Finite Group Databasebeta

← #11900185

Subgroups — #11900185

Order 1152.

3533 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic
2C2×#64090C211yesmaximal, characteristic, complemented
3C3×#5486C212yesmaximal, complemented
4#10595510C211yesmaximal, characteristic, complemented
5C2×#67⋊Dic3C212yesmaximal, complemented
6#10595058C212yesmaximal, complemented
7C4×#3811C212yesmaximal, complemented
8#10594876C212yesmaximal, complemented
9C4×#3805C212yesmaximal, complemented
10#10594254C214yesmaximal, complemented
11D3×#67⋊C4C214yesmaximal, complemented
12#10594049C214yesmaximal, complemented
13#10594048C214yesmaximal, complemented
14#85857—32nomaximal
15C22×#638C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic, complemented
17C22×C4×C3⋊D3C2211yescharacteristic, complemented
18C22×C3×#67C2212yes—
19#64330C4116yescomplemented
20C2×#3811C2212yes—
21C2×D3×#67C2214yes—
22C2×#3805C2212yes—
23C2×#3804C2214yes—
24C22×D3×Dic3C2212yescomplemented
25C2×C4×D32C2212yescomplemented
26C2×C32×C22⋊C4C2211yescharacteristic, complemented
27C2×#3752C2211yescharacteristic, complemented
28C2×#3750C2211yescharacteristic, complemented
29C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
30#64090C2214yescomplemented
31#64090C2214yescomplemented
32C2×C3×#217C2212yescomplemented
33C3×C4×#67C2214yescomplemented
34C3×C4×#67C2214yescomplemented
35C3×#67⋊C4C2214yescomplemented
36C3×#67⋊C4C2214yescomplemented
37C3×D3×C22⋊C4C2214yescomplemented
38C3×#877C2214yescomplemented
39#63974C2212yescomplemented
40#67⋊Dic3C2214yescomplemented
41#67⋊Dic3C2214yescomplemented
42#67⋊Dic3C2214yescomplemented
43#67⋊Dic3C2214yescomplemented
44C2×Dic3⋊Dic3C2212yescomplemented
45C2×(C2×D3)⋊Dic3C2212yescomplemented
46#63957C2212yescomplemented
47C2×Dic32C2212yescomplemented
48#63952C2214yescomplemented
49#63952C2214yescomplemented
50#63921C2212yescomplemented
51D3×(C2×D3)⋊C4C2214yescomplemented
52C4×#627C2212yescomplemented
53#63904C2214yescomplemented
54C4×#626C2214yescomplemented
55#63902C2212yescomplemented
56C4×#625C2212yescomplemented
57#63883C2212yescomplemented
58C4×#624C2212yescomplemented
59#63881C2214yescomplemented
60#63880C2214yescomplemented
61#63879C2214yescomplemented
62#63878C2214yescomplemented
63#63877C2214yescomplemented
64D3×Dic3⋊C4C2214yescomplemented
65C4×D3×Dic3C2214yescomplemented
66#63838C2212yescomplemented
67#63837C2214yescomplemented
68#63836C2214yescomplemented
69C2×#1004—32no—
70C3×#518—32no—
71C2×D4×Dic3—32no—
72#5546—34no—
73#5546—34no—
74#5545—34no—
75#5545—34no—
76C4×D3×D4—34no—
77C4×D3×D4—34no—
78C4×#237—34no—
79C4×#237—34no—
80#5523—34no—
81#5522—34no—
82#5486—32no—
83#5486—34no—
84#5486D312yescomplemented
85C2×#67⋊C4—32no—
86C2×#67⋊C4—32no—
87C2×#67⋊C4—34no—
88C2×#67⋊C4—61no—
89C24×C32C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2312yes—
