Finite Group Databasebeta

← C2×#10594170 #11901869

Subgroups — C2×#10594170 #11901869

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×#64087C211yesmaximal, characteristic, complemented
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
3C2×C3×#878C211yesmaximal, characteristic, complemented
4C2×#63982C211yesmaximal, characteristic, complemented
5C2×D3×#217C211yesmaximal, characteristic
6C2×#63964C211yesmaximal, characteristic, complemented
7C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
8C2×#63899C211yesmaximal, characteristic, complemented
9C2×#63896C211yesmaximal, characteristic, complemented
10C2×#63893C211yesmaximal, characteristic, complemented
11C2×#63887C211yesmaximal, characteristic, complemented
12C2×#63857C211yesmaximal, characteristic, complemented
13C2×#63856C211yesmaximal, characteristic, complemented
14C2×#63851C211yesmaximal, characteristic, complemented
15C2×#63851C211yesmaximal, characteristic, complemented
16#10594170C2116yesmaximal, direct product factor
17C2×#5634—31nomaximal
18C2×#5483—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic, complemented
26C22×#627C2211yescharacteristic, complemented
27C22×#627C2211yescharacteristic, complemented
28C22×D3×Dic3C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C2×#3750C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35#64087C2218yescomplemented
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C3×D3×C22⋊C4C2218yes—
44C3×#878C2218yescomplemented
45#63982C2218yescomplemented
46D3×#217C2218yes—
47C2×#3724C2211yescharacteristic, complemented
48C2×#3724C2211yescharacteristic, complemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53#63964C2218yescomplemented
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2218yes—
61#63899C2218yescomplemented
62#63896C2218yescomplemented
63#63893C2218yescomplemented
64#63887C2218yescomplemented
65#63857C2218yescomplemented
66#63856C2218yescomplemented
67#63851C2218yescomplemented
68#63851C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C22×C3×C22⋊C4—31no—
71C22×#217—31no—
72C22×#217—31no—
73C2×#946—31no—
74C2×#946—31no—
75C22×(C2×D3)⋊C4—31no—
76C2×#924—31no—
77C2×#924—31no—
78C2×#924—31no—
79C2×#924—31no—
80C2×#924—31no—
81#5634—316no—
82C2×#897—31no—
83C2×#897—31no—
84C2×#896—31no—
85C2×#896—31no—
86C2×#896—31no—
87C2×#896—31no—
88C2×D3×C22⋊C4—31no—
89C2×D3×C22⋊C4D311yescharacteristic
90#5483—316no—
91C2×#878—31no—
92C2×#878—31no—
93C2×#878—31no—
94C2×#878—31no—
95C2×#878—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—61no—
101C2×#878D311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C23×C3×D3—42no—
104C23×C3×D3—42no—
105C23×C3×D3Q818yescomplemented
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2314yes—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C3⋊Dic3—42no—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2314yes—
117C2×#634—42no—
118C2×#634C2314yescomplemented
119C22×C3×Dic3—42no—
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2314yes—
127C2×C3×C4×D3—42no—
128C2×C3×C4×D3—42no—
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2314yes—
131C2×C3×Dic6—42no—
132C2×C3×Dic6C2314yescomplemented
133C2×#627—42no—
134C2×#627—42no—
135C2×#627C2314yescomplemented
136C2×#627C2314yescomplemented
137C2×D3×Dic3—42no—
138C2×D3×Dic3—42no—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141C32×C22⋊C4C2314yes—
142#3757C2314yes—
143C4⋊(C3⋊Dic3)C2314yescomplemented
144#3750C2314yescomplemented
145#3750C2314yescomplemented
146C3×#217C2314yes—
