Finite Group Databasebeta

← C2×#10594635 #11901874

Subgroups — C2×#10594635 #11901874

Order 1152.

2753 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64105C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C3×#896C211yesmaximal, characteristic, complemented
4C2×#63921C211yesmaximal, characteristic
5C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
6C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
7C2×#63899C211yesmaximal, characteristic, complemented
8C2×#63896C211yesmaximal, characteristic, complemented
9C2×#63895C211yesmaximal, characteristic, complemented
10C2×#63888C211yesmaximal, characteristic, complemented
11C2×#63887C211yesmaximal, characteristic, complemented
12C2×#63887C211yesmaximal, characteristic, complemented
13C2×#63871C211yesmaximal, characteristic, complemented
14C2×#63857C211yesmaximal, characteristic, complemented
15C2×#63851C211yesmaximal, characteristic, complemented
16#10594635C2116yesmaximal, direct product factor
17C2×#5634—31nomaximal
18C2×#5634—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic, complemented
25C22×C3×Dic6C2211yescharacteristic, complemented
26C22×#627C2211yescharacteristic, complemented
27C22×#624C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C2×C32×C4⋊C4C2211yescharacteristic, complemented
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3750C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35#64105C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C3×#897C2218yescomplemented
45C3×#896C2218yescomplemented
46C2×#3724C2211yescharacteristic, complemented
47C2×Dic3⋊Dic3C2211yescharacteristic, complemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63921C2218yes—
58D3×(C2×D3)⋊C4C2218yes—
59D3×(C2×D3)⋊C4C2218yes—
60#63899C2218yescomplemented
61#63896C2218yescomplemented
62#63895C2218yescomplemented
63#63888C2218yescomplemented
64#63887C2218yescomplemented
65#63887C2218yescomplemented
66#63871C2218yescomplemented
67#63857C2218yescomplemented
68#63851C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×#946—31no—
74C2×#946—31no—
75C22×(C2×D3)⋊C4—31no—
76C22×(C2×D3)⋊C4—31no—
77C2×#924—31no—
78C2×#924—31no—
79#5634—316no—
80#5634—316no—
81C2×#897—31no—
82C2×#897—31no—
83C2×#897—31no—
84C2×#897D311yescharacteristic, complemented
85C2×#896—31no—
86C2×#896—31no—
87C2×#896—31no—
88C2×#896—31no—
89C2×#896—31no—
90C2×#896—31no—
91C2×#896—31no—
92C2×#896—61no—
93C2×#896D311yescharacteristic, complemented
94C2×D3×C22⋊C4—31no—
95C2×D3×C22⋊C4—31no—
96C2×D3×C22⋊C4—31no—
97C2×D3×C22⋊C4—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—31no—
101C2×#878—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×D32—42no—
106C22×D32—42no—
107C22×D32Q818yescomplemented
108C22×D32C2314yes—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4×C3⋊D3—42no—
116C2×C4×C3⋊D3C2314yes—
117C2×#634—42no—
118C2×#634C2314yescomplemented
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×C4×D3—42no—
126C2×C3×C4×D3—42no—
127C2×C3×C4×D3C2314yes—
128C2×C3×C4×D3C2314yes—
129C2×C3×Dic6—42no—
130C2×C3×Dic6—42no—
131C2×C3×Dic6C2314yescomplemented
132C2×C3×Dic6C2314yescomplemented
133C2×#627—42no—
134C2×#627C2314yescomplemented
135C2×#624—42no—
136C2×#624C2314yes—
137C2×D3×Dic3—42no—
138C2×D3×Dic3—42no—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141C32×C4⋊C4C2314yescomplemented
142#3752C2314yes—
143#3752C2314yes—
144#3750C2314yescomplemented
145#3750C2314yescomplemented
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×C4⋊Dic3C2314yescomplemented
151C3×C4⋊Dic3C2314yescomplemented
152C3×Dic3⋊C4C2314yescomplemented
