Finite Group Databasebeta

← C2×D3×#879 #11900554

Subgroups — C2×D3×#879 #11900554

Order 1152.

2763 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64088C211yesmaximal, characteristic, complemented
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
3C2×C3×#879C211yesmaximal, characteristic, complemented
4C2×D3×#217C211yesmaximal, characteristic
5C2×D3×#217C211yesmaximal, characteristic
6C2×#63956C211yesmaximal, characteristic, complemented
7C2×#63956C211yesmaximal, characteristic, complemented
8C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
10C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
12C2×#63862C211yesmaximal, characteristic, complemented
13C2×#63861C211yesmaximal, characteristic, complemented
14C2×#63859C211yesmaximal, characteristic, complemented
15C2×#63858C211yesmaximal, characteristic, complemented
16D3×#879C2116yesmaximal, direct product factor
17C2×D3×#126—31nomaximal
18C22×#879—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C2×#3750C2211yescharacteristic, complemented
31C2×#3750C2211yescharacteristic, complemented
32C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
33#64088C2218yescomplemented
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
40C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×C4×Dic3C2211yescharacteristic, complemented
43C3×D3×C22⋊C4C2218yes—
44C3×#879C2218yescomplemented
45D3×#217C2218yes—
46D3×#217C2218yes—
47C2×#3724C2211yescharacteristic, complemented
48C2×#3724C2211yescharacteristic, complemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63956C2218yescomplemented
58#63956C2218yescomplemented
59C2×Dic32C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61D3×C4⋊Dic3C2218yescomplemented
62D3×Dic3⋊C4C2218yescomplemented
63D3×Dic3⋊C4C2218yescomplemented
64C4×D3×Dic3C2218yescomplemented
65#63862C2218yescomplemented
66#63861C2218yescomplemented
67#63859C2218yescomplemented
68#63858C2218yescomplemented
69C2×C3×#126—31no—
70C22×C3×C22⋊C4—31no—
71C22×#217—31no—
72C22×#217—31no—
73C22×C4⋊Dic3—31no—
74C22×Dic3⋊C4—31no—
75C22×Dic3⋊C4—31no—
76C22×C4×Dic3—31no—
77D3×#126—316no—
78C2×#898—31no—
79C2×#898—31no—
80C2×#898—31no—
81C2×D3×C4⋊C4—31no—
82C2×D3×C4⋊C4—31no—
83C2×D3×C4⋊C4—31no—
84C2×D3×C22⋊C4—31no—
85C2×D3×C22⋊C4—31no—
86C2×D3×C22⋊C4D311yescharacteristic
87C2×#879—31no—
88C2×#879—31no—
89C2×#879—31no—
90C2×#879—31no—
91C2×#879—31no—
92C2×#879—31no—
93C2×#879—31no—
94C2×#879—31no—
95C2×#879—31no—
96C2×#879—31no—
97C2×#879—316no—
98C2×#879—61no—
99C2×#879D311yescharacteristic, direct product factor
100C2×#876—31no—
101C2×C42×D3—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3—24no—
104C23×C3×D3—24no—
105C23×C3×D3—24no—
106C23×C3×D3C2314yes—
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
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—24no—
122C2×C3×C4×D3—24no—
123C2×C3×C4×D3C2314yes—
124C2×C3×C4×D3C2314yes—
125C2×D3×Dic3—24no—
126C2×D3×Dic3—24no—
127C2×D3×Dic3—24no—
128C2×D3×Dic3—24no—
129C2×D3×Dic3C2314yes—
130C2×D3×Dic3C2314yes—
131C2×D3×Dic3C2314yes—
132C2×D3×Dic3C2314yes—
133C32×C22⋊C4C2314yes—
134#3757C2314yes—
135#3757C2314yes—
136C4⋊(C3⋊Dic3)C2314yescomplemented
137#3750C2314yescomplemented
138#3750C2314yescomplemented
139C4×C3⋊Dic3C2314yescomplemented
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×#217C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×C4⋊Dic3C2314yescomplemented
146C3×Dic3⋊C4C2314yescomplemented
147C3×Dic3⋊C4C2314yescomplemented
148C3×C4×Dic3C2314yescomplemented