147C3×#217C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×C4⋊Dic3C2314yescomplemented
151C3×Dic3⋊C4C2314yescomplemented
152C3×Dic3⋊C4C2314yescomplemented
153#3724C2314yescomplemented
154#3724C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156Dic3⋊Dic3C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165C2×#543—91noSylow
166C25×C3—31no—
167C24×D3C2×D311yescharacteristic
168C22×C3×Q8—31no—
169C23×C3×C4—31no—
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C23×Dic3—31no—
173C23×Dic3—31no—
174C23×Dic3—31no—
175C23×Dic3—31no—
176C23×Dic3—61no—
177C23×Dic3C2×D311yescharacteristic
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3C2×D311yescharacteristic
181C22×C4×D3C2×D311yescharacteristic
182C22×Dic6—31no—
183C22×Dic6—31no—
184C22×Dic6—31no—
185C22×Dic6—31no—
186C22×Dic6—31no—
187C22×Dic6—31no—
188C22×Dic6—61no—
189C22×Dic6C2×D311yescharacteristic, complemented
190C3×C22⋊Q8—38no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C22⋊C4—21no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—38no—
200C2×C3×C22⋊C4C2×D311yescharacteristic
201C2×C3×C22⋊C4C2×D311yescharacteristic
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—38no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—38no—
212C2×#217—61no—
213C2×#217C2×D311yescharacteristic
214C2×#217C2×D311yescharacteristic
215#946—38no—
216#946—38no—
217C2×(C2×D3)⋊C4—38no—
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—31no—
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×(C2×D3)⋊C4C2×D311yescharacteristic
226C2×C4⋊Dic3—31no—
227C2×C4⋊Dic3—31no—
228C2×C4⋊Dic3—31no—
229C2×C4⋊Dic3—31no—
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—61no—
233C2×C4⋊Dic3C2×D311yescharacteristic, complemented
234#924—38no—
235#924—38no—
236#924—38no—
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—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—61no—
252C2×Dic3⋊C4—61no—
253C2×Dic3⋊C4C2×D311yescharacteristic, complemented
254C2×Dic3⋊C4C2×D311yescharacteristic, complemented
255#897—38no—
256#897—38no—
257#896—38no—
258#896—38no—
259#896—38no—
260#896—38no—
261D3×C22⋊C4—38no—
262D3×C22⋊C4C2×D318yes—
263#878—38no—
264#878—38no—
265#878—38no—
266#878—38no—
267#878—38no—
268#878—38no—
269#878—38no—
270#878—38no—
271#878—38no—
272#878—68no—
273#878C2×D318yescomplemented
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2×Q814yes—
277C23×C32C2412yes—
278C23×C32C2411yescharacteristic
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—416no—
284C22×C3×D3—44no—
285C22×C3×D3—44no—
286C22×C3×D3C2×Q814yes—
287C22×C3×D3C2×Q814yes—
288C22×C3×D3C2×Q8116yescomplemented
289C22×C3×D3C2412yes—
290C22×C3×D3C2412yes—
291C2×C32×C4—22no—
292C2×C32×C4—22no—
293C2×C32×C4C2412yes—
294C2×C32×C4C2412yes—
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—44no—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2412yes—
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×Dic3—44no—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C3×C4×D3—44no—
319C3×C4×D3—44no—
320C3×Dic6—44no—
321#627—44no—
322#627—44no—
323D3×Dic3—44no—
324D3×Dic3—44no—
325#543—916no—
326C2×C22⋊Q8—31no—
327C2×C22⋊Q8—91no—
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—31no—
339C22×C22⋊C4—91no—
340C22×C22⋊C4—91no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3—31no—
344C24×C3—38no—
345C24×C3—34no—
346C24×C3—122no—
347C24×C3—122no—
348C24×C3C22×D311yescharacteristic
349C24×C3C22×D311yescharacteristic
350C23×D3—42no—
351C23×D3—42no—
352C23×D3Dic618yescomplemented
