Finite Group Databasebeta

← C2×#10594535 #11903285

Subgroups — C2×#10594535 #11903285

Order 1152.

2513 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64098C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C3×#896C211yesmaximal, characteristic, complemented
4C2×#63902C211yesmaximal, characteristic
5C2×#63899C211yesmaximal, characteristic, complemented
6C2×#63893C211yesmaximal, characteristic, complemented
7C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63887C211yesmaximal, characteristic, complemented
9C2×#63887C211yesmaximal, characteristic, complemented
10C2×#63879C211yesmaximal, characteristic
11C2×#63879C211yesmaximal, characteristic
12C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13C2×#63847C211yesmaximal, characteristic, complemented
14C2×#63843C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10594535C2116yesmaximal, direct product factor
17C2×#5636—31nomaximal
18C2×#5635—31nomaximal
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36#64098C2218yescomplemented
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×C4⋊Dic3C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C3×#897C2218yescomplemented
46C3×#896C2218yescomplemented
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63902C2218yes—
58#63899C2218yescomplemented
59#63893C2218yescomplemented
60D3×C4⋊Dic3C2218yescomplemented
61#63887C2218yescomplemented
62#63887C2218yescomplemented
63#63879C2218yes—
64#63879C2218yes—
65D3×Dic3⋊C4C2218yescomplemented
66#63847C2218yescomplemented
67#63843C2218yescomplemented
68#63839C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×Q8×Dic3—31no—
74C2×#944—31no—
75C2×C4×#67—31no—
76C2×C4×#67—31no—
77C22×C4⋊Dic3—31no—
78C22×Dic3⋊C4—31no—
79#5636—316no—
80#5635—316no—
81C2×#897—31no—
82C2×#897D311yescharacteristic, complemented
83C2×#896—31no—
84C2×#896D311yescharacteristic, complemented
85C2×D3×C4⋊C4—31no—
86C2×D3×C4⋊C4—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#889—31no—
91C2×#889—61no—
92C2×#888—31no—
93C2×#887—31no—
94C2×#67⋊C4—31no—
95C2×#67⋊C4—31no—
96C2×#67⋊C4—31no—
97C2×#67⋊C4—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—31no—
101C2×#878—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
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×C4×D3—24no—
118C2×C3×C4×D3—42no—
119C2×C3×C4×D3C2314yes—
120C2×C3×C4×D3C2314yes—
121C2×C3×Dic6—24no—
122C2×C3×Dic6—42no—
123C2×C3×Dic6C2314yes—
124C2×C3×Dic6C2314yes—
125C2×#627—42no—
126C2×#627C2314yes—
127C2×#625Q818yescomplemented
128C2×#625C2314yes—
129C2×D3×Dic3—24no—
130C2×D3×Dic3—42no—
131C2×D3×Dic3—42no—
132C2×D3×Dic3—42no—
133C2×D3×Dic3C2314yes—
134C2×D3×Dic3C2314yes—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2314yes—
137C32×C4⋊C4C2314yes—
138C4⋊(C3⋊Dic3)C2314yes—
139#3750C2314yes—
140#3750C2314yes—
141#3750C2314yes—
142#3750C2314yes—
143C4×C3⋊Dic3C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×C4⋊Dic3C2314yes—
149C3×C4⋊Dic3C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152#3724C2314yes—
