Finite Group Databasebeta

← C2×D3×#918 #11918700

Subgroups — C2×D3×#918 #11918700

Order 1152.

3057 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic
2C2×D32×Q8C211yesmaximal, characteristic, complemented
3C2×#64127C211yesmaximal, characteristic, complemented
4C2×C3×#918C211yesmaximal, characteristic, complemented
5C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
6C2×#63951C211yesmaximal, characteristic, complemented
7C2×#63948C211yesmaximal, characteristic, complemented
8C2×#63945C211yesmaximal, characteristic, complemented
9C2×#63943C211yesmaximal, characteristic, complemented
10C2×D3×#216C211yesmaximal, characteristic, complemented
11C2×D3×#215C211yesmaximal, characteristic, complemented
12D3×#918C2116yesmaximal, direct product factor
13C2×#63811C211yesmaximal, characteristic, complemented
14C2×#63801C211yesmaximal, characteristic, complemented
15C2×D3×#204C211yesmaximal, characteristic, complemented
16C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
17C2×D3×#137—31nomaximal
18C22×#918—31nomaximal
19C2×#3832C2211yescharacteristic
20C2×Q8×C3⋊D3C2211yescharacteristic, complemented
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×D3×Q8C2211yescharacteristic
24C2×C3×D3×Q8C2211yescharacteristic, complemented
25D3×#239—24no—
26D3×#239C2218yes—
27D32×Q8—24no—
28D32×Q8C2218yescomplemented
29C2×D3×D12—21no—
30C2×D3×D12C2211yescharacteristic
31C2×C4×D32—21no—
32C2×C4×D32—21no—
33C2×C4×D32C2211yescharacteristic
34C2×#3799—21no—
35C2×#3799C2211yescharacteristic
36C2×#3797—21no—
37C2×#3797C2211yescharacteristic, complemented
38C2×#3796—21no—
39C2×#3796C2211yescharacteristic
40C2×D3×Dic6—21no—
41C2×D3×Dic6—21no—
42C2×D3×Dic6C2211yescharacteristic
43C2×D3×Dic6C2211yescharacteristic, complemented
44C2×C32×Q16C2211yescharacteristic, complemented
45C2×#3756C2211yescharacteristic, complemented
46C2×#3755C2211yescharacteristic, complemented
47#64127C2218yescomplemented
48C2×#3744C2211yescharacteristic, complemented
49C2×#3743C2211yescharacteristic, complemented
50C2×C3×#216C2211yescharacteristic, complemented
51C2×C3×#216C2211yescharacteristic, complemented
52C2×C3×#216C2211yescharacteristic, complemented
53C2×C3×#215C2211yescharacteristic, complemented
54C3×#918C2218yescomplemented
55C3×D3×Q16C2218yescomplemented
56C2×C3×Dic12C2211yescharacteristic, complemented
57C2×C3×#204C2211yescharacteristic, complemented
58C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
59C2×C3×D3×C8C2211yescharacteristic
60#63951C2218yescomplemented
61#63948C2218yescomplemented
62#63945C2218yescomplemented
63#63943C2218yescomplemented
64D3×#216C2218yescomplemented
65D3×#215C2218yescomplemented
66C2×#3719C2211yescharacteristic, complemented
67C2×#3718C2211yescharacteristic, complemented
68C2×#3717C2211yescharacteristic, complemented
69C2×#3717C2211yescharacteristic, complemented
70C2×#3716C2211yescharacteristic, complemented
71C2×#3715C2211yescharacteristic, complemented
72C2×#3712C2211yescharacteristic, complemented
73C2×#3711C2211yescharacteristic, complemented
74C2×D3×C3⋊C8C2211yescharacteristic
75#63811C2218yescomplemented
76#63801C2218yescomplemented
77D3×#204C2218yescomplemented
78D3×ΓL(1,𝔽25)C2218yescomplemented
79C2×D3×#41—31no—
80C22×#239—31no—
81C22×D3×Q8—31no—
82C22×D3×Q8—31no—
83C2×C3×#137—31no—
84C22×C3×Q16—31no—
85C2×#951—31no—
86C22×#216—31no—
87C2×#942—31no—
88C22×#215—31no—
89D3×#137—316no—
90C2×#918—31no—
91C2×#918—31no—
92C2×#918—31no—