353C23×D3C22×D311yescharacteristic
354C23×D3C22×D311yescharacteristic
355C23×D3C22×D314yes—
356C2×C3×Q8—34no—
357C2×C3×Q8—122no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—34no—
367C22×C3×C4—34no—
368C22×C3×C4—34no—
369C22×C3×C4—122no—
370C22×C3×C4—122no—
371C22×C3×C4—122no—
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—34no—
385C22×Dic3—34no—
386C22×Dic3—34no—
387C22×Dic3—34no—
388C22×Dic3—42no—
389C22×Dic3—61no—
390C22×Dic3—64no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—122no—
395C22×Dic3—122no—
396C22×Dic3—122no—
397C22×Dic3—122no—
398C22×Dic3—124no—
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D314yes—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—42no—
409C2×C4×D3—42no—
410C2×C4×D3—122no—
411C2×C4×D3—122no—
412C2×C4×D3C22×D314yes—
413C2×C4×D3C22×D314yes—
414C2×Dic6—34no—
415C2×Dic6—34no—
416C2×Dic6—34no—
417C2×Dic6—34no—
418C2×Dic6—34no—
419C2×Dic6—34no—
420C2×Dic6—42no—
421C2×Dic6—64no—
422C2×Dic6—122no—
423C2×Dic6—122no—
424C2×Dic6—122no—
425C2×Dic6—122no—
426C2×Dic6—122no—
427C2×Dic6—122no—
428C2×Dic6—124no—
429C2×Dic6C22×D314yescomplemented
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C22⋊C4—24no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4C22×D314yes—
439C3×C22⋊C4C22×D314yes—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217—34no—
445#217—34no—
446#217—34no—
447#217—34no—
448#217—64no—
449#217C22×D314yes—
450#217C22×D314yes—
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)⋊C4C22×D314yes—
458(C2×D3)⋊C4C22×D314yes—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3—64no—
466C4⋊Dic3C22×D314yescomplemented
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
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×C32—28no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32C22×Q814yes—
487C22×C32C22×Q812yes—
488C22×C32H(5,𝔽2)12yes—
489C22×C32H(5,𝔽2)12yes—
490C22×C32C2511yescharacteristic
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×D3—416no—
498C2×C3×D3C22×Q814yes—
499C2×C3×D3C22×Q814yes—
500C32×C4—22no—
501C32×C4—22no—
502C3⋊Dic3—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—31no—
513C22×Q8—31no—
514C22×Q8—91no—
515C22×Q8—91no—
516C22×Q8—91no—
517C23×C4—31no—
518C23×C4—31no—
519C23×C4—31no—
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523C22⋊Q8—38no—
524C22⋊Q8—98no—
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—91no—
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⋊C4—91no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—38no—
552C2×C22⋊C4—98no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—98no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4D3211yescharacteristic
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—21no—
568C23×C3—24no—
569C23×C3—34no—
570C23×C3—34no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—316no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3—62no—
580C23×C3—1216no—
581C23×C3—124no—
582C23×C3—124no—
583C23×C3C2×Dic614yes—
584C23×C3D3×Q814yes—
585C23×C3C23×D312yes—
586C23×C3C23×D312yes—
587C23×C3C23×D311yescharacteristic
588C23×C3C23×D311yescharacteristic
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—416no—
594C22×D3—44no—
595C22×D3—44no—
596C22×D3C2×Dic614yes—
597C22×D3C2×Dic614yes—
598C22×D3C2×Dic6116yescomplemented
599C22×D3C23×D312yes—
600C22×D3C23×D312yes—
601C3×Q8—124no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—42no—
615C2×C3×C4—42no—
616C2×C3×C4—62no—
617C2×C3×C4—62no—
618C2×C3×C4—62no—