149#3724C2314yescomplemented
150#3724C2314yescomplemented
151Dic3⋊Dic3C2314yescomplemented
152Dic3⋊Dic3C2314yescomplemented
153Dic3⋊Dic3C2314yescomplemented
154Dic3⋊Dic3C2314yescomplemented
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159Dic32C2314yescomplemented
160Dic32C2314yescomplemented
161C22×#126—91noSylow
162C25×C3—31no—
163C24×D3C2×D311yescharacteristic
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C23×Dic3—31no—
167C23×Dic3—31no—
168C23×Dic3—31no—
169C23×Dic3—31no—
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3C2×D311yescharacteristic
175C22×C4×D3C2×D311yescharacteristic
176C3×#126—38no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C22⋊C4—21no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—38no—
187C2×C3×C22⋊C4C2×D311yescharacteristic
188C2×C3×C22⋊C4C2×D311yescharacteristic
189C2×C3×C42—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×#217—31no—
194C2×#217—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—38no—
199C2×#217—38no—
200C2×#217—61no—
201C2×#217—61no—
202C2×#217C2×D311yescharacteristic
203C2×#217C2×D311yescharacteristic
204C2×#217C2×D311yescharacteristic
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×(C2×D3)⋊C4C2×D311yescharacteristic
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—31no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3—38no—
218C2×C4⋊Dic3—61no—
219C2×C4⋊Dic3C2×D311yescharacteristic, complemented
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—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—38no—
233C2×Dic3⋊C4—38no—
234C2×Dic3⋊C4—61no—
235C2×Dic3⋊C4—61no—
236C2×Dic3⋊C4C2×D311yescharacteristic, complemented
237C2×Dic3⋊C4C2×D311yescharacteristic, complemented
238C2×C4×Dic3—31no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3—38no—
245C2×C4×Dic3—61no—
246C2×C4×Dic3C2×D311yescharacteristic, complemented
247#898—38no—
248#898—38no—
249#898—38no—
250D3×C4⋊C4—38no—
251D3×C4⋊C4—38no—
252D3×C4⋊C4—38no—
253D3×C22⋊C4—38no—
254D3×C22⋊C4—38no—
255D3×C22⋊C4C2×D318yes—
256#879—38no—
257#879—38no—
258#879—38no—
259#879—38no—
260#879—38no—
261#879—38no—
262#879—38no—
263#879—38no—
264#879—38no—
265#879—38no—
266#879—68no—
267#879C2×D318yesdirect product factor
268#876—38no—
269C42×D3—38no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2412yes—
274C23×C32C2411yescharacteristic
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—28no—
279C22×C3×D3—28no—
280C22×C3×D3—28no—
281C22×C3×D3—416no—
282C22×C3×D3#4114yes—
283C22×C3×D3#4114yes—
284C22×C3×D3#4114yes—
285C22×C3×D3C2412yes—
286C22×C3×D3C2412yes—
287C2×C32×C4—22no—
288C2×C32×C4—22no—
289C2×C32×C4C2412yes—
290C2×C32×C4C2412yes—
291C2×C3⋊Dic3—22no—
292C2×C3⋊Dic3—22no—
293C2×C3⋊Dic3—22no—
294C2×C3⋊Dic3—22no—
295C2×C3⋊Dic3C2412yes—
296C2×C3⋊Dic3C2412yes—
297C2×C3⋊Dic3C2412yes—
298C2×C3⋊Dic3C2412yes—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C3×C4×D3—28no—
312C3×C4×D3—28no—
313D3×Dic3—28no—
314D3×Dic3—28no—
315D3×Dic3—28no—
316D3×Dic3—28no—
317C2×#126—31no—
318C2×#126—91no—
319C2×#126—91no—
320C2×#126—91no—
321C2×#126—91no—
322C2×#126—91no—
323C2×#126—91no—
324C2×#126—916no—
325C2×#126—91no—
326C22×C4⋊C4—91no—
327C22×C4⋊C4—91no—
328C22×C4⋊C4—91no—
329C22×C22⋊C4—31no—
330C22×C22⋊C4—91no—
331C22×C22⋊C4—91no—
332C22×C42—91no—
333C24×C3—21no—
334C24×C3—31no—
335C24×C3—34no—
336C24×C3—31no—
337C24×C3—64no—
338C24×C3—64no—
339C24×C3—64no—
340C24×C3C22×D311yescharacteristic
341C24×C3C22×D311yescharacteristic
342C23×D3—24no—
343C23×D3—24no—