153C3×Dic3⋊C4C2314yescomplemented
154#3724C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156Dic3⋊Dic3C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165C2×#543—91noSylow
166C24×D3—31no—
167C24×D3—31no—
168C22×C3×Q8—31no—
169C22×C3×Q8—31no—
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C23×Dic3—31no—
173C23×Dic3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3—61no—
181C22×C4×D3C2×D311yescharacteristic
182C22×C4×D3C2×D311yescharacteristic
183C22×Dic6—31no—
184C22×Dic6—31no—
185C22×Dic6—31no—
186C22×Dic6—31no—
187C22×Dic6—61no—
188C22×Dic6C2×D311yescharacteristic, complemented
189C22×Dic6C2×D311yescharacteristic, complemented
190C3×C22⋊Q8—38no—
191C3×C22⋊Q8—38no—
192C2×C3×C4⋊C4—21no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
198C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
199C2×C3×C22⋊C4—31no—
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207#946—38no—
208#946—38no—
209#946—38no—
210#946—38no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—38no—
224C2×(C2×D3)⋊C4—38no—
225C2×(C2×D3)⋊C4—61no—
226C2×(C2×D3)⋊C4—61no—
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229C2×(C2×D3)⋊C4C2×D311yescharacteristic
230C2×(C2×D3)⋊C4C2×D311yescharacteristic
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—31no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3C2×D311yescharacteristic, complemented
236C2×C4⋊Dic3C2×D311yescharacteristic, complemented
237#924—38no—
238#924—38no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—61no—
250C2×Dic3⋊C4—61no—
251C2×Dic3⋊C4C2×D311yescharacteristic, complemented
252C2×Dic3⋊C4C2×D311yescharacteristic, complemented
253#897—38no—
254#897—38no—
255#897—38no—
256#897C2×D318yescomplemented
257#896—38no—
258#896—38no—
259#896—38no—
260#896—38no—
261#896—38no—
262#896—38no—
263#896—38no—
264#896—68no—
265#896C2×D318yescomplemented
266D3×C22⋊C4—38no—
267D3×C22⋊C4—38no—
268D3×C22⋊C4—38no—
269D3×C22⋊C4—38no—
270#878—38no—
271#878—38no—
272#878—38no—
273#878—38no—
274C23×C32C2411yescharacteristic
275C22×C3⋊D3—22no—
276C22×C3⋊D3—22no—
277C22×C3⋊D3C2×Q814yes—
278C22×C3⋊D3C2412yes—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3C2×Q814yes—
284C22×C3×D3C2×Q814yes—
285C22×C3×D3C2412yes—
286C22×C3×D3C2412yes—
287C2×D32—416no—
288C2×D32—44no—
289C2×D32—44no—
290C2×D32C2×Q8116yescomplemented
291C2×C32×C4—22no—
292C2×C32×C4—22no—
293C2×C32×C4—22no—
294C2×C32×C4C2412yes—
295C2×C32×C4C2412yes—
296C2×C32×C4C2412yes—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C4×C3⋊D3—44no—
304#634—44no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C3×C4×D3—44no—
318C3×C4×D3—44no—
319C3×Dic6—44no—
320C3×Dic6—44no—
321#627—44no—
322#624—44no—
323D3×Dic3—44no—
324D3×Dic3—44no—
325#543—916no—
326C2×C22⋊Q8—31no—
327C2×C22⋊Q8—31no—
328C2×C22⋊Q8—91no—
329C2×C22⋊Q8—91no—
330C2×C22⋊Q8—91no—
331C2×C22⋊Q8—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×C22⋊Q8—91no—
335C2×C22⋊Q8—91no—
336C2×C22⋊Q8—91no—
337C2×C22⋊Q8—91no—
338C22×C22⋊C4—91no—
339C22×C22⋊C4—91no—
340C22×C22⋊C4—91no—
341C24×C3—31no—
342C24×C3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—38no—
346C23×D3—38no—
347C23×D3—34no—
348C23×D3—34no—
349C23×D3—61no—
350C23×D3—122no—
351C23×D3—122no—
352C23×D3—122no—
353C23×D3—122no—
354C23×D3C22×D311yescharacteristic
355C23×D3C22×D311yescharacteristic
356C2×C3×Q8—34no—
357C2×C3×Q8—34no—
358C2×C3×Q8—122no—
359C2×C3×Q8—122no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—34no—
370C22×C3×C4—34no—
371C22×C3×C4—122no—
372C22×C3×C4—122no—
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—34no—
