Finite Group Databasebeta

← C2×#10595175 #11902919

Subgroups — C2×#10595175 #11902919

Order 1152.

2827 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×Dic3×#67C211yesmaximal, characteristic, complemented
5C2×#63969C211yesmaximal, characteristic, complemented
6C2×D3×#217C211yesmaximal, characteristic, complemented
7C2×#63964C211yesmaximal, characteristic, complemented
8C2×#63961C211yesmaximal, characteristic, complemented
9C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
10C2×#63959C211yesmaximal, characteristic, complemented
11C2×#63957C211yesmaximal, characteristic, complemented
12#10595175C2116yesmaximal, direct product factor
13C2×#63899C211yesmaximal, characteristic, complemented
14C2×#63877C211yesmaximal, characteristic, complemented
15C2×#63859C211yesmaximal, characteristic, complemented
16C2×#63858C211yesmaximal, characteristic, complemented
17C2×#5587—31nomaximal
18C2×#5556—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic, complemented
26C22×#627C2211yescharacteristic, complemented
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic, complemented
31C2×#3757C2211yescharacteristic, complemented
32#64144C2218yescomplemented
33C2×#3750C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic, complemented
38C3×#937C2218yes—
39C3×D4×Dic3C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
43C2×C3×C4×Dic3C2211yescharacteristic, complemented
44Dic3×#67C2218yescomplemented
45#63969C2218yescomplemented
46D3×#217C2218yescomplemented
47C2×#3724C2211yescharacteristic, complemented
48C2×#3724C2211yescharacteristic, complemented
49C2×#3724C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52#63964C2218yescomplemented
53#63961C2218yescomplemented
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)⋊Dic3C2218yescomplemented
61#63959C2218yescomplemented
62#63957C2218yescomplemented
63C2×Dic32C2211yescharacteristic, complemented
64C2×Dic32C2211yescharacteristic, complemented
65#63899C2218yescomplemented
66#63877C2218yescomplemented
67#63859C2218yescomplemented
68#63858C2218yescomplemented
69C2×C3×#120—31no—
70C2×C3×C4×D4—31no—
71C22×#217—31no—
72C22×#217—31no—
73C2×#937D311yescharacteristic
74C2×#936—31no—
75C2×#935—31no—
76C2×#935—31no—
77C2×#935—31no—
78C2×#935—31no—
79C2×#935—61no—
80C2×D4×Dic3—31no—
81C2×D4×Dic3D311yescharacteristic, complemented
82C2×#929—31no—
83C2×C4×#67—31no—
84C22×(C2×D3)⋊C4—31no—
85C2×#924—31no—
86#5587—316no—
87#5556—316no—
88C2×#898—31no—
89C2×#896—31no—
90C2×#885—31no—
91C2×#883—31no—
92C2×D3×C22⋊C4—31no—
93C2×#879—31no—
94C2×#879—31no—
95C2×#878—31no—
96C2×#878—31no—
97C2×#877—31no—
98C2×#877—31no—
99C2×#877—31no—
100C2×#876—31no—
101C2×#872—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3—24no—
105C23×C3×D3—24no—
106C23×C3×D3—42no—
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2314yes—
109C23×C3×D3C2311yescharacteristic
110C2×C32×D4—24no—
111C2×C32×D4C2314yes—
112C22×C32×C4C2311yescharacteristic
113C22×C3⋊Dic3—24no—
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2314yes—
119C2×C3×#67—24no—
120C2×C3×#67—42no—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C22×C3×Dic3—42no—
124C22×C3×Dic3—42no—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2314yes—
132C22×C3×Dic3C2314yescomplemented
133C2×#627—42no—
134C2×#627C2314yescomplemented
135C2×D3×Dic3—24no—
136C2×D3×Dic3—42no—
137C2×D3×Dic3C2314yes—
138C2×D3×Dic3C2314yes—
139#3757C2314yes—
140#3757C2314yescomplemented
141#3757C2314yescomplemented
142#3750C2314yescomplemented
143#3750C2314yescomplemented
144C3×#217C2314yes—
145C3×#217C2314yes—
146C3×#217C2314yescomplemented
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×C4⋊Dic3C2314yescomplemented