153#3724C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160Dic32C2314yes—
161Dic32C2314yes—
162C2×#554—91noSylow
163C22×C3×Q8—31no—
164C22×C3×Q8—31no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C22×#67—31no—
168C22×#67—31no—
169C23×Dic3—31no—
170C23×Dic3—31no—
171C23×Dic3—31no—
172C23×Dic3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3C2×D311yescharacteristic
178C22×C4×D3C2×D311yescharacteristic
179C22×Dic6—31no—
180C22×Dic6—31no—
181C22×Dic6C2×D311yescharacteristic
182C22×Dic6C2×D311yescharacteristic
183C3×C22⋊Q8—38no—
184C3×C22⋊Q8—38no—
185C2×C3×C4⋊C4—21no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C4⋊C4C2×D311yescharacteristic
191C2×C3×C4⋊C4C2×D311yescharacteristic
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×#217—31no—
197C2×#217—31no—
198#946—38no—
199#946—38no—
200Q8×Dic3—38no—
201#944—38no—
202C4×#67—38no—
203C4×#67—38no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—31no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—38no—
217C2×C4⋊Dic3—61no—
218C2×C4⋊Dic3C2×D311yescharacteristic
219C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—38no—
237C2×Dic3⋊C4—61no—
238C2×Dic3⋊C4—61no—
239C2×Dic3⋊C4—61no—
240C2×Dic3⋊C4—61no—
241C2×Dic3⋊C4C2×D311yescharacteristic
242C2×Dic3⋊C4C2×D311yescharacteristic
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—61no—
250#897—38no—
251#897C2×D318yescomplemented
252#896—38no—
253#896C2×D318yescomplemented
254D3×C4⋊C4—38no—
255D3×C4⋊C4—38no—
256#889—38no—
257#889—38no—
258#889—38no—
259#889—38no—
260#889—68no—
261#888—38no—
262#887—38no—
263#67⋊C4—38no—
264#67⋊C4—38no—
265#67⋊C4—38no—
266#67⋊C4—38no—
267#878—38no—
268#878—38no—
269#878—38no—
270#878—38no—
271C23×C32C2411yescharacteristic
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3—22no—
276C22×C3×D3C2×Q814yes—
277C22×C3×D3C2×Q814yes—
278C22×C3×D3C2412yes—
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⋊Dic3C2×Q814yes—
290C2×C3⋊Dic3C2412yes—
291C2×C3⋊Dic3C2412yes—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3#4114yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C3×C4×D3—28no—
307C3×C4×D3—44no—
308C3×Dic6—28no—
309C3×Dic6—44no—
310#627—44no—
311#625C2×Q8116yescomplemented
312D3×Dic3—28no—
313D3×Dic3—44no—
314D3×Dic3—44no—
315D3×Dic3—44no—
316#554—916no—
317C2×C4⋊Q8—91no—
318C2×#125—91no—
319C2×#125—91no—
320C2×C22⋊Q8—31no—
321C2×C22⋊Q8—31no—
322C2×C22⋊Q8—91no—
323C2×C22⋊Q8—91no—
324C2×C22⋊Q8—91no—
325C2×C22⋊Q8—91no—
326C2×C4×Q8—91no—
327C2×C4×D4—91no—
328C2×C4×D4—91no—
329C2×C4×D4—91no—
330C22×C4⋊C4—91no—
331C22×C4⋊C4—91no—
332C24×C3—31no—
333C24×C3—31no—
334C23×D3C22×D311yescharacteristic
335C23×D3C22×D311yescharacteristic
336C2×C3×Q8—34no—
337C2×C3×Q8—34no—
338C2×C3×Q8—64no—
339C2×C3×Q8—122no—
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—31no—
349C22×C3×C4—34no—
350C22×C3×C4—34no—
351C22×C3×C4—64no—
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—38no—
361C2×#67—34no—
362C2×#67—34no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—34no—
372C22×Dic3—34no—
373C22×Dic3—34no—