619C2×C3×C4—62no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—124no—
623C2×C3×C4—124no—
624C2×C3×C4—124no—
625C2×C3×C4C23×D312yes—
626C2×C3×C4C23×D312yes—
627C2×C3×C4C23×D312yes—
628C2×C3×C4C23×D312yes—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—32no—
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—44no—
644C2×Dic3—62no—
645C2×Dic3—62no—
646C2×Dic3—62no—
647C2×Dic3—62no—
648C2×Dic3—64no—
649C2×Dic3—62no—
650C2×Dic3—62no—
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—122no—
660C2×Dic3—124no—
661C2×Dic3—124no—
662C2×Dic3—124no—
663C2×Dic3—124no—
664C2×Dic3—128no—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C4×D3—44no—
672C4×D3—44no—
673C4×D3—124no—
674C4×D3—124no—
675Dic6—44no—
676Dic6—124no—
677Dic6—124no—
678Dic6—124no—
679Dic6—124no—
680Dic6—124no—
681Dic6—124no—
682Dic6—128no—
683C2×C32—24no—
684C2×C32#54314yescomplemented
685C2×C32C23×Q811yescharacteristic
686C2×C32C2×H(5,𝔽2)11yescharacteristic
687C2×C32C2×H(5,𝔽2)11yescharacteristic
688C3×D3—24no—
689C3×D3—24no—
690C24—31no—
691C24—31no—
692C24—34no—
693C24—38no—
694C24—122no—
695C24—122no—
696C24C2×D3211yescharacteristic
697C2×Q8—34no—
698C2×Q8—94no—
699C2×Q8—94no—
700C2×Q8—94no—
701C2×Q8—122no—
702C2×Q8—362no—
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—34no—
714C22×C4—94no—
715C22×C4—94no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—94no—
721C22×C4—122no—
722C22×C4—122no—
723C22×C4—122no—
724C22×C4—362no—
725C22×C4—362no—
726C22×C4—362no—
727C22×C4C2×D3211yescharacteristic
728C22×C4C2×D3211yescharacteristic
729C4⋊C4—34no—
730C4⋊C4—34no—
731C4⋊C4—34no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
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⋊C4C2×D3214yes—
753C22×C3—28no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—28no—
759C22×C3—22no—
760C22×C3—24no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—21no—
764C22×C3—34no—
765C22×C3—34no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—48no—
769C22×C3—68no—
770C22×C3—68no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—1216no—
776C22×C3C22×Dic614yes—
777C22×C3C22×Dic612yes—
778C22×C3#100412yes—
779C22×C3#100412yes—
780C22×C3#100412yes—
781C22×C3C2×D3×Q814yes—
782C22×C3C2×D3×Q812yes—
783C22×C3#100912yes—
784C22×C3C24×D311yescharacteristic
785C22×C3C24×D311yescharacteristic
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—28no—
791C2×D3—28no—
792C2×D3—416no—
793C2×D3C22×Dic614yes—
794C2×D3C22×Dic614yes—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—42no—
800C3×C4—42no—
801C3×C4—62no—
802C3×C4—62no—
803C3×C4—62no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—62no—
807Dic3—22no—
808Dic3—22no—
809Dic3—22no—
810Dic3—22no—
811Dic3—22no—
812Dic3—22no—
813Dic3—64no—
814Dic3—62no—
815Dic3—62no—
816Dic3—62no—
817Dic3—62no—
818Dic3—62no—
819Dic3—62no—
820Dic3—62no—
821Dic3—62no—
822Dic3—122no—
823Dic3—122no—
824Dic3—122no—
825C32C2×#54311yescharacteristic, complemented, Sylow
826C23—22no—
827C23—22no—
828C23—34no—
829C23—34no—
830C23—32no—
831C23—32no—
832C23—316no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—124no—
838C23—124no—
839C23—1216no—
840C23D3×Dic614yes—
841C23C22×D3212yes—
842C23C22×D3211yescharacteristic
843Q8—124no—
844Q8—364no—
845Q8—364no—
846Q8—364no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—92no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—92no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4—124no—
868C2×C4—182no—
869C2×C4—182no—
870C2×C4—182no—
871C2×C4—182no—
872C2×C4—364no—
873C2×C4—364no—