93C2×#918—31no—
94C2×#918—31no—
95C2×#918—31no—
96C2×#918—31no—
97C2×#918—316no—
98C2×#918—31no—
99C2×#918—31no—
100C2×#918—61no—
101C2×#918D311yescharacteristic, direct product factor
102C2×D3×Q16—31no—
103C2×D3×Q16D311yescharacteristic, complemented
104C2×#915—31no—
105C2×#915—31no—
106C2×D3×SD16—31no—
107C2×D3×SD16—31no—
108C2×#909—31no—
109C2×D3×M16—31no—
110C22×#204—31no—
111C22×ΓL(1,𝔽25)—31no—
112C22×D32—21no—
113C22×D32D411yescharacteristic
114C2×C32×Q8C2311yescharacteristic
115C2×C32×Q8C2311yescharacteristic
116#3832—22no—
117#3832C2314yes—
118Q8×C3⋊D3—22no—
119Q8×C3⋊D3C2314yescomplemented
120C2×C4⋊(C3⋊D3)—21no—
121C2×C4⋊(C3⋊D3)C2311yescharacteristic
122C2×C4×C3⋊D3—21no—
123C2×C4×C3⋊D3—21no—
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×#634—21no—
126C2×#634C2311yescharacteristic
127C3×#239—22no—
128C3×#239C2314yes—
129C3×D3×Q8—22no—
130C3×D3×Q8—22no—
131C3×D3×Q8—22no—
132C3×D3×Q8C2314yes—
133C3×D3×Q8C2314yes—
134C3×D3×Q8C2314yescomplemented
135C2×C3×D12—21no—
136C2×C3×D12C2311yescharacteristic
137C2×C3×C4×D3—21no—
138C2×C3×C4×D3—21no—
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—21no—
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×Dic6—21no—
144C2×C3×Dic6—21no—
145C2×C3×Dic6—21no—
146C2×C3×Dic6C2311yescharacteristic
147C2×C3×Dic6C2311yescharacteristic
148C2×C3×Dic6C2311yescharacteristic
149C2×#627—21no—
150C2×#627—21no—
151C2×#627—21no—
152C2×#626—21no—
153C2×#626—21no—
154C2×#626—21no—
155C2×#624—21no—
156C2×#624—21no—
157C2×#624D411yescharacteristic
158C2×D3×Dic3—21no—
159C2×D3×Dic3—21no—
160C2×D3×Dic3—21no—
161C2×D3×Dic3D411yescharacteristic
162C2×D3×Dic3D411yescharacteristic
163D3×D12—28no—
164D3×D12—22no—
165D3×D12C2314yes—
166C4×D32—28no—
167C4×D32—28no—
168C4×D32D414yes—
169C4×D32C2314yes—
170#3799—22no—
171#3799—28no—
172#3799C2314yes—
173#3797—22no—
174#3797—28no—
175#3797C2314yescomplemented
176#3796—22no—
177#3796—28no—
178#3796C2314yes—
179D3×Dic6—22no—
180D3×Dic6—22no—
181D3×Dic6—28no—
182D3×Dic6—28no—
183D3×Dic6C2314yes—
184D3×Dic6C2314yescomplemented
185C32×Q16C2314yescomplemented
186C2×C32×C8C2311yescharacteristic
187#3756C2314yescomplemented
188#3755C2314yescomplemented
189C2×C3⋊(C3⋊C8)C2311yescharacteristic
190#3744C2314yescomplemented
191#3743C2314yescomplemented
192C3×#216C2314yescomplemented
193C3×#216C2314yescomplemented
194C3×#216C2314yescomplemented
195C3×#215C2314yescomplemented
196C2×C3×C3⋊C8C2311yescharacteristic
197C2×C3×C3⋊C8C2311yescharacteristic
198C3×Dic12C2314yescomplemented
199C3×#204C2314yescomplemented
200C3×ΓL(1,𝔽25)C2314yescomplemented
201C3×D3×C8C2314yes—
202#3719C2314yescomplemented
203#3718C2314yescomplemented
204#3717C2314yescomplemented
205#3717C2314yescomplemented
206#3716C2314yescomplemented
207#3715C2314yescomplemented
208#3712C2314yescomplemented
209#3711C2314yescomplemented
210D3×C3⋊C8C2314yes—
211C22×#137—91noSylow
212C2×C3×#41—31no—
213C22×C3×Q8—31no—
214C22×C3×Q8—31no—
215C22×C3×Q8—31no—
216D3×#41—38no—
217D3×#41—64no—
218C2×#239—31no—
219C2×#239—31no—
220C2×#239—38no—
221C2×#239—31no—
222C2×#239—31no—
223C2×#239—61no—
224C2×#239—61no—
225C2×#239—61no—
226C2×#239—64no—
227C2×#239C2×D311yescharacteristic
228C2×D3×Q8—31no—
229C2×D3×Q8—31no—
230C2×D3×Q8—38no—
231C2×D3×Q8—38no—
232C2×D3×Q8—31no—
233C2×D3×Q8—31no—
234C2×D3×Q8—31no—
235C2×D3×Q8—31no—
236C2×D3×Q8—61no—
237C2×D3×Q8—61no—
238C2×D3×Q8—61no—
239C2×D3×Q8—61no—
240C2×D3×Q8—61no—
241C2×D3×Q8—64no—