92C22×D32C2312yes—
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638C2×C418yescomplemented
96C2×#638C2314yes—
97C22×C3⋊Dic3—42no—
98C22×C3⋊Dic3C2312yes—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2312yes—
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C2×C4×C3⋊D3—42no—
104C2×C4×C3⋊D3C2312yes—
105C2×C4×C3⋊D3C2312yes—
106C2×C3×#67C2×C4116yescomplemented
107C2×C3×#67C2314yes—
108C2×C3×#67C2314yes—
109C22×C3×Dic3C2312yes—
110C22×C3×Dic3C2312yes—
111C22×C3×Dic3C2312yes—
112C2×C3×C4×D3C2314yes—
113C2×C3×C4×D3C2314yes—
114#3811C2×C4116yescomplemented
115D3×#67C2×C4132yescomplemented
116C2×#627C2312yes—
117C2×#626C2314yes—
118C2×#625C2312yes—
119C2×#624C2312yes—
120C2×#624C2312yes—
121C2×#624C2312yes—
122#3805C2×C4116yescomplemented
123#3804C2×C4132yescomplemented
124C2×D3×Dic3—44no—
125C2×D3×Dic3C2314yes—
126C2×D3×Dic3C2314yes—
127C2×D3×Dic3C2314yes—
128C4×D32—44no—
129C32×C22⋊C4C2314yes—
130#3752C2314yes—
131#3750C2314yes—
132C4×C3⋊Dic3C2312yes—
133C4×C3⋊Dic3C2312yes—
134C3×#217C2314yes—
135C3×#217C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×C4×Dic3C2314yes—
141C3×C4×Dic3C2314yes—
142#3724C2312yes—
143#3724C2312yes—
144Dic3⋊Dic3C2314yes—
145Dic3⋊Dic3C2314yes—
146#3722C2314yes—
147(C2×D3)⋊Dic3C2314yes—
148(C2×D3)⋊Dic3C2314yes—
149Dic32C2314yes—
150Dic32C2314yes—
151Dic32C2314yes—
152C4×H(5,𝔽2)—91noSylow
153C22×C3×D4—32no—
154C22×#67—32no—
155C22×#67—34no—
156C22×#67—61no—
157C22×#67C2×D312yes—
158C23×Dic3—32no—
159C23×Dic3—32no—
160C23×Dic3—61no—
161#1004—332no—
162C2×#237—34no—
163C2×#237—34no—
164C2×D3×D4—34no—
165C2×D3×D4—34no—
166C2×#235—34no—
167C22×C4×D3—32no—
168C22×C4×D3—32no—
169C22×C4×D3—34no—
170C22×C4×D3—61no—
171C3×C4×D4—34no—
172C3×C4×D4—34no—
173C3×C4×D4—34no—
174C3×C4×D4—34no—
175C3×#117—34no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—32no—
178C2×C3×C22⋊C4—34no—
179C2×C3×C22⋊C4C2×D312yescomplemented
180C2×#217—32no—
181C2×#217C2×D312yescomplemented
182D4×Dic3—34no—
183D4×Dic3—34no—
184D4×Dic3—34no—
185D4×Dic3—34no—
186C4×#67—34no—
187C4×#67—34no—
188C4×#67—34no—
189C4×#67—34no—
190C4×#67—34no—
191C4×#67—34no—
192C4×#67C2×D314yescomplemented
193C4×#67C2×D314yescomplemented
194C2×(C2×D3)⋊C4—32no—
195C2×(C2×D3)⋊C4—32no—
196C2×(C2×D3)⋊C4—34no—
197C2×(C2×D3)⋊C4—61no—
198C2×C4⋊Dic3—32no—
199C2×Dic3⋊C4—32no—
200C2×Dic3⋊C4—32no—
201C2×Dic3⋊C4—34no—
202C2×Dic3⋊C4—61no—
203C2×C4×Dic3—32no—
204C2×C4×Dic3—32no—
205C2×C4×Dic3—32no—
206C2×C4×Dic3—34no—
207C2×C4×Dic3—61no—
208#893—34no—
209#893—34no—
210#892—34no—
211#892—34no—
212D3×C4⋊C4—34no—
213D3×C4⋊C4—34no—
214#887—34no—
215#887—34no—
216#67⋊C4—34no—
217#67⋊C4—34no—
218#67⋊C4—34no—
219#67⋊C4—34no—
220#67⋊C4—34no—
221#67⋊C4—34no—
222#67⋊C4—34no—
223#67⋊C4—34no—
224#67⋊C4—34no—
225#67⋊C4—34no—
226#67⋊C4—34no—
227#67⋊C4—34no—
228#67⋊C4—34no—
229#67⋊C4—34no—