386C22×Dic3—34no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—122no—
391C22×Dic3—122no—
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C2×C4×D3—34no—
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—34no—
402C2×C4×D3—34no—
403C2×C4×D3—34no—
404C2×C4×D3—42no—
405C2×C4×D3—42no—
406C2×C4×D3—64no—
407C2×C4×D3—122no—
408C2×C4×D3—122no—
409C2×C4×D3—122no—
410C2×C4×D3—122no—
411C2×C4×D3—124no—
412C2×C4×D3—122no—
413C2×C4×D3—122no—
414C2×C4×D3C22×D314yes—
415C2×C4×D3C22×D314yes—
416C2×Dic6—34no—
417C2×Dic6—34no—
418C2×Dic6—34no—
419C2×Dic6—34no—
420C2×Dic6—42no—
421C2×Dic6—42no—
422C2×Dic6—64no—
423C2×Dic6—122no—
424C2×Dic6—122no—
425C2×Dic6—122no—
426C2×Dic6—122no—
427C2×Dic6—124no—
428C2×Dic6C22×D314yescomplemented
429C2×Dic6C22×D314yescomplemented
430C3×C4⋊C4—24no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—34no—
435C3×C4⋊C4C22×D314yescomplemented
436C3×C4⋊C4C22×D314yescomplemented
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4—34no—
440C3×C22⋊C4—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—64no—
458(C2×D3)⋊C4—64no—
459(C2×D3)⋊C4C22×D314yes—
460(C2×D3)⋊C4C22×D314yes—
461(C2×D3)⋊C4C22×D314yes—
462(C2×D3)⋊C4C22×D314yes—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3—34no—
466C4⋊Dic3—34no—
467C4⋊Dic3C22×D314yescomplemented
468C4⋊Dic3C22×D314yescomplemented
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—34no—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4—34no—
479Dic3⋊C4—64no—
480Dic3⋊C4—64no—
481Dic3⋊C4C22×D314yescomplemented
482Dic3⋊C4C22×D314yescomplemented
483C22×C32C22×Q812yes—
484C22×C32H(5,𝔽2)12yes—
485C22×C32H(5,𝔽2)12yes—
486C22×C32C2511yescharacteristic
487C2×C3⋊D3—28no—
488C2×C3⋊D3—22no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3C22×Q814yes—
491C2×C3×D3—28no—
492C2×C3×D3—28no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3C22×Q814yes—
498C2×C3×D3C22×Q814yes—
499D32—416no—
500C32×C4—22no—
501C32×C4—22no—
502C32×C4—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C25—91no—
513C22×Q8—31no—
514C22×Q8—31no—
515C22×Q8—91no—
516C22×Q8—91no—
517C23×C4—31no—
518C23×C4—31no—
519C23×C4—91no—
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523C22⋊Q8—38no—
524C22⋊Q8—38no—
525C22⋊Q8—98no—
526C22⋊Q8—98no—
527C22⋊Q8—98no—
528C22⋊Q8—98no—
529C22⋊Q8—98no—
530C22⋊Q8—98no—
531C22⋊Q8—98no—
532C22⋊Q8—98no—
533C22⋊Q8—98no—
534C22⋊Q8—98no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4D3211yescharacteristic, complemented
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—98no—
552C2×C22⋊C4—98no—
553C2×C22⋊C4—98no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4—91no—
562C23×C3—21no—
563C23×C3—34no—
564C23×C3—34no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—62no—
568C23×C3—62no—
569C23×C3—62no—
570C23×C3—62no—
571C23×C3C23×D311yescharacteristic
572C23×C3C23×D311yescharacteristic
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—34no—
578C22×D3—34no—
579C22×D3—32no—
580C22×D3—32no—
581C22×D3—316no—
582C22×D3—316no—
583C22×D3—64no—
584C22×D3—62no—
585C22×D3—62no—
586C22×D3—62no—
587C22×D3—62no—
588C22×D3—62no—
589C22×D3—122no—
590C22×D3—122no—
591C22×D3—1216no—
592C22×D3—1216no—
593C22×D3—124no—
594C22×D3—124no—
595C22×D3—124no—
596C22×D3—124no—
597C22×D3D3×Q814yes—
598C22×D3D3×Q814yes—
599C22×D3C23×D312yes—
600C22×D3C23×D312yes—
601C3×Q8—124no—
602C3×Q8—124no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—42no—
619C2×C3×C4—42no—
620C2×C3×C4—42no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—124no—