242C2×D3×Q8—64no—
243C2×D3×Q8C2×D311yescharacteristic
244C2×D3×Q8C2×D311yescharacteristic
245C2×D3×Q8C2×D311yescharacteristic, complemented
246C2×#237—31no—
247C2×#237—61no—
248C2×D3×D4—31no—
249C2×D3×D4—61no—
250C2×#235—31no—
251C2×#235—61no—
252C22×D12—31no—
253C22×D12—61no—
254C22×C4×D3—31no—
255C22×C4×D3—31no—
256C22×C4×D3—61no—
257C22×C4×D3—61no—
258C22×C4×D3—61no—
259C22×C4×D3—61no—
260C22×Dic6—31no—
261C22×Dic6—31no—
262C22×Dic6—61no—
263C22×Dic6—61no—
264C3×#137—38no—
265C2×C3×Q16—21no—
266C2×C3×Q16—31no—
267C2×C3×Q16—31no—
268C2×C3×Q16—31no—
269C2×C3×Q16—38no—
270C2×C3×Q16—31no—
271C2×C3×Q16C2×D311yescharacteristic, complemented
272C2×C3×Q16C2×D311yescharacteristic, complemented
273C2×C3×SD16—31no—
274C2×C3×SD16—31no—
275C2×C3×M16—31no—
276C22×C3×C8—31no—
277#951—38no—
278C2×#216—31no—
279C2×#216—31no—
280C2×#216—31no—
281C2×#216—31no—
282C2×#216—38no—
283C2×#216—31no—
284C2×#216—61no—
285C2×#216C2×D311yescharacteristic, complemented
286C2×#216C2×D311yescharacteristic, complemented
287C2×#216C2×D311yescharacteristic, complemented
288#942—38no—
289C2×#215—31no—
290C2×#215—31no—
291C2×#215—31no—
292C2×#215—38no—
293C2×#215—31no—
294C2×#215—31no—
295C2×#215—61no—
296C2×#215C2×D311yescharacteristic, complemented
297C2×#214—31no—
298C2×#214—31no—
299C2×#208—31no—
300C22×C3⋊C8—31no—
301#918—38no—
302#918—38no—
303#918—38no—
304#918—38no—
305#918—38no—
306#918—38no—
307#918—38no—
308#918—38no—
309#918—38no—
310#918—68no—
311#918C2×D318yesdirect product factor
312D3×Q16—38no—
313D3×Q16C2×D318yescomplemented
314#915—38no—
315#915—38no—
316D3×SD16—38no—
317D3×SD16—38no—
318#909—38no—
319D3×M16—38no—
320C2×Dic12—31no—
321C2×Dic12C2×D311yescharacteristic, complemented
322C2×#204—31no—
323C2×#204—31no—
324C2×#204—31no—
325C2×#204—31no—
326C2×#204—31no—
327C2×#204—38no—
328C2×#204—61no—
329C2×#204C2×D311yescharacteristic, complemented
330C2×ΓL(1,𝔽25)—31no—
331C2×ΓL(1,𝔽25)—31no—
332C2×ΓL(1,𝔽25)—31no—
333C2×ΓL(1,𝔽25)—31no—
334C2×ΓL(1,𝔽25)—31no—
335C2×ΓL(1,𝔽25)—38no—
336C2×ΓL(1,𝔽25)—61no—
337C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
338C2×D3×C8—31no—
339C2×D3×C8C2×D311yescharacteristic
340C22×C3⋊D3—21no—
341C22×C3⋊D3C2×D411yescharacteristic
342C22×C3×D3—21no—
343C22×C3×D3C2×D411yescharacteristic
344C22×C3×D3C2×D411yescharacteristic
345C2×D32—24no—
346C2×D32—24no—
347C2×D32—44no—
348C2×D32C2×D414yes—
349C32×Q8—21no—
350C32×Q8—21no—
351C32×Q8C2412yes—
352C32×Q8C2412yes—
353C2×C32×C4—21no—
354C2×C32×C4—21no—
355C2×C32×C4C2411yescharacteristic
356C2×C3⋊Dic3—21no—
357C2×C3⋊Dic3C2×D411yescharacteristic
358C4⋊(C3⋊D3)—24no—
359C4⋊(C3⋊D3)—21no—
360C4⋊(C3⋊D3)C2412yes—
361C4×C3⋊D3—24no—
362C4×C3⋊D3—24no—
363C4×C3⋊D3C2×D412yes—
364C4×C3⋊D3C2412yes—
365#634—21no—
366#634—24no—
367#634C2412yes—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3C2×D411yescharacteristic
372C2×C3×Dic3C2×D411yescharacteristic
373C3×D12—24no—
374C3×D12—21no—
375C3×D12C2412yes—
376C3×C4×D3—24no—
377C3×C4×D3—24no—
378C3×C4×D3—24no—
379C3×C4×D3—24no—
380C3×C4×D3C2×D412yes—
381C3×C4×D3C2×D412yes—
382C3×C4×D3C2412yes—
383C3×C4×D3C2412yes—
384C3×Dic6—21no—
385C3×Dic6—21no—
386C3×Dic6—21no—
387C3×Dic6—24no—
388C3×Dic6—24no—
389C3×Dic6—24no—
390C3×Dic6C2412yes—
391C3×Dic6C2412yes—
392C3×Dic6C2412yes—
393#627—24no—
394#627—24no—
395#627—24no—
396#626—24no—
397#626—24no—
398#626—24no—
399#624—24no—
400#624—24no—
401#624C2×D414yes—
402D3×Dic3—24no—
403D3×Dic3—24no—
404D3×Dic3—24no—