150C3×C4×Dic3C2314yescomplemented
151#3724C2314yescomplemented
152#3724C2314yescomplemented
153#3724C2314yescomplemented
154Dic3⋊Dic3C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162Dic32C2314yescomplemented
163Dic32C2314yescomplemented
164C2×#551—91noSylow
165C25×C3—31no—
166C24×D3C2×D311yescharacteristic
167C22×C3×D4—21no—
168C22×C3×D4—31no—
169C22×C3×D4—31no—
170C22×C3×D4C2×D311yescharacteristic
171C22×C3×D4C2×D311yescharacteristic
172C23×C3×C4—31no—
173C23×C3×C4—31no—
174C22×#67C2×D311yescharacteristic
175C22×#67C2×D311yescharacteristic
176C23×Dic3—31no—
177C23×Dic3—31no—
178C23×Dic3—31no—
179C23×Dic3—31no—
180C23×Dic3—61no—
181C23×Dic3C2×D311yescharacteristic
182C23×Dic3C2×D311yescharacteristic, complemented
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×Dic6—31no—
186C22×Dic6—31no—
187C3×#120—38no—
188C3×C4×D4—38no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C42—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217—31no—
208C2×#217—38no—
209C2×#217—38no—
210C2×#217—61no—
211C2×#217—61no—
212C2×#217—61no—
213C2×#217C2×D311yescharacteristic
214C2×#217C2×D311yescharacteristic
215C2×#217C2×D311yescharacteristic, complemented
216#937C2×D318yes—
217#936—38no—
218#935—38no—
219#935—38no—
220#935—38no—
221#935—38no—
222#935—68no—
223D4×Dic3—38no—
224D4×Dic3C2×D318yescomplemented
225#929—38no—
226C4×#67—38no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—38no—
234C2×(C2×D3)⋊C4C2×D311yescharacteristic
235C2×(C2×D3)⋊C4C2×D311yescharacteristic
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—31no—
238C2×C4⋊Dic3C2×D311yescharacteristic, complemented
239#924—38no—
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—31no—
252C2×Dic3⋊C4—61no—
253C2×Dic3⋊C4—61no—
254C2×C4×Dic3—31no—
255C2×C4×Dic3—31no—
256C2×C4×Dic3—31no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3C2×D311yescharacteristic, complemented
259#898—38no—
260#896—38no—
261#885—38no—
262#883—38no—
263D3×C22⋊C4—38no—
264#879—38no—
265#879—38no—
266#878—38no—
267#878—38no—
268#877—38no—
269#877—38no—
270#877—38no—
271#876—38no—
272#872—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32#4114yes—
279C23×C32C2412yes—
280C23×C32C2412yes—
281C23×C32C2411yescharacteristic
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—28no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—28no—
289C22×C3×D3—44no—
290C22×C3×D3—416no—
291C22×C3×D3#4114yes—
292C22×C3×D3C2412yes—
293C22×C3×D3C2412yes—
294C32×D4—28no—
295C2×C32×C4—22no—
296C2×C32×C4C2412yes—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—28no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3—22no—
301C2×C3⋊Dic3—22no—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2412yes—
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2412yes—
306C3×#67—28no—
307C3×#67—44no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—44no—
315C2×C3×Dic3—44no—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322#627—44no—
323D3×Dic3—28no—
324D3×Dic3—44no—
325#551—916no—
326C2×#126—91no—
327C2×#126—91no—
328C2×#124—91no—
329C2×#123—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×#120—31no—
335C2×C4×D4—31no—
336C2×C4×D4—91no—
337C2×#117—91no—
338C2×#117—91no—
339C22×C22⋊C4—91no—
340C22×C22⋊C4—91no—
341C24×C3—21no—
342C24×C3—21no—
343C24×C3—31no—
344C24×C3—31no—
345C24×C3—34no—
346C24×C3—64no—
347C24×C3—64no—
348C24×C3—122no—
349C24×C3C22×D311yescharacteristic
350C24×C3C22×D311yescharacteristic
351C24×C3C22×D311yescharacteristic
352C24×C3C22×D311yescharacteristic
353C23×D3—24no—
354C23×D3—24no—
355C23×D3—42no—
356C23×D3C22×D311yescharacteristic
357C23×D3C22×D314yes—
358C23×D3C22×D311yescharacteristic