628C2×C3×C4—124no—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631C2×C3×C4C23×D312yes—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D312yes—
634C2×C3×C4C23×D312yes—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—62no—
648C2×Dic3—62no—
649C2×Dic3—62no—
650C2×Dic3—64no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—122no—
658C2×Dic3—122no—
659C2×Dic3—124no—
660C2×Dic3—124no—
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D312yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667C4×D3—44no—
668C4×D3—44no—
669C4×D3—124no—
670C4×D3—124no—
671C4×D3—124no—
672C4×D3—124no—
673C4×D3—128no—
674C4×D3—124no—
675C4×D3—124no—
676Dic6—44no—
677Dic6—44no—
678Dic6—124no—
679Dic6—124no—
680Dic6—124no—
681Dic6—124no—
682Dic6—128no—
683C2×C32#54314yescomplemented
684C2×C32C23×Q811yescharacteristic
685C2×C32C2×H(5,𝔽2)11yescharacteristic
686C2×C32C2×H(5,𝔽2)11yescharacteristic
687C3⋊D3—24no—
688C3×D3—24no—
689C3×D3—24no—
690C24—31no—
691C24—31no—
692C24—94no—
693C24—98no—
694C24—91no—
695C24—362no—
696C24—362no—
697C2×Q8—34no—
698C2×Q8—34no—
699C2×Q8—94no—
700C2×Q8—94no—
701C2×Q8—122no—
702C2×Q8—122no—
703C2×Q8—362no—
704C2×Q8—362no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—34no—
712C22×C4—34no—
713C22×C4—94no—
714C22×C4—94no—
715C22×C4—94no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—94no—
720C22×C4—122no—
721C22×C4—122no—
722C22×C4—362no—
723C22×C4—362no—
724C22×C4—362no—
725C22×C4—362no—
726C22×C4C2×D3211yescharacteristic
727C22×C4C2×D3211yescharacteristic
728C22×C4C2×D3211yescharacteristic
729C4⋊C4—34no—
730C4⋊C4—34no—
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4C2×D3214yescomplemented
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—21no—
757C22×C3—34no—
758C22×C3—34no—
759C22×C3—68no—
760C22×C3—68no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3#100412yes—
766C22×C3#100412yes—
767C22×C3C2×D3×Q812yes—
768C22×C3C2×D3×Q812yes—
769C22×C3#100912yes—
770C22×C3#100912yes—
771C22×C3C24×D311yescharacteristic
772C22×C3C24×D311yescharacteristic
773C2×D3—28no—
774C2×D3—28no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—34no—
780C2×D3—34no—
781C2×D3—64no—
782C2×D3—68no—
783C2×D3—68no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—122no—
789C2×D3—122no—
790C2×D3—128no—
791C2×D3—1216no—
792C2×D3—1216no—
793C2×D3C2×D3×Q814yes—
794C2×D3C2×D3×Q814yes—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—42no—
802C3×C4—42no—
803C3×C4—42no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—62no—
808C3×C4—62no—
809C3×C4—62no—
810Dic3—22no—
811Dic3—22no—
812Dic3—22no—
813Dic3—22no—
814Dic3—22no—
815Dic3—22no—
816Dic3—64no—
817Dic3—62no—
818Dic3—62no—
819Dic3—62no—
820Dic3—62no—
821Dic3—62no—
822Dic3—62no—
823Dic3—122no—
824Dic3—122no—
825C32C2×#54311yescharacteristic, complemented, Sylow
826C23—34no—
827C23—34no—
828C23—32no—
829C23—32no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—916no—
835C23—94no—
836C23—92no—
837C23—182no—
838C23—182no—
839C23—364no—
840C23—364no—
841C23—3616no—
842C23C22×D3211yescharacteristic
843Q8—124no—
844Q8—124no—
845Q8—364no—
846Q8—364no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—92no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4—182no—
868C2×C4—182no—
869C2×C4—182no—
870C2×C4—364no—
871C2×C4—364no—
872C2×C4—364no—
873C2×C4—364no—
874C2×C4C22×D3212yes—
875C2×C4C22×D3212yes—
876C2×C4C22×D3212yes—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—24no—
881C2×C3—64no—
882C2×C3—64no—
883C2×C3#563414yescomplemented
884C2×C3#563414yescomplemented
885C2×C3C2×#100411yescharacteristic
886C2×C3C2×#100411yescharacteristic