405D3×Dic3C2×D414yes—
406D3×Dic3C2×D414yes—
407C32×C8C2412yes—
408C3⋊(C3⋊C8)C2412yes—
409C3×C3⋊C8C2412yes—
410C3×C3⋊C8C2412yes—
411C22×#41—91no—
412C23×Q8—91no—
413C2×#137—31no—
414C2×#137—91no—
415C2×#137—91no—
416C2×#137—91no—
417C2×#137—91no—
418C2×#137—916no—
419C2×#137—91no—
420C2×#137—91no—
421C2×#137—91no—
422C22×Q16—31no—
423C22×Q16—91no—
424C22×SD16—91no—
425C22×SD16—91no—
426C22×M16—91no—
427C23×D3—31no—
428C23×D3—31no—
429C23×D3—61no—
430C23×D3—61no—
431C3×#41—34no—
432C3×#41—62no—
433C2×C3×Q8—21no—
434C2×C3×Q8—21no—
435C2×C3×Q8—34no—
436C2×C3×Q8—34no—
437C2×C3×Q8—34no—
438C2×C3×Q8—31no—
439C2×C3×Q8—31no—
440C2×C3×Q8—31no—
441C2×C3×Q8—61no—
442C2×C3×Q8—61no—
443C2×C3×Q8—61no—
444C2×C3×Q8—62no—
445C2×C3×Q8—62no—
446C2×C3×Q8—62no—
447C2×C3×Q8C22×D311yescharacteristic
448C2×C3×Q8C22×D311yescharacteristic
449C2×C3×Q8C22×D311yescharacteristic
450C2×C3×Q8C22×D311yescharacteristic
451C2×C3×D4—31no—
452C2×C3×D4—61no—
453C22×C3×C4—31no—
454C22×C3×C4—31no—
455C22×C3×C4—61no—
456C22×C3×C4—61no—
457C22×C3×C4—61no—
458C22×C3×C4—61no—
459C2×#67—61no—
460C2×#67—61no—
461C2×#67—61no—
462C22×Dic3—31no—
463C22×Dic3—31no—
464C22×Dic3—61no—
465C22×Dic3—61no—
466C22×Dic3—61no—
467#239—22no—
468#239—34no—
469#239—34no—
470#239—34no—
471#239—34no—
472#239—64no—
473#239—68no—
474#239—68no—
475#239—62no—
476#239—62no—
477#239—62no—
478#239—62no—
479#239—122no—
480#239C22×D314yes—
481D3×Q8—22no—
482D3×Q8—22no—
483D3×Q8—22no—
484D3×Q8—34no—
485D3×Q8—34no—
486D3×Q8—34no—
487D3×Q8—34no—
488D3×Q8—34no—
489D3×Q8—34no—
490D3×Q8—64no—
491D3×Q8—62no—
492D3×Q8—62no—
493D3×Q8—68no—
494D3×Q8—68no—
495D3×Q8—68no—
496D3×Q8—68no—
497D3×Q8—62no—
498D3×Q8—62no—
499D3×Q8—62no—
500D3×Q8—62no—
501D3×Q8—122no—
502D3×Q8C22×D314yes—
503D3×Q8C22×D314yes—
504D3×Q8C22×D314yescomplemented
505#237—34no—
506#237—62no—
507#237—68no—
508D3×D4—34no—
509D3×D4—68no—
510D3×D4—62no—
511#235—34no—
512#235—68no—
513#235—62no—
514C2×D12—21no—
515C2×D12—31no—
516C2×D12—31no—
517C2×D12—34no—
518C2×D12—61no—
519C2×D12—62no—
520C2×D12—68no—
521C2×D12—61no—
522C2×D12—61no—
523C2×D12—61no—
524C2×D12—61no—
525C2×D12—61no—
526C2×D12—121no—
527C2×D12C22×D311yescharacteristic
528C2×C4×D3—21no—
529C2×C4×D3—21no—
530C2×C4×D3—21no—
531C2×C4×D3—21no—
532C2×C4×D3—31no—
533C2×C4×D3—31no—
534C2×C4×D3—31no—
535C2×C4×D3—31no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—34no—
539C2×C4×D3—34no—
540C2×C4×D3—34no—
541C2×C4×D3—34no—
542C2×C4×D3—61no—
543C2×C4×D3—68no—
544C2×C4×D3—68no—
545C2×C4×D3—68no—
546C2×C4×D3—68no—
547C2×C4×D3—61no—
548C2×C4×D3—61no—
549C2×C4×D3—61no—
550C2×C4×D3—61no—
551C2×C4×D3—61no—
552C2×C4×D3—61no—
553C2×C4×D3—61no—
554C2×C4×D3—61no—
555C2×C4×D3—61no—
556C2×C4×D3—61no—
557C2×C4×D3—61no—
558C2×C4×D3—121no—
559C2×C4×D3—121no—
560C2×C4×D3C22×D311yescharacteristic
561C2×C4×D3C22×D311yescharacteristic
562C2×Dic6—21no—
563C2×Dic6—21no—
564C2×Dic6—21no—
565C2×Dic6—31no—
566C2×Dic6—31no—
567C2×Dic6—34no—
568C2×Dic6—34no—
569C2×Dic6—61no—
570C2×Dic6—68no—
571C2×Dic6—68no—
572C2×Dic6—62no—
573C2×Dic6—62no—
574C2×Dic6—61no—
575C2×Dic6—61no—
576C2×Dic6—61no—
577C2×Dic6—61no—
578C2×Dic6—61no—
579C2×Dic6—61no—
580C2×Dic6—61no—
581C2×Dic6—61no—
582C2×Dic6—121no—
583C2×Dic6C22×D311yescharacteristic
584C2×Dic6C22×D311yescharacteristic
585C2×Dic6C22×D311yescharacteristic
586C3×Q16—24no—
587C3×Q16—34no—
588C3×Q16—34no—
589C3×Q16—34no—
590C3×Q16—34no—
591C3×Q16C22×D314yescomplemented