230#67⋊C4—64no—
231#67⋊C4—64no—
232#67⋊C4C2×D314yescomplemented
233#67⋊C4C2×D314yescomplemented
234D3×C22⋊C4—34no—
235D3×C22⋊C4—34no—
236D3×C22⋊C4—34no—
237D3×C22⋊C4C2×D314yescomplemented
238#877—34no—
239#877—34no—
240#877—34no—
241#877C2×D314yescomplemented
242C4×D12—34no—
243C4×D12—34no—
244#872—34no—
245#872—34no—
246C42×D3—34no—
247C42×D3—34no—
248C4×Dic6—34no—
249C4×Dic6—34no—
250C23×C32—41no—
251C23×C32—41no—
252C23×C32C22×C414yescomplemented
253C23×C32C2412yes—
254C23×C32C2411yescharacteristic
255C22×C3⋊D3—41no—
256C22×C3⋊D3—41no—
257C22×C3⋊D3C22×C414yescomplemented
258C22×C3⋊D3C2412yes—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3C22×C418yescomplemented
262C22×C3×D3C2414yes—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32C22×C418yescomplemented
266C2×C32×C4—41no—
267C2×C32×C4—41no—
268C2×C32×C4C2412yes—
269C2×C32×C4C2412yes—
270#638C22×C4116yescomplemented
271C2×C3⋊Dic3—22no—
272C2×C3⋊Dic3—24no—
273C2×C3⋊Dic3—42no—
274C2×C3⋊Dic3—41no—
275C2×C3⋊Dic3C22×C414yescomplemented
276C2×C3⋊Dic3C2412yes—
277C2×C3⋊Dic3C2411yescharacteristic
278C2×C3⋊Dic3C2412yes—
279C2×C3⋊Dic3C2411yescharacteristic
280C4×C3⋊D3—24no—
281C4×C3⋊D3—42no—
282C3×#67C22×C4116yescomplemented
283C3×#67C22×C4116yescomplemented
284C2×C3×Dic3—42no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3C22×C418yescomplemented
287C2×C3×Dic3C2414yes—
288C2×C3×Dic3C2414yes—
289C2×C3×Dic3C2414yes—
290C3×C4×D3—44no—
291C3×C4×D3—44no—
292#627C22×C418yescomplemented
293#626C22×C4116yescomplemented
294#625C22×C418yescomplemented
295#624—42no—
296#624—42no—
297#624C22×C418yescomplemented
298D3×Dic3—28no—
299D3×Dic3—44no—
300D3×Dic3C22×C4116yescomplemented
301C2×H(5,𝔽2)—91no—
302#520—94no—
303#520—92no—
304#518—32no—
305#518—91no—
306#518—94no—
307#518—92no—
308C4×#41—94no—
309C4×#41—92no—
310C2×C4×D4—94no—
311C2×C4×D4—92no—
312C2×C4×D4—92no—
313C2×C4×D4—91no—
314C24×C3—21no—
315C24×C3—32no—
316C24×C3C22×D312yes—
317C23×D3—32no—
318C23×D3—34no—
319C23×D3—61no—
320C23×D3C22×D312yes—
321C2×C3×D4—316no—
322C2×C3×D4—34no—
323C2×C3×D4—34no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—32no—
327C22×C3×C4—32no—
328C22×C3×C4—32no—
329C22×C3×C4—34no—
330C22×C3×C4—34no—
331C22×C3×C4C22×D312yes—
332C22×C3×C4C22×D312yes—
333C2×#67—316no—
334C2×#67—34no—
335C2×#67—34no—
336C2×#67—34no—
337C2×#67—332no—
338C2×#67—34no—
339C2×#67—64no—
340C2×#67—68no—
341C2×#67C4×D3116yescomplemented
342C2×#67C22×D314yes—
343C2×#67C22×D314yes—
344C22×Dic3—32no—
345C22×Dic3—34no—
346C22×Dic3—32no—
347C22×Dic3—32no—
348C22×Dic3—32no—
349C22×Dic3—32no—
350C22×Dic3—32no—
351C22×Dic3—32no—
352C22×Dic3—34no—
353C22×Dic3—34no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—62no—
357C22×Dic3—62no—
358C22×Dic3—61no—
359C22×Dic3—124no—
360C22×Dic3—124no—
361C22×Dic3—124no—
362C22×Dic3C22×D312yes—