374C22×Dic3—34no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—64no—
380C22×Dic3—122no—
381C22×Dic3—122no—
382C22×Dic3—122no—
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C2×C4×D3—24no—
390C2×C4×D3—34no—
391C2×C4×D3—34no—
392C2×C4×D3—34no—
393C2×C4×D3—34no—
394C2×C4×D3—42no—
395C2×C4×D3—64no—
396C2×C4×D3—122no—
397C2×C4×D3—122no—
398C2×C4×D3—122no—
399C2×C4×D3C22×D314yes—
400C2×C4×D3C22×D314yes—
401C2×Dic6—24no—
402C2×Dic6—34no—
403C2×Dic6—34no—
404C2×Dic6—42no—
405C2×Dic6—122no—
406C2×Dic6—122no—
407C2×Dic6C22×D314yes—
408C2×Dic6C22×D314yes—
409C3×C4⋊C4—24no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4C22×D314yes—
415C3×C4⋊C4C22×D314yes—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420#217—34no—
421#217—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4C22×D314yes—
425(C2×D3)⋊C4C22×D314yes—
426(C2×D3)⋊C4C22×D314yes—
427(C2×D3)⋊C4C22×D314yes—
428C4⋊Dic3—34no—
429C4⋊Dic3—34no—
430C4⋊Dic3—34no—
431C4⋊Dic3—34no—
432C4⋊Dic3—34no—
433C4⋊Dic3—34no—
434C4⋊Dic3—64no—
435C4⋊Dic3C22×D314yes—
436C4⋊Dic3C22×D314yes—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
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⋊C4—64no—
456Dic3⋊C4—64no—
457Dic3⋊C4C22×D314yes—
458Dic3⋊C4C22×D314yes—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—64no—
466C22×C32C22×Q812yes—
467C22×C32C2×#4112yes—
468C22×C32H(5,𝔽2)12yes—
469C22×C32C2511yescharacteristic
470C2×C3×D3—28no—
471C2×C3×D3—28no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3C22×Q814yes—
477C2×C3×D3C22×Q814yes—
478C32×C4—22no—
479C32×C4—22no—
480C32×C4—22no—
481C3⋊Dic3—22no—
482C3⋊Dic3—22no—
483C3⋊Dic3—22no—
484C3⋊Dic3C22×Q814yes—
485C3×Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3C2×#4114yes—
491C22×Q8—31no—
492C22×Q8—31no—
493C22×Q8—91no—
494C22×D4—91no—
495C23×C4—31no—
496C23×C4—31no—
497C23×C4—91no—
498C23×C4—91no—
499C23×C4—91no—
500C23×C4—91no—
501C4⋊Q8—98no—
502#125—98no—
503#125—98no—
504C22⋊Q8—38no—
505C22⋊Q8—38no—
506C22⋊Q8—98no—
507C22⋊Q8—98no—
508C22⋊Q8—98no—
509C22⋊Q8—98no—
510C4×Q8—98no—
511C4×D4—98no—
512C4×D4—98no—
513C4×D4—98no—
514C2×C4⋊C4—31no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—98no—
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×C4⋊C4—91no—
531C2×C4⋊C4D3211yescharacteristic
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C42—91no—
539C2×C42—91no—
540C2×C42—91no—
541C23×C3—21no—
542C23×C3—34no—
543C23×C3—34no—
544C23×C3—32no—
545C23×C3—32no—
546C23×C3—62no—
547C23×C3—62no—
548C23×C3—62no—
549C23×C3—62no—
550C23×C3C23×D311yescharacteristic
551C23×C3C23×D311yescharacteristic
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3D3×Q814yes—
557C22×D3D3×Q814yes—
558C22×D3C23×D312yes—
559C22×D3C23×D312yes—
560C3×Q8—68no—
561C3×Q8—124no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—34no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—42no—
579C2×C3×C4—42no—
580C2×C3×C4—42no—
581C2×C3×C4—68no—
582C2×C3×C4—62no—
583C2×C3×C4—62no—
584C2×C3×C4—62no—
585C2×C3×C4—62no—
586C2×C3×C4—62no—
587C2×C3×C4—124no—
588C2×C3×C4C23×D312yes—