344C23×D3—24no—
345C23×D3C22×D314yes—
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—34no—
357C22×C3×C4—34no—
358C22×C3×C4—64no—
359C22×C3×C4—64no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—34no—
373C22×Dic3—34no—
374C22×Dic3—34no—
375C22×Dic3—34no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—64no—
381C22×Dic3—64no—
382C22×Dic3—64no—
383C22×Dic3—64no—
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C2×C4×D3—24no—
391C2×C4×D3—24no—
392C2×C4×D3—34no—
393C2×C4×D3—34no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—64no—
397C2×C4×D3—64no—
398C2×C4×D3—64no—
399C2×C4×D3—64no—
400C2×C4×D3C22×D314yes—
401C2×C4×D3C22×D314yes—
402C3×C4⋊C4—34no—
403C3×C4⋊C4—34no—
404C3×C4⋊C4—34no—
405C3×C22⋊C4—24no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4C22×D314yes—
412C3×C22⋊C4C22×D314yes—
413C3×C42—34no—
414#217—34no—
415#217—34no—
416#217—34no—
417#217—34no—
418#217—34no—
419#217—34no—
420#217—34no—
421#217—34no—
422#217—64no—
423#217—64no—
424#217C22×D314yes—
425#217C22×D314yes—
426#217C22×D314yes—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4C22×D314yes—
432(C2×D3)⋊C4C22×D314yes—
433C4⋊Dic3—34no—
434C4⋊Dic3—34no—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3—34no—
439C4⋊Dic3—64no—
440C4⋊Dic3C22×D314yescomplemented
441Dic3⋊C4—34no—
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—64no—
454Dic3⋊C4—64no—
455Dic3⋊C4C22×D314yescomplemented
456Dic3⋊C4C22×D314yescomplemented
457C4×Dic3—34no—
458C4×Dic3—34no—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—64no—
464C4×Dic3C22×D314yescomplemented
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—44no—
469C22×C32C2×#4112yes—
470C22×C32C2×#4112yes—
471C22×C32C2×#4112yes—
472C22×C32C2511yescharacteristic
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—44no—
477C2×C3×D3—416no—
478C2×C3×D3#126116yescomplemented
479C2×C3×D3C2×#4114yes—
480C2×C3×D3C2×#4114yes—
481C2×C3×D3C2×#4114yes—
482C32×C4—22no—
483C32×C4—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—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C25—31no—
495C23×C4—31no—
496C23×C4—31no—
497C23×C4—91no—
498C23×C4—91no—
499C23×C4—91no—
500C23×C4—91no—
501#126—38no—
502#126—98no—
503#126—98no—
504#126—98no—
505#126—98no—
506#126—98no—
507#126—98no—
508#126—98no—
509C2×C4⋊C4—31no—
510C2×C4⋊C4—31no—
511C2×C4⋊C4—31no—
512C2×C4⋊C4—98no—
513C2×C4⋊C4—98no—
514C2×C4⋊C4—98no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4—91no—
518C2×C4⋊C4—91no—
519C2×C4⋊C4—91no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—38no—
530C2×C22⋊C4—98no—
531C2×C22⋊C4—98no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4D3211yescharacteristic
539C2×C42—31no—
540C2×C42—98no—
541C2×C42—91no—
542C2×C42—91no—
543C2×C42—91no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—21no—
552C23×C3—34no—
553C23×C3—34no—
554C23×C3—34no—
555C23×C3—32no—
556C23×C3—32no—
557C23×C3—42no—
558C23×C3—42no—
559C23×C3—42no—
560C23×C3—68no—
561C23×C3—68no—
562C23×C3—68no—
563C23×C3—62no—
564C23×C3—62no—
565C23×C3—62no—
566C23×C3—1216no—
567C23×C3C23×D312yes—
568C23×C3C23×D312yes—
569C23×C3C23×D311yescharacteristic
570C23×C3C23×D311yescharacteristic
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—28no—
575C22×D3—28no—
576C22×D3—28no—
577C22×D3—416no—
578C22×D3#23514yes—
579C22×D3#23714yes—
580C22×D3#23714yes—
581C22×D3C23×D312yes—
582C22×D3C23×D312yes—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—42no—
596C2×C3×C4—42no—
597C2×C3×C4—68no—