363C22×Dic3C22×D312yes—
364C22×Dic3C22×D312yes—
365#237—332no—
366#237—332no—
367D3×D4—332no—
368D3×D4—332no—
369#235—332no—
370C2×D12—34no—
371C2×C4×D3—34no—
372C2×C4×D3—34no—
373C2×C4×D3—34no—
374C2×C4×D3—34no—
375C2×C4×D3—34no—
376C2×C4×D3—34no—
377C2×C4×D3—34no—
378C2×C4×D3—34no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—128no—
382C2×C4×D3—124no—
383C2×C4×D3—124no—
384C2×C4×D3—124no—
385C2×C4×D3C22×D314yes—
386C2×C4×D3C22×D314yes—
387C2×Dic6—34no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C22⋊C4—24no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4C22×D314yes—
396C3×C22⋊C4C22×D314yes—
397C3×C42—34no—
398C3×C42—34no—
399#217—34no—
400#217—34no—
401#217C22×D314yes—
402#217C22×D314yes—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—64no—
410(C2×D3)⋊C4C22×D314yes—
411(C2×D3)⋊C4C22×D314yes—
412C4⋊Dic3—34no—
413C4⋊Dic3—34no—
414Dic3⋊C4—34no—
415Dic3⋊C4—34no—
416Dic3⋊C4—34no—
417Dic3⋊C4—34no—
418Dic3⋊C4—34no—
419Dic3⋊C4—34no—
420Dic3⋊C4—64no—
421Dic3⋊C4C22×D314yes—
422Dic3⋊C4C22×D314yes—
423C4×Dic3—34no—
424C4×Dic3—34no—
425C4×Dic3—34no—
426C4×Dic3—34no—
427C4×Dic3—34no—
428C4×Dic3—34no—
429C4×Dic3—34no—
430C4×Dic3—34no—
431C4×Dic3—62no—
432C4×Dic3—62no—
433C4×Dic3C22×D314yes—
434C4×Dic3C22×D314yes—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—44no—
440C22×C32C23×C414yes—
441C22×C32C23×C412yes—
442C22×C32C2511yescharacteristic
443C2×C3⋊D3—22no—
444C2×C3⋊D3—22no—
445C2×C3⋊D3—44no—
446C2×C3⋊D3C23×C414yes—
447C2×C3×D3—24no—
448C2×C3×D3—24no—
449C2×C3×D3—48no—
450C2×C3×D3C23×C418yes—
451D32—48no—
452C32×C4—22no—
453C32×C4—22no—
454C3⋊Dic3—21no—
455C3⋊Dic3—22no—
456C3⋊Dic3C23×C414yes—
457C3⋊Dic3H(5,𝔽2)12yescomplemented
458C3×Dic3—24no—
459C3×Dic3—24no—
460C3×Dic3C23×C418yes—
461H(5,𝔽2)—916no—
462C2×#41—94no—
463C2×#41—92no—
464C22×D4—32no—
465C22×D4—92no—
466C22×D4—94no—
467C22×D4—91no—
468C23×C4—92no—
469C23×C4—92no—
470C23×C4—91no—
471C23×C4—91no—
472C4×Q8—92no—
473C4×Q8—94no—
474C4×Q8—92no—
475C4×D4—34no—
476C4×D4—34no—
477C4×D4—34no—
478C4×D4—34no—
479C4×D4—94no—
480C4×D4—94no—
481C4×D4—92no—
482C4×D4—94no—
483C4×D4—94no—
484C4×D4—94no—
485C4×D4—94no—
486C4×D4—94no—
487C4×D4—94no—
488C4×D4—94no—
489C4×D4—94no—
490C4×D4—94no—
491C4×D4—92no—
492C4×D4—94no—
493C4×D4—94no—
494#117—34no—
495#117—94no—
496#117—94no—
497#117—92no—
498#117—94no—
499C2×C4⋊C4—92no—
500C2×C4⋊C4—94no—
501C2×C4⋊C4—92no—
502C2×C4⋊C4—91no—
503C2×C22⋊C4—32no—
504C2×C22⋊C4—34no—
505C2×C22⋊C4—92no—
506C2×C22⋊C4—92no—
507C2×C22⋊C4—94no—
508C2×C22⋊C4—92no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4D3211yescharacteristic, complemented
511C2×C42—92no—
512C2×C42—94no—
513C2×C42—92no—
514C2×C42—91no—
515C23×C3—21no—
516C23×C3—22no—
517C23×C3—24no—
518C23×C3—34no—
519C23×C3—38no—
520C23×C3—42no—
521C23×C3—42no—
522C23×C3—42no—
523C23×C3—42no—