359C2×C3×D4—24no—
360C2×C3×D4—24no—
361C2×C3×D4—24no—
362C2×C3×D4—34no—
363C2×C3×D4—34no—
364C2×C3×D4—44no—
365C2×C3×D4—64no—
366C2×C3×D4—122no—
367C2×C3×D4C22×D314yes—
368C2×C3×D4C22×D314yes—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—34no—
377C22×C3×C4—34no—
378C22×C3×C4—122no—
379C22×C3×C4—122no—
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C2×#67—24no—
383C2×#67—42no—
384C2×#67C22×D314yes—
385C2×#67C22×D314yes—
386C22×Dic3—34no—
387C22×Dic3—34no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—34no—
397C22×Dic3—34no—
398C22×Dic3—42no—
399C22×Dic3—42no—
400C22×Dic3—61no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—64no—
405C22×Dic3—64no—
406C22×Dic3—64no—
407C22×Dic3—64no—
408C22×Dic3—124no—
409C22×Dic3—122no—
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D314yes—
417C22×Dic3C22×D314yescomplemented
418C2×C4×D3—34no—
419C2×C4×D3—34no—
420C2×C4×D3—64no—
421C2×C4×D3—122no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—122no—
425C2×Dic6—122no—
426C3×C4⋊C4—34no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C42—34no—
433#217—34no—
434#217—34no—
435#217—34no—
436#217—34no—
437#217—34no—
438#217—34no—
439#217—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217—34no—
445#217—64no—
446#217—64no—
447#217—64no—
448#217C22×D314yes—
449#217C22×D314yes—
450#217C22×D314yescomplemented
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⋊Dic3C22×D314yescomplemented
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—64no—
475Dic3⋊C4—64no—
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3C22×D314yescomplemented
481C22×C32—28no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—44no—
488C22×C32C2×#4114yes—
489C22×C32C2×#4112yes—
490C22×C32C2×#4112yes—
491C22×C32H(5,𝔽2)12yes—
492C22×C32C2511yescharacteristic
493C2×C3×D3—28no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—416no—
500C2×C3×D3—44no—
501C2×C3×D3C2×#4114yes—
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—
512C3×Dic3—22no—
513C25—31no—
514C22×Q8—91no—
515C22×D4—31no—
516C22×D4—31no—
517C22×D4D3211yescharacteristic
518C23×C4—31no—
519C23×C4—31no—
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523#126—98no—
524#126—98no—
525#124—98no—
526#123—98no—
527#123—98no—
528#123—98no—
529C22⋊Q8—98no—
530C22⋊Q8—98no—
531#120—38no—
532C4×D4—38no—
533C4×D4—98no—
534#117—98no—
535#117—98no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—91no—
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×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—98no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—98no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C42—31no—
561C2×C42—91no—
562C2×C42—91no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—21no—
576C23×C3—24no—
577C23×C3—34no—
578C23×C3—32no—
579C23×C3—32no—
580C23×C3—42no—
581C23×C3—42no—
582C23×C3—42no—
583C23×C3—42no—
584C23×C3—42no—
585C23×C3—68no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—68no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3—62no—
592C23×C3—124no—
593C23×C3—1216no—
594C23×C3#23514yes—
595C23×C3#23714yes—
596C23×C3C23×D312yes—
597C23×C3C23×D312yes—
598C23×C3C23×D312yes—
599C23×C3C23×D312yes—
600C23×C3C23×D311yescharacteristic
601C23×C3C23×D311yescharacteristic
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—28no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—28no—
609C22×D3—44no—
610C22×D3—416no—
611C22×D3#23714yes—
612C22×D3C23×D312yes—
613C22×D3C23×D312yes—
614C3×D4—28no—
615C3×D4—28no—
616C3×D4—48no—
617C3×D4—68no—
618C3×D4—124no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—32no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—32no—