592C3×Q16C22×D314yescomplemented
593C3×SD16—34no—
594C3×SD16—34no—
595C3×M16—34no—
596C2×C3×C8—21no—
597C2×C3×C8—31no—
598C2×C3×C8—31no—
599C2×C3×C8—34no—
600C2×C3×C8C22×D311yescharacteristic
601C2×C3×C8C22×D311yescharacteristic
602#216—34no—
603#216—34no—
604#216—34no—
605#216—34no—
606#216—34no—
607#216—64no—
608#216C22×D314yescomplemented
609#216C22×D314yescomplemented
610#216C22×D314yescomplemented
611#215—34no—
612#215—34no—
613#215—34no—
614#215—34no—
615#215—34no—
616#215—64no—
617#215C22×D314yescomplemented
618#214—34no—
619#214—34no—
620#208—34no—
621C2×C3⋊C8—31no—
622C2×C3⋊C8—31no—
623C2×C3⋊C8—34no—
624C2×C3⋊C8—61no—
625C2×C3⋊C8C22×D311yescharacteristic
626C2×C3⋊C8C22×D311yescharacteristic
627Dic12—34no—
628Dic12C22×D314yescomplemented
629#204—34no—
630#204—34no—
631#204—34no—
632#204—34no—
633#204—34no—
634#204—64no—
635#204C22×D314yescomplemented
636ΓL(1,𝔽25)—34no—
637ΓL(1,𝔽25)—34no—
638ΓL(1,𝔽25)—34no—
639ΓL(1,𝔽25)—34no—
640ΓL(1,𝔽25)—34no—
641ΓL(1,𝔽25)—64no—
642ΓL(1,𝔽25)C22×D314yescomplemented
643D3×C8—34no—
644D3×C8C22×D314yes—
645C22×C32C22×D411yescharacteristic
646C2×C3⋊D3—22no—
647C2×C3⋊D3—22no—
648C2×C3⋊D3—42no—
649C2×C3⋊D3C22×D412yes—
650C2×C3×D3—22no—
651C2×C3×D3—22no—
652C2×C3×D3—42no—
653C2×C3×D3#13714yescomplemented
654C2×C3×D3C22×D412yes—
655C2×C3×D3C22×D412yes—
656D32—28no—
657D32—48no—
658C32×C4—22no—
659C32×C4—22no—
660C32×C4C22×D411yescharacteristic
661C32×C4C2511yescharacteristic
662C3⋊Dic3—22no—
663C3⋊Dic3C22×D412yes—
664C3×Dic3—22no—
665C3×Dic3—22no—
666C3×Dic3—22no—
667C3×Dic3C22×D412yes—
668C3×Dic3C22×D412yes—
669C2×#41—31no—
670C2×#41—91no—
671C2×#41—91no—
672C2×#41—98no—
673C2×#41—91no—
674C2×#41—181no—
675C2×#41—181no—
676C2×#41—184no—
677C22×Q8—31no—
678C22×Q8—31no—
679C22×Q8—31no—
680C22×Q8—91no—
681C22×Q8—91no—
682C22×Q8—98no—
683C22×Q8—91no—
684C22×Q8—91no—
685C22×Q8—181no—
686C22×Q8—181no—
687C22×Q8—181no—
688C22×Q8—184no—
689C22×D4—91no—
690C22×D4—181no—
691C23×C4—91no—
692C23×C4—181no—
693C23×C4—181no—
694#137—38no—
695#137—98no—
696#137—98no—
697#137—98no—
698#137—98no—
699#137—98no—
700#137—98no—
701#137—98no—
702C2×Q16—31no—
703C2×Q16—31no—
704C2×Q16—31no—
705C2×Q16—38no—
706C2×Q16—31no—
707C2×Q16—91no—
708C2×Q16—98no—
709C2×Q16—91no—
710C2×Q16—91no—
711C2×Q16D3211yescharacteristic, complemented
712C2×SD16—31no—
713C2×SD16—31no—
714C2×SD16—98no—
715C2×SD16—91no—
716C2×SD16—91no—
717C2×SD16—91no—
718C2×SD16—98no—
719C2×SD16—91no—
720C2×SD16—91no—
721C2×SD16—91no—
722C2×M16—31no—
723C2×M16—91no—
724C2×M16—98no—
725C2×M16—91no—
726C2×M16—91no—
727C22×C8—31no—
728C22×C8—91no—
729C23×C3—31no—
730C23×C3—31no—
731C23×C3—61no—
732C22×D3—21no—
733C22×D3—31no—
734C22×D3—31no—
735C22×D3—34no—
736C22×D3—34no—
737C22×D3—61no—
738C22×D3—64no—
739C22×D3—64no—
740C22×D3—64no—
741C22×D3—61no—
742C22×D3—61no—
743C22×D3—64no—
744C22×D3—121no—
745C22×D3—124no—
746C22×D3—124no—
747C22×D3D3×D411yescharacteristic
748C22×D3D3×D411yescharacteristic
749C3×Q8—21no—
750C3×Q8—21no—
751C3×Q8—21no—
752C3×Q8—21no—
753C3×Q8—22no—
754C3×Q8—22no—
755C3×Q8—32no—
756C3×Q8—32no—
757C3×Q8—32no—
758C3×Q8—41no—
759C3×Q8—41no—
760C3×Q8—64no—
761C3×Q8—64no—
762C3×Q8—64no—
763C3×Q8—61no—
764C3×Q8—61no—
765C3×Q8—61no—
766C3×Q8C23×D312yes—
767C3×Q8C23×D312yes—
768C3×Q8C23×D312yes—
769C3×Q8C23×D312yes—
770C3×D4—32no—
771C3×D4—64no—
772C3×D4—61no—
773C2×C3×C4—21no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—31no—
779C2×C3×C4—31no—
780C2×C3×C4—32no—