524C23×C3—122no—
525C23×C3—122no—
526C23×C3C2×C4×D318yescomplemented
527C23×C3C23×D312yes—
528C23×C3C23×D312yes—
529C23×C3C23×D312yes—
530C22×D3—34no—
531C22×D3—38no—
532C22×D3—316no—
533C22×D3—42no—
534C22×D3—42no—
535C22×D3—64no—
536C22×D3—62no—
537C22×D3—124no—
538C22×D3—124no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3C2×C4×D318yescomplemented
544C22×D3C23×D314yes—
545C3×D4—316no—
546C3×D4—316no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—38no—
550C2×C3×C4—34no—
551C2×C3×C4—34no—
552C2×C3×C4—34no—
553C2×C3×C4—42no—
554C2×C3×C4—42no—
555C2×C3×C4—42no—
556C2×C3×C4—42no—
557C2×C3×C4—124no—
558C2×C3×C4—124no—
559C2×C3×C4—122no—
560C2×C3×C4—122no—
561C2×C3×C4C23×D314yes—
562C2×C3×C4C23×D314yes—
563#67—316no—
564#67—316no—
565#67—316no—
566#67—316no—
567#67—616no—
568#67C2×C4×D3116yescomplemented
569#67C2×C4×D3116yescomplemented
570C2×Dic3—38no—
571C2×Dic3—32no—
572C2×Dic3—34no—
573C2×Dic3—316no—
574C2×Dic3—32no—
575C2×Dic3—32no—
576C2×Dic3—32no—
577C2×Dic3—42no—
578C2×Dic3—42no—
579C2×Dic3—64no—
580C2×Dic3—62no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—62no—
584C2×Dic3—68no—
585C2×Dic3—64no—
586C2×Dic3—64no—
587C2×Dic3—64no—
588C2×Dic3—64no—
589C2×Dic3—124no—
590C2×Dic3—124no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3—122no—
594C2×Dic3—124no—
595C2×Dic3—122no—
596C2×Dic3C2×C4×D318yescomplemented
597C2×Dic3C23×D314yes—
598C2×Dic3C23×D314yes—
599C2×Dic3C23×D314yes—
600D12—316no—
601C4×D3—316no—
602C4×D3—316no—
603C4×D3—44no—
604C4×D3—44no—
605C4×D3—68no—
606C4×D3—68no—
607C4×D3—124no—
608C4×D3—124no—
609C4×D3—124no—
610C4×D3—124no—
611C4×D3—124no—
612C4×D3—124no—
613Dic6—316no—
614C2×C32—22no—
615C2×C32—24no—
616C2×C32C24×C411yescharacteristic
617C2×C32C2×H(5,𝔽2)11yescharacteristic
618C2×C32#58511yescharacteristic
619C3⋊D3—24no—
620C3×D3—28no—
621C24—32no—
622C24—92no—
623C24—91no—
624C24C2×D3211yescharacteristic
625#41—932no—
626#41—916no—
627C2×Q8—92no—
628C2×D4—34no—
629C2×D4—34no—
630C2×D4—316no—
631C2×D4—94no—
632C2×D4—916no—
633C2×D4—932no—
634C2×D4—92no—
635C2×D4—94no—
636C2×D4—98no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—34no—
641C22×C4—34no—
642C22×C4—92no—
643C22×C4—92no—
644C22×C4—92no—
645C22×C4—94no—
646C22×C4—94no—
647C22×C4—94no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—92no—
651C22×C4—91no—
652C22×C4—92no—
653C22×C4—92no—
654C22×C4—92no—
655C22×C4—362no—
656C22×C4—364no—
657C22×C4—364no—
658C22×C4—362no—
659C22×C4C2×D3211yescharacteristic
660C22×C4C2×D3211yescharacteristic
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—92no—
664C4⋊C4—94no—
665C4⋊C4—94no—
666C4⋊C4—92no—
667C4⋊C4—94no—
668C22⋊C4—34no—
669C22⋊C4—34no—
670C22⋊C4—34no—
671C22⋊C4—34no—
672C22⋊C4—94no—
673C22⋊C4—94no—
674C22⋊C4—94no—
675C22⋊C4—94no—
676C22⋊C4C2×D3214yes—
677C42—34no—
678C42—34no—