589C2×C3×C4C23×D312yes—
590C2×C3×C4C23×D312yes—
591C2×C3×C4C23×D312yes—
592C2×C3×C4C23×D312yes—
593C2×C3×C4C23×D312yes—
594#67—316no—
595#67—316no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—34no—
602C2×Dic3—34no—
603C2×Dic3—32no—
604C2×Dic3—32no—
605C2×Dic3—32no—
606C2×Dic3—32no—
607C2×Dic3—32no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—64no—
612C2×Dic3—62no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3—62no—
616C2×Dic3—62no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—68no—
623C2×Dic3—122no—
624C2×Dic3—122no—
625C2×Dic3—122no—
626C2×Dic3—124no—
627C2×Dic3—124no—
628C2×Dic3—124no—
629C2×Dic3#23714yes—
630C2×Dic3C23×D312yes—
631C2×Dic3C23×D312yes—
632C2×Dic3C23×D312yes—
633C2×Dic3C23×D312yes—
634C2×Dic3C23×D312yes—
635C2×Dic3C23×D312yes—
636C4×D3—28no—
637C4×D3—44no—
638C4×D3—68no—
639C4×D3—124no—
640C4×D3—124no—
641C4×D3—124no—
642Dic6—28no—
643Dic6—44no—
644Dic6—124no—
645Dic6—124no—
646C2×C32#55414yescomplemented
647C2×C32C23×Q811yescharacteristic
648C2×C32C22×#4111yescharacteristic
649C2×C32C2×H(5,𝔽2)11yescharacteristic
650C3×D3—24no—
651C3×D3—24no—
652C24—31no—
653C24—31no—
654C2×Q8—34no—
655C2×Q8—34no—
656C2×Q8—64no—
657C2×Q8—94no—
658C2×Q8—122no—
659C2×Q8—362no—
660C2×D4—94no—
661C2×D4—98no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—34no—
669C22×C4—34no—
670C22×C4—64no—
671C22×C4—94no—
672C22×C4—94no—
673C22×C4—94no—
674C22×C4—94no—
675C22×C4—91no—
676C22×C4—91no—
677C22×C4—91no—
678C22×C4—91no—
679C22×C4—122no—
680C22×C4—184no—
681C22×C4—362no—
682C22×C4—362no—
683C22×C4—362no—
684C22×C4C2×D3211yescharacteristic
685C22×C4C2×D3211yescharacteristic
686C22×C4C2×D3211yescharacteristic
687C4⋊C4—34no—
688C4⋊C4—34no—
689C4⋊C4—34no—
690C4⋊C4—34no—
691C4⋊C4—94no—
692C4⋊C4—94no—
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⋊C4C2×D3214yes—
703C22⋊C4—34no—
704C22⋊C4—34no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—94no—
708C22⋊C4—94no—
709C42—94no—
710C42—94no—
711C42—94no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—21no—
716C22×C3—34no—
717C22×C3—34no—
718C22×C3—68no—
719C22×C3—68no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3C2×#23712yes—
725C22×C3#100412yes—
726C22×C3C2×D3×Q812yes—
727C22×C3C2×D3×Q812yes—
728C22×C3D3×#4112yes—
729C22×C3#100912yes—
730C22×C3C24×D311yescharacteristic
731C22×C3C24×D311yescharacteristic
732C2×D3—28no—
733C2×D3—28no—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—22no—
738C2×D3C2×D3×Q814yes—
739C2×D3C2×D3×Q814yes—
740C3×C4—22no—
741C3×C4—22no—
742C3×C4—22no—
743C3×C4—22no—
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—34no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—62no—
751C3×C4—62no—
752C3×C4—62no—
753C3×C4—62no—
754C3×C4—62no—
755Dic3—22no—
756Dic3—22no—
757Dic3—22no—
758Dic3—22no—
759Dic3—22no—
760Dic3—34no—
761Dic3—34no—
762Dic3—64no—
763Dic3—62no—
764Dic3—62no—
765Dic3—62no—
766Dic3—62no—
767Dic3—62no—
768Dic3—62no—
769Dic3—122no—
770Dic3—122no—
771Dic3—122no—
772Dic3C2×#23714yes—
773C32C2×#55411yescharacteristic, complemented, Sylow