781C2×C3×C4—32no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—41no—
785C2×C3×C4—41no—
786C2×C3×C4—64no—
787C2×C3×C4—64no—
788C2×C3×C4—64no—
789C2×C3×C4—64no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—61no—
793C2×C3×C4C23×D311yescharacteristic
794C2×C3×C4C23×D311yescharacteristic
795#67—64no—
796#67—64no—
797#67—64no—
798C2×Dic3—21no—
799C2×Dic3—21no—
800C2×Dic3—21no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—34no—
804C2×Dic3—34no—
805C2×Dic3—61no—
806C2×Dic3—64no—
807C2×Dic3—64no—
808C2×Dic3—64no—
809C2×Dic3—61no—
810C2×Dic3—61no—
811C2×Dic3—121no—
812C2×Dic3D3×D411yescharacteristic
813C2×Dic3D3×D411yescharacteristic
814D12—24no—
815D12—21no—
816D12—32no—
817D12—32no—
818D12—62no—
819D12—64no—
820D12—64no—
821D12—64no—
822D12—64no—
823D12—64no—
824D12—61no—
825D12—61no—
826D12—121no—
827D12—124no—
828D12C23×D312yes—
829C4×D3—24no—
830C4×D3—24no—
831C4×D3—24no—
832C4×D3—24no—
833C4×D3—34no—
834C4×D3—34no—
835C4×D3—32no—
836C4×D3—32no—
837C4×D3—32no—
838C4×D3—32no—
839C4×D3—34no—
840C4×D3—34no—
841C4×D3—62no—
842C4×D3—62no—
843C4×D3—64no—
844C4×D3—64no—
845C4×D3—64no—
846C4×D3—64no—
847C4×D3—64no—
848C4×D3—64no—
849C4×D3—64no—
850C4×D3—64no—
851C4×D3—64no—
852C4×D3—64no—
853C4×D3—64no—
854C4×D3—124no—
855C4×D3—124no—
856C4×D3D3×D412yes—
857C4×D3D3×D412yes—
858C4×D3C23×D312yes—
859C4×D3C23×D312yes—
860Dic6—21no—
861Dic6—21no—
862Dic6—21no—
863Dic6—24no—
864Dic6—24no—
865Dic6—24no—
866Dic6—32no—
867Dic6—32no—
868Dic6—62no—
869Dic6—64no—
870Dic6—64no—
871Dic6—64no—
872Dic6—64no—
873Dic6—64no—
874Dic6—64no—
875Dic6—61no—
876Dic6—61no—
877Dic6—64no—
878Dic6—64no—
879Dic6—124no—
880Dic6—121no—
881Dic6C23×D312yes—
882Dic6C23×D312yes—
883Dic6C23×D312yes—
884C3×C8—22no—
885C3×C8—32no—
886C3×C8—32no—
887C3×C8C23×D312yes—
888C3×C8C23×D312yes—
889C3⋊C8—32no—
890C3⋊C8—32no—
891C3⋊C8—62no—
892C3⋊C8C23×D312yes—
893C3⋊C8C23×D312yes—
894C2×C32C2×#13712yescomplemented
895C2×C32C23×D411yescharacteristic
896C3⋊D3—22no—
897C3⋊D3—42no—
898C3×D3—22no—
899C3×D3—42no—
900C3×D3C2×#13714yescomplemented
901C24—91no—
902C24—181no—
903#41—34no—
904#41—62no—
905#41—94no—
906#41—94no—
907#41—94no—
908#41—182no—
909#41—188no—
910#41—188no—
911#41—182no—
912#41—182no—
913C2×Q8—34no—
914C2×Q8—34no—
915C2×Q8—34no—
916C2×Q8—31no—
917C2×Q8—31no—
918C2×Q8—31no—
919C2×Q8—61no—
920C2×Q8—61no—
921C2×Q8—61no—
922C2×Q8—62no—
923C2×Q8—62no—
924C2×Q8—62no—
925C2×Q8—94no—
926C2×Q8—94no—
927C2×Q8—94no—
928C2×Q8—94no—
929C2×Q8—91no—
930C2×Q8—181no—
931C2×Q8—181no—
932C2×Q8—181no—
933C2×Q8—182no—
934C2×Q8—182no—
935C2×Q8—181no—
936C2×Q8—188no—
937C2×Q8—188no—
938C2×Q8—182no—
939C2×Q8—188no—
940C2×Q8—182no—
941C2×Q8C2×D3211yescharacteristic
942C2×Q8C2×D3211yescharacteristic
943C2×D4—31no—
944C2×D4—61no—
945C2×D4—94no—
946C2×D4—91no—
947C2×D4—181no—
948C2×D4—182no—
949C2×D4—181no—
950C2×D4—188no—
951C2×D4—181no—
952C2×D4—181no—
953C22×C4—31no—
954C22×C4—31no—
955C22×C4—61no—
956C22×C4—61no—
957C22×C4—61no—
958C22×C4—61no—
959C22×C4—94no—
960C22×C4—91no—
961C22×C4—94no—
962C22×C4—91no—
963C22×C4—91no—
964C22×C4—91no—
965C22×C4—181no—
966C22×C4—181no—
967C22×C4—181no—
968C22×C4—188no—
969C22×C4—188no—
970C22×C4—181no—
971C22×C4—181no—
972C22×C4—181no—
973C22×C4—181no—
974Q16—34no—
975Q16—34no—
976Q16—34no—
977Q16—34no—
978Q16—94no—
979Q16—94no—
980Q16—94no—
981Q16C2×D3214yescomplemented
982SD16—34no—
983SD16—34no—
984SD16—94no—
985SD16—94no—
986SD16—94no—