679C42—94no—
680C42—94no—
681C42—94no—
682C42—92no—
683C42—92no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—24no—
694C22×C3—21no—
695C22×C3—38no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—48no—
699C22×C3—48no—
700C22×C3—64no—
701C22×C3—64no—
702C22×C3—128no—
703C22×C3C22×C4×D314yes—
704C22×C3C22×C4×D314yes—
705C22×C3C22×C4×D314yes—
706C22×C3C24×D312yes—
707C2×D3—24no—
708C2×D3—24no—
709C2×D3—38no—
710C2×D3—48no—
711C2×D3—64no—
712C2×D3—64no—
713C2×D3—64no—
714C2×D3—122no—
715C2×D3—122no—
716C2×D3—1216no—
717C2×D3—128no—
718C2×D3—128no—
719C2×D3C22×C4×D318yes—
720C3×C4—24no—
721C3×C4—24no—
722C3×C4—38no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—64no—
726C3×C4—64no—
727Dic3—24no—
728Dic3—24no—
729Dic3—38no—
730Dic3—34no—
731Dic3—62no—
732Dic3—64no—
733Dic3—62no—
734Dic3—62no—
735Dic3—62no—
736Dic3—62no—
737Dic3—122no—
738Dic3C22×C4×D318yes—
739C32C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
740C23—34no—
741C23—38no—
742C23—41no—
743C23—41no—
744C23—98no—
745C23—92no—
746C23—94no—
747C23—122no—
748C23—122no—
749C23—361no—
750C23—361no—
751C23—362no—
752C23—362no—
753C23C4×D3214yescomplemented
754C23C22×D3211yescharacteristic
755C23C22×D3212yes—
756Q8—98no—
757D4—316no—
758D4—316no—
759D4—916no—
760D4—98no—
761D4—916no—
762C2×C4—38no—
763C2×C4—34no—
764C2×C4—34no—
765C2×C4—34no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—98no—
769C2×C4—916no—
770C2×C4—94no—
771C2×C4—91no—
772C2×C4—92no—
773C2×C4—91no—
774C2×C4—92no—
775C2×C4—124no—
776C2×C4—124no—
777C2×C4—122no—
778C2×C4—122no—
779C2×C4—184no—
780C2×C4—188no—
781C2×C4—182no—
782C2×C4—184no—
783C2×C4—362no—
784C2×C4—362no—
785C2×C4—362no—
786C2×C4—364no—
787C2×C4—362no—
788C2×C4—361no—
789C2×C4C22×D3212yes—
790C2×C4C22×D3212yes—
791C2×C3—24no—
792C2×C3—24no—
793C2×C3—24no—
794C2×C3—24no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—44no—
799C2×C3—68no—
800C2×C3C23×C4×D312yes—
801C2×C3D3×H(5,𝔽2)12yes—
802C2×C3#596612yes—
803D3—28no—
804D3—68no—
805D3—124no—
806C22—21no—
807C22—22no—
808C22—21no—
809C22—22no—
810C22—38no—
811C22—44no—
812C22—64no—
813C22—64no—
814C22—94no—
815C22—128no—
816C22—182no—
817C22—182no—
818C22—364no—
819C22—368no—
820C22C2×C4×D3214yes—
821C22C2×C4×D3212yes—
822C22C23×D3211yescharacteristic
823C4—22no—
824C4—22no—
825C4—38no—
826C4—64no—
827C4—64no—
828C4—94no—
829C4—92no—
830C4—181no—
831C4—182no—
832C3—21no—
833C3#8585712yescomplemented
834C2—24no—
835C2—22no—
836C2—68no—
837C2—184no—
838C2C22×C4×D3211yescharacteristic
839C2#1059667511yescharacteristic
840C2#1059667911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC22×C32C25
prime radicalC2×#64330C2
hypercenterC2×C22⋊C4D32
hypocenterC32C4×H(5,𝔽2)
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#64090C2semidirect
3. C3×#5486C2semidirect
