direct (N × H)
35. #64079C22semidirect
45. C3×#876C22semidirect
46. C3×C4×D12C22semidirect
57. #63905C22semidirect
58. #63899C22semidirect
59. #63893C22semidirect
60. #63891C22semidirect
61. #63891C22semidirect
63. #63884C22semidirect
64. #63879C22semidirect
65. D3×Dic3⋊C4C22semidirect
66. #63861C22semidirect
67. #63851C22semidirect
68. #63846C22semidirect
97. C2×#876D3semidirect
98. C2×C4×D12D3semidirect
265. #876C2×D3semidirect
266. C4×D12C2×D3semidirect
649. C2×C32#539semidirect
782. C32C2×#539semidirect
836. C2×C3#5564semidirect
837. C2×C3#5707semidirect
876. C3C2×#5564semidirect
877. C3C2×#5707semidirect
881. C2#10593914direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640792
C2×C3×#8762
C2×C3×C4×D122
C2×#639052
C2×#638992
C2×#638932
C2×#638912
C2×#638852
C2×#638842
C2×#638792
C2×D3×Dic3⋊C42
C2×#638612
C2×#638512
C2×#638462
#105939142
C2×#57073
C2×#55643