874C2×C4—364no—
875C2×C4C22×D3212yes—
876C2×C4C22×D3212yes—
877C2×C3—24no—
878C2×C3—24no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—24no—
883C2×C3—44no—
884C2×C3—64no—
885C2×C3—64no—
886C2×C3#548314yescomplemented
887C2×C3#563414yescomplemented
888C2×C3C23×Dic611yescharacteristic
889C2×C3C2×#100411yescharacteristic
890C2×C3C2×#100411yescharacteristic
891C2×C3C2×#100411yescharacteristic
892C2×C3C22×D3×Q811yescharacteristic
893C2×C3C2×#100911yescharacteristic
894D3—24no—
895D3—24no—
896C22—22no—
897C22—22no—
898C22—28no—
899C22—34no—
900C22—34no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—62no—
905C22—68no—
906C22—68no—
907C22—1216no—
908C22C2×D3×Dic614yes—
909C22C2×D3×Dic612yes—
910C22#6431312yes—
911C22#6431412yes—
912C22C23×D3211yescharacteristic
913C4—22no—
914C4—22no—
915C4—62no—
916C4—62no—
917C4—62no—
918C4—62no—
919C4—62no—
920C4—62no—
921C4—182no—
922C4—182no—
923C4—182no—
924C4—182no—
925C3—21no—
926C3C2×#548311yescharacteristic, complemented
927C3C2×#563411yescharacteristic, complemented
928C2—24no—
929C2—64no—
930C2—64no—
931C2#1059417014yesdirect product factor
932C2C22×D3×Dic611yescharacteristic
933C2C2×#6431311yescharacteristic
934C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#543
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×#64087C2semidirect
3. C2×C3×#878C2semidirect
4. C2×#63982C2semidirect
6. C2×#63964C2semidirect
8. C2×#63899C2semidirect
9. C2×#63896C2semidirect
10. C2×#63893C2semidirect
11. C2×#63887C2semidirect
12. C2×#63857C2semidirect
13. C2×#63856C2semidirect
14. C2×#63851C2semidirect
15. C2×#63851C2semidirect
16. #10594170C2direct (N × H)
21. C22×#634C22semidirect
25. C22×C3×Dic6C22semidirect
26. C22×#627C22semidirect
27. C22×#627C22semidirect
32. C2×C4⋊(C3⋊Dic3)C22semidirect
33. C2×#3750C22semidirect
34. C2×#3750C22semidirect
35. #64087C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
44. C3×#878C22semidirect
45. #63982C22semidirect
47. C2×#3724C22semidirect
48. C2×#3724C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
53. #63964C22semidirect
61. #63899C22semidirect
62. #63896C22semidirect
63. #63893C22semidirect
64. #63887C22semidirect
65. #63857C22semidirect
66. #63856C22semidirect
67. #63851C22semidirect
68. #63851C22semidirect
101. C2×#878D3semidirect
105. C23×C3×D3Q8semidirect
118. C2×#634C23semidirect
132. C2×C3×Dic6C23semidirect
135. C2×#627C23semidirect
136. C2×#627C23semidirect
143. C4⋊(C3⋊Dic3)C23semidirect
144. #3750C23semidirect
145. #3750C23semidirect
150. C3×C4⋊Dic3C23semidirect
151. C3×Dic3⋊C4C23semidirect
152. C3×Dic3⋊C4C23semidirect
153. #3724C23semidirect
154. #3724C23semidirect
155. Dic3⋊Dic3C23semidirect
156. Dic3⋊Dic3C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
189. C22×Dic6C2×D3semidirect
233. C2×C4⋊Dic3C2×D3semidirect
253. C2×Dic3⋊C4C2×D3semidirect
254. C2×Dic3⋊C4C2×D3semidirect
273. #878C2×D3semidirect
288. C22×C3×D3C2×Q8semidirect
352. C23×D3Dic6semidirect
429. C2×Dic6C22×D3semidirect
466. C4⋊Dic3C22×D3semidirect
481. Dic3⋊C4C22×D3semidirect
482. Dic3⋊C4C22×D3semidirect
598. C22×D3C2×Dic6semidirect
684. C2×C32#543semidirect
825. C32C2×#543semidirect
886. C2×C3#5483semidirect
887. C2×C3#5634semidirect
926. C3C2×#5483semidirect
927. C3C2×#5634semidirect
931. C2#10594170direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640872
C2×C3×D3×C22⋊C42
C2×C3×#8782
C2×#639822
C2×D3×#2172
C2×#639642
C22×(C2×D3)⋊Dic32
C2×#638992
C2×#638962
C2×#638932
C2×#638872
C2×#638572
C2×#638562
C2×#638512
#105941702
C2×#56343
C2×#54833