4. #10595510C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. #10595058C2semidirect
7. C4×#3811C2semidirect
8. #10594876C2semidirect
9. C4×#3805C2semidirect
10. #10594254C2semidirect
11. D3×#67⋊C4C2semidirect
12. #10594049C2semidirect
13. #10594048C2semidirect
16. C23×C3⋊Dic3C22semidirect
17. C22×C4×C3⋊D3C22semidirect
19. #64330C4semidirect
24. C22×D3×Dic3C22semidirect
25. C2×C4×D32C22semidirect
26. C2×C32×C22⋊C4C22semidirect
27. C2×#3752C22semidirect
28. C2×#3750C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
30. #64090C22semidirect
31. #64090C22semidirect
32. C2×C3×#217C22semidirect
33. C3×C4×#67C22semidirect
34. C3×C4×#67C22semidirect
35. C3×#67⋊C4C22semidirect
36. C3×#67⋊C4C22semidirect
37. C3×D3×C22⋊C4C22semidirect
38. C3×#877C22semidirect
39. #63974C22semidirect
40. #67⋊Dic3C22semidirect
41. #67⋊Dic3C22semidirect
42. #67⋊Dic3C22semidirect
43. #67⋊Dic3C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. #63957C22semidirect
47. C2×Dic32C22semidirect
48. #63952C22semidirect
49. #63952C22semidirect
50. #63921C22semidirect
51. D3×(C2×D3)⋊C4C22semidirect
52. C4×#627C22semidirect
53. #63904C22semidirect
54. C4×#626C22semidirect
55. #63902C22semidirect
56. C4×#625C22semidirect
57. #63883C22semidirect
58. C4×#624C22semidirect
59. #63881C22semidirect
60. #63880C22semidirect
61. #63879C22semidirect
62. #63878C22semidirect
63. #63877C22semidirect
64. D3×Dic3⋊C4C22semidirect
65. C4×D3×Dic3C22semidirect
66. #63838C22semidirect
67. #63837C22semidirect
68. #63836C22semidirect
84. #5486D3semidirect
95. C2×#638C2×C4semidirect
106. C2×C3×#67C2×C4semidirect
114. #3811C2×C4semidirect
115. D3×#67C2×C4semidirect
122. #3805C2×C4semidirect
123. #3804C2×C4semidirect
179. C2×C3×C22⋊C4C2×D3semidirect
181. C2×#217C2×D3semidirect
192. C4×#67C2×D3semidirect
193. C4×#67C2×D3semidirect
232. #67⋊C4C2×D3semidirect
233. #67⋊C4C2×D3semidirect
237. D3×C22⋊C4C2×D3semidirect
241. #877C2×D3semidirect
252. C23×C32C22×C4semidirect
257. C22×C3⋊D3C22×C4semidirect
261. C22×C3×D3C22×C4semidirect
265. C2×D32C22×C4semidirect
270. #638C22×C4semidirect
275. C2×C3⋊Dic3C22×C4semidirect
282. C3×#67C22×C4semidirect
283. C3×#67C22×C4semidirect
286. C2×C3×Dic3C22×C4semidirect
292. #627C22×C4semidirect
293. #626C22×C4semidirect
294. #625C22×C4semidirect
297. #624C22×C4semidirect
300. D3×Dic3C22×C4semidirect
341. C2×#67C4×D3semidirect
457. C3⋊Dic3H(5,𝔽2)semidirect
510. C2×C22⋊C4D32semidirect
526. C23×C3C2×C4×D3semidirect
543. C22×D3C2×C4×D3semidirect
568. #67C2×C4×D3semidirect
569. #67C2×C4×D3semidirect
596. C2×Dic3C2×C4×D3semidirect
739. C32C4×H(5,𝔽2)semidirect
753. C23C4×D32semidirect
833. C3#85857semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C2×#640902
C3×#54862
#105955102
C2×#67⋊Dic32
#105950582
C4×#38112
#105948762
C4×#38052
#105942542
D3×#67⋊C42
#105940492
#105940482
#858573