887C2×C3C22×D3×Q811yescharacteristic
888C2×C3C22×D3×Q811yescharacteristic
889C2×C3C2×#100911yescharacteristic
890C2×C3C2×#100911yescharacteristic
891D3—24no—
892D3—24no—
893D3—64no—
894D3—64no—
895D3—124no—
896C22—34no—
897C22—34no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—68no—
903C22—68no—
904C22—94no—
905C22—182no—
906C22—182no—
907C22—188no—
908C22—3616no—
909C22#6430712yes—
910C22#6431412yes—
911C22D32×Q812yes—
912C22C23×D3211yescharacteristic
913C4—22no—
914C4—22no—
915C4—22no—
916C4—62no—
917C4—62no—
918C4—62no—
919C4—62no—
920C4—62no—
921C4—62no—
922C4—182no—
923C4—182no—
924C4—182no—
925C3—21no—
926C3C2×#563411yescharacteristic, complemented
927C3C2×#563411yescharacteristic, complemented
928C2—64no—
929C2—64no—
930C2—184no—
931C2#1059463514yesdirect product factor
932C2C2×#6430711yescharacteristic
933C2C2×#6431411yescharacteristic
934C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×D32C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#543
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×#897C2semidirect
3. C2×C3×#896C2semidirect
7. C2×#63899C2semidirect
8. C2×#63896C2semidirect
9. C2×#63895C2semidirect
10. C2×#63888C2semidirect
11. C2×#63887C2semidirect
12. C2×#63887C2semidirect
13. C2×#63871C2semidirect
14. C2×#63857C2semidirect
15. C2×#63851C2semidirect
16. #10594635C2direct (N × H)
21. C22×#634C22semidirect
24. C22×C3×Dic6C22semidirect
25. C22×C3×Dic6C22semidirect
26. C22×#627C22semidirect
30. C2×C32×C4⋊C4C22semidirect
33. C2×#3750C22semidirect
34. C2×#3750C22semidirect
35. #64105C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
41. C2×C3×C4⋊Dic3C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C3×#897C22semidirect
45. C3×#896C22semidirect
46. C2×#3724C22semidirect
47. C2×Dic3⋊Dic3C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
60. #63899C22semidirect
61. #63896C22semidirect
62. #63895C22semidirect
63. #63888C22semidirect
64. #63887C22semidirect
65. #63887C22semidirect
66. #63871C22semidirect
67. #63857C22semidirect
68. #63851C22semidirect
84. C2×#897D3semidirect
93. C2×#896D3semidirect
107. C22×D32Q8semidirect
118. C2×#634C23semidirect
131. C2×C3×Dic6C23semidirect
132. C2×C3×Dic6C23semidirect
134. C2×#627C23semidirect
141. C32×C4⋊C4C23semidirect
144. #3750C23semidirect
145. #3750C23semidirect
150. C3×C4⋊Dic3C23semidirect
151. C3×C4⋊Dic3C23semidirect
152. C3×Dic3⋊C4C23semidirect
153. C3×Dic3⋊C4C23semidirect
154. #3724C23semidirect
155. Dic3⋊Dic3C23semidirect
156. Dic3⋊Dic3C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
188. C22×Dic6C2×D3semidirect
189. C22×Dic6C2×D3semidirect
197. C2×C3×C4⋊C4C2×D3semidirect
198. C2×C3×C4⋊C4C2×D3semidirect
235. C2×C4⋊Dic3C2×D3semidirect
236. C2×C4⋊Dic3C2×D3semidirect
251. C2×Dic3⋊C4C2×D3semidirect
252. C2×Dic3⋊C4C2×D3semidirect
256. #897C2×D3semidirect
265. #896C2×D3semidirect
290. C2×D32C2×Q8semidirect
428. C2×Dic6C22×D3semidirect
429. C2×Dic6C22×D3semidirect
435. C3×C4⋊C4C22×D3semidirect
436. C3×C4⋊C4C22×D3semidirect
467. C4⋊Dic3C22×D3semidirect
468. C4⋊Dic3C22×D3semidirect
481. Dic3⋊C4C22×D3semidirect
482. Dic3⋊C4C22×D3semidirect
546. C2×C4⋊C4D32semidirect
683. C2×C32#543semidirect
740. C4⋊C4C2×D32semidirect
825. C32C2×#543semidirect
883. C2×C3#5634semidirect
884. C2×C3#5634semidirect
926. C3C2×#5634semidirect
927. C3C2×#5634semidirect
931. C2#10594635direct (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×#8972
C2×C3×#8962
C2×#639212
C2×D3×(C2×D3)⋊C42
C2×#638992
C2×#638962
C2×#638952
C2×#638882
C2×#638872
C2×#638712
C2×#638572
C2×#638512
#105946352
C2×#56343