628C2×C3×C4—42no—
629C2×C3×C4—62no—
630C2×C3×C4—62no—
631C2×C3×C4—62no—
632C2×C3×C4—62no—
633C2×C3×C4—62no—
634C2×C3×C4—62no—
635C2×C3×C4—124no—
636C2×C3×C4—124no—
637C2×C3×C4C23×D312yes—
638C2×C3×C4C23×D312yes—
639#67—28no—
640#67—44no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—44no—
656C2×Dic3—44no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—68no—
662C2×Dic3—68no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—68no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—62no—
672C2×Dic3—122no—
673C2×Dic3—122no—
674C2×Dic3—122no—
675C2×Dic3—122no—
676C2×Dic3—128no—
677C2×Dic3—124no—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D312yes—
684C4×D3—68no—
685C4×D3—124no—
686Dic6—124no—
687Dic6—124no—
688C2×C32—24no—
689C2×C32—42no—
690C2×C32#55114yescomplemented
691C2×C32C22×#4111yescharacteristic
692C2×C32C22×#4111yescharacteristic
693C2×C32C2×H(5,𝔽2)11yescharacteristic
694C3×D3—24no—
695C3×D3—42no—
696C24—31no—
697C24—31no—
698C24—34no—
699C24—64no—
700C24—64no—
701C24—122no—
702C24C2×D3211yescharacteristic
703C24C2×D3211yescharacteristic
704C2×Q8—94no—
705C2×Q8—362no—
706C2×D4—24no—
707C2×D4—34no—
708C2×D4—34no—
709C2×D4—64no—
710C2×D4—122no—
711C2×D4C2×D3214yes—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—34no—
719C22×C4—34no—
720C22×C4—94no—
721C22×C4—94no—
722C22×C4—94no—
723C22×C4—91no—
724C22×C4—91no—
725C22×C4—91no—
726C22×C4—91no—
727C22×C4—122no—
728C22×C4—122no—
729C22×C4—184no—
730C22×C4—184no—
731C22×C4—362no—
732C22×C4C2×D3211yescharacteristic
733C4⋊C4—34no—
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—34no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C22⋊C4—94no—
755C42—34no—
756C42—94no—
757C42—94no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—28no—
763C22×C3—28no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—24no—
774C22×C3—21no—
775C22×C3—34no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—48no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—44no—
783C22×C3—44no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—68no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—84no—
791C22×C3—1216no—
792C22×C3—124no—
793C22×C3C2×#23514yes—
794C22×C3C2×#23512yes—
795C22×C3C2×#23712yes—
796C22×C3C2×#23714yes—
797C22×C3C2×#23712yes—
798C22×C3#100412yes—
799C22×C3#100412yes—
800C22×C3D3×#4112yes—
801C22×C3C24×D311yescharacteristic
802C22×C3C24×D311yescharacteristic
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—28no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—416no—
810C2×D3—44no—
811C2×D3C2×#23714yes—
812C3×C4—22no—
813C3×C4—22no—
814C3×C4—42no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—62no—
819C3×C4—62no—
820C3×C4—62no—
821Dic3—22no—
822Dic3—22no—
823Dic3—22no—
824Dic3—22no—
825Dic3—22no—
826Dic3—22no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—62no—
831Dic3—62no—
832Dic3—62no—
833Dic3—62no—
834Dic3—62no—
835Dic3—122no—
836Dic3—122no—
837Dic3—122no—
838Dic3—122no—
839C32C2×#55111yescharacteristic, complemented, Sylow
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—34no—
846C23—32no—
847C23—32no—
848C23—68no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—62no—
853C23—68no—
854C23—62no—
855C23—124no—
856C23—1216no—
857C23#380414yes—
858C23C22×D3212yes—
859C23C22×D3212yes—
860C23C22×D3211yescharacteristic
861Q8—364no—
862D4—28no—
863D4—68no—
864D4—124no—
865C2×C4—22no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—32no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—92no—
879C2×C4—92no—
880C2×C4—92no—
881C2×C4—92no—
882C2×C4—124no—
883C2×C4—124no—
884C2×C4—188no—
885C2×C4—182no—
886C2×C4—182no—
887C2×C4—188no—
888C2×C4—182no—