987SD16—94no—
988SD16—94no—
989SD16—94no—
990M16—34no—
991M16—94no—
992M16—94no—
993M16—94no—
994C2×C8—31no—
995C2×C8—31no—
996C2×C8—34no—
997C2×C8—94no—
998C2×C8—91no—
999C2×C8C2×D3211yescharacteristic
1000C22×C3—21no—
1001C22×C3—32no—
1002C22×C3—34no—
1003C22×C3—32no—
1004C22×C3—62no—
1005C22×C3—62no—
1006C22×C3—122no—
1007C22×C3C2×D3×D411yescharacteristic
1008C22×C3C2×D3×D411yescharacteristic
1009C2×D3—22no—
1010C2×D3—22no—
1011C2×D3—32no—
1012C2×D3—32no—
1013C2×D3—42no—
1014C2×D3—62no—
1015C2×D3—68no—
1016C2×D3—62no—
1017C2×D3—62no—
1018C2×D3—68no—
1019C2×D3—62no—
1020C2×D3—62no—
1021C2×D3—122no—
1022C2×D3—122no—
1023C2×D3—128no—
1024C2×D3—122no—
1025C2×D3—122no—
1026C2×D3—128no—
1027C2×D3—242no—
1028C2×D3#91814yesdirect product factor
1029C2×D3C2×D3×D412yes—
1030C2×D3C2×D3×D412yes—
1031C3×C4—22no—
1032C3×C4—22no—
1033C3×C4—22no—
1034C3×C4—22no—
1035C3×C4—21no—
1036C3×C4—21no—
1037C3×C4—32no—
1038C3×C4—32no—
1039C3×C4—42no—
1040C3×C4—42no—
1041C3×C4—62no—
1042C3×C4—62no—
1043C3×C4—62no—
1044C3×C4C2×D3×D411yescharacteristic
1045C3×C4C2×D3×D411yescharacteristic
1046C3×C4C24×D311yescharacteristic
1047C3×C4C24×D311yescharacteristic
1048Dic3—22no—
1049Dic3—22no—
1050Dic3—22no—
1051Dic3—32no—
1052Dic3—32no—
1053Dic3—62no—
1054Dic3—62no—
1055Dic3—62no—
1056Dic3—122no—
1057Dic3C2×D3×D412yes—
1058Dic3C2×D3×D412yes—
1059C32C22×#13711yescharacteristic, complemented, Sylow
1060C23—31no—
1061C23—31no—
1062C23—61no—
1063C23—94no—
1064C23—91no—
1065C23—184no—
1066C23—184no—
1067C23—181no—
1068C23—364no—
1069Q8—21no—
1070Q8—21no—
1071Q8—32no—
1072Q8—32no—
1073Q8—32no—
1074Q8—64no—
1075Q8—64no—
1076Q8—64no—
1077Q8—61no—
1078Q8—61no—
1079Q8—61no—
1080Q8—92no—
1081Q8—184no—
1082Q8—184no—
1083Q8—184no—
1084Q8—184no—
1085Q8—181no—
1086Q8C22×D3212yes—
1087Q8C22×D3212yes—
1088D4—32no—
1089D4—64no—
1090D4—61no—
1091D4—92no—
1092D4—184no—
1093D4—184no—
1094D4—184no—
1095D4—184no—
1096D4—181no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—31no—
1100C2×C4—31no—
1101C2×C4—32no—
1102C2×C4—32no—
1103C2×C4—32no—
1104C2×C4—32no—
1105C2×C4—64no—
1106C2×C4—64no—
1107C2×C4—64no—
1108C2×C4—64no—
1109C2×C4—61no—
1110C2×C4—61no—
1111C2×C4—61no—
1112C2×C4—94no—
1113C2×C4—94no—
1114C2×C4—94no—
1115C2×C4—91no—
1116C2×C4—92no—
1117C2×C4—92no—
1118C2×C4—184no—
1119C2×C4—184no—
1120C2×C4—184no—
1121C2×C4—184no—
1122C2×C4—184no—
1123C2×C4—184no—
1124C2×C4—184no—
1125C2×C4—181no—
1126C2×C4C22×D3211yescharacteristic
1127C8—32no—
1128C8—32no—
1129C8—92no—
1130C8C22×D3212yes—
1131C2×C3—21no—
1132C2×C3—22no—
1133C2×C3—34no—
1134C2×C3—62no—
1135C2×C3—122no—
1136C2×C3C2×#91812yescomplemented
1137C2×C3D3×#13712yescomplemented
1138C2×C3C22×D3×D411yescharacteristic
1139C2×C3C22×D3×D411yescharacteristic
1140D3—22no—
1141D3—42no—
1142D3—62no—
1143D3—62no—
1144D3—122no—
1145D3—122no—
1146D3—122no—
1147D3—242no—
1148D3C2×#91814yesdirect product factor
1149C22—32no—
1150C22—34no—
1151C22—32no—
1152C22—62no—
1153C22—62no—
1154C22—92no—
1155C22—122no—
1156C22—188no—
1157C22—182no—
1158C22—182no—
1159C22—368no—
1160C22—362no—
1161C22D32×D411yescharacteristic
1162C4—22no—
1163C4—22no—
1164C4—32no—
1165C4—32no—
1166C4—62no—
1167C4—62no—
1168C4—62no—
1169C4—92no—
1170C4—182no—
1171C4D32×D411yescharacteristic
1172C4C23×D3211yescharacteristic
1173C3—21no—
1174C3C22×#91811yescharacteristic, complemented
1175C3C2×D3×#13711yescharacteristic, complemented
1176C2—34no—
1177C2—62no—
1178C2—122no—
1179C2—182no—