774C23—34no—
775C23—34no—
776C23—32no—
777C23—32no—
778C23—62no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23C22×D3211yescharacteristic
783Q8—68no—
784Q8—124no—
785Q8—364no—
786D4—916no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—34no—
791C2×C4—32no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—32no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—68no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—94no—
804C2×C4—92no—
805C2×C4—92no—
806C2×C4—92no—
807C2×C4—92no—
808C2×C4—124no—
809C2×C4—188no—
810C2×C4—182no—
811C2×C4—182no—
812C2×C4—182no—
813C2×C4—364no—
814C2×C4—364no—
815C2×C4—364no—
816C2×C4C22×D3212yes—
817C2×C4C22×D3212yes—
818C2×C4C22×D3212yes—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—24no—
823C2×C3—64no—
824C2×C3—64no—
825C2×C3#563514yescomplemented
826C2×C3#563614yescomplemented
827C2×C3C22×#23711yescharacteristic
828C2×C3C2×#100411yescharacteristic
829C2×C3C22×D3×Q811yescharacteristic
830C2×C3C22×D3×Q811yescharacteristic
831C2×C3C2×D3×#4111yescharacteristic
832C2×C3C2×#100911yescharacteristic
833D3—24no—
834D3—24no—
835C22—34no—
836C22—34no—
837C22—62no—
838C22—62no—
839C22—62no—
840C22—62no—
841C22—68no—
842C22—68no—
843C22#6430712yes—
844C22D3×#23712yes—
845C22D32×Q812yes—
846C22C23×D3211yescharacteristic
847C4—22no—
848C4—22no—
849C4—22no—
850C4—34no—
851C4—62no—
852C4—62no—
853C4—62no—
854C4—62no—
855C4—62no—
856C4—94no—
857C4—182no—
858C4—182no—
859C4—182no—
860C3—21no—
861C3C2×#563511yescharacteristic, complemented
862C3C2×#563611yescharacteristic, complemented
863C2—64no—
864C2—64no—
865C2#1059453514yesdirect product factor
866C2C2×#6430711yescharacteristic
867C2C2×D3×#23711yescharacteristic
868C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#625C22
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×#64098C2semidirect
2. C2×C3×#897C2semidirect
3. C2×C3×#896C2semidirect
5. C2×#63899C2semidirect
6. C2×#63893C2semidirect
7. C2×D3×C4⋊Dic3C2semidirect
8. C2×#63887C2semidirect
9. C2×#63887C2semidirect
12. C2×D3×Dic3⋊C4C2semidirect
13. C2×#63847C2semidirect
14. C2×#63843C2semidirect
15. C2×#63839C2semidirect
16. #10594535C2direct (N × H)
36. #64098C22semidirect
45. C3×#897C22semidirect
46. C3×#896C22semidirect
58. #63899C22semidirect
59. #63893C22semidirect
60. D3×C4⋊Dic3C22semidirect
61. #63887C22semidirect
62. #63887C22semidirect
65. D3×Dic3⋊C4C22semidirect
66. #63847C22semidirect
67. #63843C22semidirect
68. #63839C22semidirect
82. C2×#897D3semidirect
84. C2×#896D3semidirect
127. C2×#625Q8semidirect
251. #897C2×D3semidirect
253. #896C2×D3semidirect
311. #625C2×Q8semidirect
646. C2×C32#554semidirect
773. C32C2×#554semidirect
825. C2×C3#5635semidirect
826. C2×C3#5636semidirect
861. C3C2×#5635semidirect
862. C3C2×#5636semidirect
865. C2#10594535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640982
C2×C3×#8972
C2×C3×#8962
C2×#639022
C2×#638992
C2×#638932
C2×D3×C4⋊Dic32
C2×#638872
C2×#638792
C2×D3×Dic3⋊C42
C2×#638472
C2×#638432
C2×#638392
#105945352
C2×#56363
C2×#56353