889C2×C4—182no—
890C2×C4—364no—
891C2×C4C22×D3212yes—
892C2×C3—24no—
893C2×C3—24no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—24no—
898C2×C3—44no—
899C2×C3—42no—
900C2×C3—42no—
901C2×C3—64no—
902C2×C3—82no—
903C2×C3—122no—
904C2×C3#555614yescomplemented
905C2×C3#558714yescomplemented
906C2×C3C22×#23511yescharacteristic
907C2×C3C22×#23711yescharacteristic
908C2×C3C22×#23711yescharacteristic
909C2×C3C2×#100411yescharacteristic
910C2×C3C2×#100411yescharacteristic
911C2×C3C2×D3×#4111yescharacteristic
912D3—24no—
913D3—42no—
914C22—22no—
915C22—22no—
916C22—28no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—34no—
921C22—44no—
922C22—62no—
923C22—62no—
924C22—68no—
925C22—62no—
926C22—62no—
927C22—62no—
928C22—1216no—
929C22—124no—
930C22D3×#23712yes—
931C22#6431312yes—
932C22C2×#380414yes—
933C22C2×#380412yes—
934C22C23×D3211yescharacteristic
935C4—22no—
936C4—62no—
937C4—62no—
938C4—62no—
939C4—62no—
940C4—62no—
941C4—62no—
942C4—182no—
943C4—182no—
944C4—182no—
945C4—182no—
946C3—21no—
947C3C2×#555611yescharacteristic, complemented
948C3C2×#558711yescharacteristic, complemented
949C2—24no—
950C2—42no—
951C2—64no—
952C2—122no—
953C2#1059517514yesdirect product factor
954C2C2×D3×#23711yescharacteristic
955C2C2×#6431311yescharacteristic
956C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64144C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×Dic3×#67C2semidirect
5. C2×#63969C2semidirect
6. C2×D3×#217C2semidirect
7. C2×#63964C2semidirect
8. C2×#63961C2semidirect
9. C22×(C2×D3)⋊Dic3C2semidirect
10. C2×#63959C2semidirect
11. C2×#63957C2semidirect
12. #10595175C2direct (N × H)
13. C2×#63899C2semidirect
14. C2×#63877C2semidirect
15. C2×#63859C2semidirect
16. C2×#63858C2semidirect
25. C23×C3×Dic3C22semidirect
26. C22×#627C22semidirect
30. C2×#3757C22semidirect
31. C2×#3757C22semidirect
32. #64144C22semidirect
33. C2×#3750C22semidirect
34. C2×#3750C22semidirect
37. C2×C3×#217C22semidirect
39. C3×D4×Dic3C22semidirect
42. C2×C3×C4⋊Dic3C22semidirect
43. C2×C3×C4×Dic3C22semidirect
44. Dic3×#67C22semidirect
45. #63969C22semidirect
46. D3×#217C22semidirect
47. C2×#3724C22semidirect
48. C2×#3724C22semidirect
49. C2×#3724C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. #63964C22semidirect
53. #63961C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63959C22semidirect
62. #63957C22semidirect
63. C2×Dic32C22semidirect
64. C2×Dic32C22semidirect
65. #63899C22semidirect
66. #63877C22semidirect
67. #63859C22semidirect
68. #63858C22semidirect
81. C2×D4×Dic3D3semidirect
132. C22×C3×Dic3C23semidirect
134. C2×#627C23semidirect
140. #3757C23semidirect
141. #3757C23semidirect
142. #3750C23semidirect
143. #3750C23semidirect
146. C3×#217C23semidirect
149. C3×C4⋊Dic3C23semidirect
150. C3×C4×Dic3C23semidirect
151. #3724C23semidirect
152. #3724C23semidirect
153. #3724C23semidirect
154. Dic3⋊Dic3C23semidirect
155. Dic3⋊Dic3C23semidirect
162. Dic32C23semidirect
163. Dic32C23semidirect
182. C23×Dic3C2×D3semidirect
215. C2×#217C2×D3semidirect
224. D4×Dic3C2×D3semidirect
238. C2×C4⋊Dic3C2×D3semidirect
258. C2×C4×Dic3C2×D3semidirect
417. C22×Dic3C22×D3semidirect
450. #217C22×D3semidirect
461. C4⋊Dic3C22×D3semidirect
480. C4×Dic3C22×D3semidirect
690. C2×C32#551semidirect
839. C32C2×#551semidirect
904. C2×C3#5556semidirect
905. C2×C3#5587semidirect
947. C3C2×#5556semidirect
948. C3C2×#5587semidirect
953. C2#10595175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641442
C2×C3×#9372
C2×C3×D4×Dic32
C2×Dic3×#672
C2×#639692
C2×D3×#2172
C2×#639642
C2×#639612
C22×(C2×D3)⋊Dic32
C2×#639592
C2×#639572
#105951752
C2×#638992
C2×#638772
C2×#638592
C2×#638582
C2×#55873
C2×#55563