598C2×C3×C4—68no—
599C2×C3×C4—62no—
600C2×C3×C4—62no—
601C2×C3×C4—62no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4—62no—
605C2×C3×C4C23×D312yes—
606C2×C3×C4C23×D312yes—
607C2×C3×C4C23×D312yes—
608C2×C3×C4C23×D312yes—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—68no—
628C2×Dic3—68no—
629C2×Dic3—68no—
630C2×Dic3—68no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—62no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—122no—
640C2×Dic3—122no—
641C2×Dic3—122no—
642C2×Dic3—122no—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D312yes—
645C2×Dic3C23×D312yes—
646C2×Dic3C23×D312yes—
647C2×Dic3C23×D312yes—
648C2×Dic3C23×D312yes—
649C4×D3—28no—
650C4×D3—28no—
651C4×D3—68no—
652C4×D3—68no—
653C4×D3—68no—
654C4×D3—68no—
655C2×C32—42no—
656C2×C32C2×#12614yescomplemented
657C2×C32C22×#4111yescharacteristic
658C2×C32C22×#4111yescharacteristic
659C2×C32C22×#4111yescharacteristic
660C3×D3—42no—
661C3×D3C2×#12618yescomplemented
662C24—31no—
663C24—34no—
664C24—31no—
665C24—64no—
666C24—64no—
667C24—64no—
668C24C2×D3211yescharacteristic
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—34no—
676C22×C4—34no—
677C22×C4—64no—
678C22×C4—64no—
679C22×C4—94no—
680C22×C4—94no—
681C22×C4—94no—
682C22×C4—94no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—91no—
687C22×C4—184no—
688C22×C4—184no—
689C22×C4—184no—
690C22×C4—184no—
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3211yescharacteristic
693C4⋊C4—34no—
694C4⋊C4—34no—
695C4⋊C4—34no—
696C4⋊C4—94no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—34no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4C2×D3214yes—
717C42—34no—
718C42—94no—
719C42—94no—
720C42—94no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—316no—
732C22×C3—34no—
733C22×C3—34no—
734C22×C3—34no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—44no—
739C22×C3—44no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—84no—
744C22×C3—1216no—
745C22×C3—124no—
746C22×C3C2×#23512yes—
747C22×C3C2×#23712yes—
748C22×C3C2×#23712yes—
749C22×C3D3×#4112yes—
750C22×C3D3×#4112yes—
751C22×C3D3×#4112yes—
752C22×C3C24×D311yescharacteristic
753C22×C3C24×D311yescharacteristic
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—44no—
758C2×D3—416no—
759C2×D3#879116yesdirect product factor
760C2×D3C2×#23514yes—
761C2×D3C2×#23714yes—
762C2×D3C2×#23714yes—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—42no—
768C3×C4—42no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—62no—
775Dic3—22no—
776Dic3—22no—
777Dic3—22no—
778Dic3—22no—
779Dic3—22no—
780Dic3—22no—
781Dic3—62no—
782Dic3—62no—
783Dic3—62no—
784Dic3—62no—
785Dic3—62no—
786Dic3—62no—
787Dic3—62no—
788Dic3—62no—
789Dic3—122no—
790Dic3—122no—
791Dic3—122no—
792Dic3—122no—
793C32C22×#12611yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—22no—
797C23—34no—
798C23—34no—
799C23—34no—
800C23—32no—
801C23—32no—
802C23—68no—
803C23—68no—
804C23—68no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—1216no—
809C23C22×D3212yes—
810C23C22×D3211yescharacteristic
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—32no—
818C2×C4—32no—
819C2×C4—68no—
820C2×C4—68no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—62no—
827C2×C4—92no—
828C2×C4—92no—
829C2×C4—92no—
830C2×C4—92no—
831C2×C4—188no—
832C2×C4—188no—
833C2×C4—188no—
834C2×C4—188no—
835C2×C4—182no—
836C2×C4—182no—
837C2×C4—182no—
838C2×C4—182no—
839C2×C4C22×D3212yes—
840C2×C4C22×D3212yes—
841C2×C3—24no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—38no—
846C2×C3—42no—
847C2×C3—42no—
848C2×C3—82no—
849C2×C3—122no—
850C2×C3C2×#87914yescomplemented
851C2×C3D3×#12614yescomplemented
852C2×C3C22×#23511yescharacteristic
853C2×C3C22×#23711yescharacteristic
854C2×C3C22×#23711yescharacteristic
855C2×C3C2×D3×#4111yescharacteristic
856C2×C3C2×D3×#4111yescharacteristic
857C2×C3C2×D3×#4111yescharacteristic
858D3—42no—
859D3C2×#87918yesdirect product factor
860C22—22no—
861C22—22no—
862C22—22no—
863C22—316no—
864C22—34no—
865C22—34no—
866C22—34no—
867C22—44no—
868C22—62no—
869C22—62no—
870C22—62no—
871C22—1216no—
872C22—124no—
873C22D3×#23512yes—
874C22D3×#23712yes—
875C22D3×#23712yes—
876C22C23×D3211yescharacteristic
877C4—22no—
878C4—22no—
879C4—62no—
880C4—62no—
881C4—62no—
882C4—62no—
883C4—62no—
884C4—62no—
885C4—182no—
886C4—182no—
887C4—182no—
888C4—182no—
889C3—21no—
890C3C22×#87911yescharacteristic, complemented
891C3C2×D3×#12611yescharacteristic, complemented
892C2—38no—
893C2—42no—
894C2—122no—
895C2D3×#87914yesdirect product factor
896C2C2×D3×#23511yescharacteristic
897C2C2×D3×#23711yescharacteristic
898C2C2×D3×#23711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32C22×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64088C2semidirect
3. C2×C3×#879C2semidirect
6. C2×#63956C2semidirect
7. C2×#63956C2semidirect
8. C2×D3×C4⋊Dic3C2semidirect
9. C2×D3×Dic3⋊C4C2semidirect
10. C2×D3×Dic3⋊C4C2semidirect
11. C2×C4×D3×Dic3C2semidirect
12. C2×#63862C2semidirect
13. C2×#63861C2semidirect
14. C2×#63859C2semidirect
15. C2×#63858C2semidirect
16. D3×#879C2direct (N × H)
29. C2×C4⋊(C3⋊Dic3)C22semidirect
30. C2×#3750C22semidirect
31. C2×#3750C22semidirect
32. C2×C4×C3⋊Dic3C22semidirect
33. #64088C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C2×C3×C4×Dic3C22semidirect
44. C3×#879C22semidirect
47. C2×#3724C22semidirect
48. C2×#3724C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
57. #63956C22semidirect
58. #63956C22semidirect
59. C2×Dic32C22semidirect
60. C2×Dic32C22semidirect
61. D3×C4⋊Dic3C22semidirect
62. D3×Dic3⋊C4C22semidirect
63. D3×Dic3⋊C4C22semidirect
64. C4×D3×Dic3C22semidirect
65. #63862C22semidirect
66. #63861C22semidirect
67. #63859C22semidirect
68. #63858C22semidirect
99. C2×#879D3direct (N × H)
136. C4⋊(C3⋊Dic3)C23semidirect
137. #3750C23semidirect
138. #3750C23semidirect
139. C4×C3⋊Dic3C23semidirect
145. C3×C4⋊Dic3C23semidirect
146. C3×Dic3⋊C4C23semidirect
147. C3×Dic3⋊C4C23semidirect
148. C3×C4×Dic3C23semidirect
149. #3724C23semidirect
150. #3724C23semidirect
151. Dic3⋊Dic3C23semidirect
152. Dic3⋊Dic3C23semidirect
153. Dic3⋊Dic3C23semidirect
154. Dic3⋊Dic3C23semidirect
159. Dic32C23semidirect
160. Dic32C23semidirect
219. C2×C4⋊Dic3C2×D3semidirect
236. C2×Dic3⋊C4C2×D3semidirect
237. C2×Dic3⋊C4C2×D3semidirect
246. C2×C4×Dic3C2×D3semidirect
267. #879C2×D3direct (N × H)
440. C4⋊Dic3C22×D3semidirect
455. Dic3⋊C4C22×D3semidirect
456. Dic3⋊C4C22×D3semidirect
464. C4×Dic3C22×D3semidirect
478. C2×C3×D3#126semidirect
656. C2×C32C2×#126semidirect
661. C3×D3C2×#126semidirect
759. C2×D3#879direct (N × H)
793. C32C22×#126semidirect
850. C2×C3C2×#879semidirect
851. C2×C3D3×#126semidirect
859. D3C2×#879direct (N × H)
890. C3C22×#879semidirect
891. C3C2×D3×#126semidirect
895. C2D3×#879direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640882
C2×C3×D3×C22⋊C42
C2×C3×#8792
C2×D3×#2172
C2×#639562
C2×D3×C4⋊Dic32
C2×D3×Dic3⋊C42
C2×C4×D3×Dic32
C2×#638622
C2×#638612
C2×#638592
C2×#638582
D3×#8792
C2×D3×#1263
C22×#8793