1180C2—362no—
1181C2D3×#91812yesdirect product factor
1182C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×D3×#239C2
hypercenterC2×Q16D32
hypocenterC32C22×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×D32×Q8C2semidirect
3. C2×#64127C2semidirect
4. C2×C3×#918C2semidirect
5. C2×C3×D3×Q16C2semidirect
6. C2×#63951C2semidirect
7. C2×#63948C2semidirect
8. C2×#63945C2semidirect
9. C2×#63943C2semidirect
10. C2×D3×#216C2semidirect
11. C2×D3×#215C2semidirect
12. D3×#918C2direct (N × H)
13. C2×#63811C2semidirect
14. C2×#63801C2semidirect
15. C2×D3×#204C2semidirect
16. C2×D3×ΓL(1,𝔽25)C2semidirect
20. C2×Q8×C3⋊D3C22semidirect
24. C2×C3×D3×Q8C22semidirect
28. D32×Q8C22semidirect
37. C2×#3797C22semidirect
43. C2×D3×Dic6C22semidirect
44. C2×C32×Q16C22semidirect
45. C2×#3756C22semidirect
46. C2×#3755C22semidirect
47. #64127C22semidirect
48. C2×#3744C22semidirect
49. C2×#3743C22semidirect
50. C2×C3×#216C22semidirect
51. C2×C3×#216C22semidirect
52. C2×C3×#216C22semidirect
53. C2×C3×#215C22semidirect
54. C3×#918C22semidirect
55. C3×D3×Q16C22semidirect
56. C2×C3×Dic12C22semidirect
57. C2×C3×#204C22semidirect
58. C2×C3×ΓL(1,𝔽25)C22semidirect
60. #63951C22semidirect
61. #63948C22semidirect
62. #63945C22semidirect
63. #63943C22semidirect
64. D3×#216C22semidirect
65. D3×#215C22semidirect
66. C2×#3719C22semidirect
67. C2×#3718C22semidirect
68. C2×#3717C22semidirect
69. C2×#3717C22semidirect
70. C2×#3716C22semidirect
71. C2×#3715C22semidirect
72. C2×#3712C22semidirect
73. C2×#3711C22semidirect
75. #63811C22semidirect
76. #63801C22semidirect
77. D3×#204C22semidirect
78. D3×ΓL(1,𝔽25)C22semidirect
101. C2×#918D3direct (N × H)
103. C2×D3×Q16D3semidirect
119. Q8×C3⋊D3C23semidirect
134. C3×D3×Q8C23semidirect
175. #3797C23semidirect
184. D3×Dic6C23semidirect
185. C32×Q16C23semidirect
187. #3756C23semidirect
188. #3755C23semidirect
190. #3744C23semidirect
191. #3743C23semidirect
192. C3×#216C23semidirect
193. C3×#216C23semidirect
194. C3×#216C23semidirect
195. C3×#215C23semidirect
198. C3×Dic12C23semidirect
199. C3×#204C23semidirect
200. C3×ΓL(1,𝔽25)C23semidirect
202. #3719C23semidirect
203. #3718C23semidirect
204. #3717C23semidirect
205. #3717C23semidirect
206. #3716C23semidirect
207. #3715C23semidirect
208. #3712C23semidirect
209. #3711C23semidirect
245. C2×D3×Q8C2×D3semidirect
271. C2×C3×Q16C2×D3semidirect
272. C2×C3×Q16C2×D3semidirect
285. C2×#216C2×D3semidirect
286. C2×#216C2×D3semidirect
287. C2×#216C2×D3semidirect
296. C2×#215C2×D3semidirect
311. #918C2×D3direct (N × H)
313. D3×Q16C2×D3semidirect
321. C2×Dic12C2×D3semidirect
329. C2×#204C2×D3semidirect
337. C2×ΓL(1,𝔽25)C2×D3semidirect
504. D3×Q8C22×D3semidirect
591. C3×Q16C22×D3semidirect
592. C3×Q16C22×D3semidirect
608. #216C22×D3semidirect
609. #216C22×D3semidirect
610. #216C22×D3semidirect
617. #215C22×D3semidirect
628. Dic12C22×D3semidirect
635. #204C22×D3semidirect
642. ΓL(1,𝔽25)C22×D3semidirect
653. C2×C3×D3#137semidirect
711. C2×Q16D32semidirect
894. C2×C32C2×#137semidirect
900. C3×D3C2×#137semidirect
981. Q16C2×D32semidirect
1028. C2×D3#918direct (N × H)
1059. C32C22×#137semidirect
1136. C2×C3C2×#918semidirect
1137. C2×C3D3×#137semidirect
1148. D3C2×#918direct (N × H)
1174. C3C22×#918semidirect
1175. C3C2×D3×#137semidirect
1181. C2D3×#918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×D32×Q82
C2×#641272
C2×C3×#9182
C2×C3×D3×Q162
C2×#639512
C2×#639482
C2×#639452
C2×#639432
C2×D3×#2162
C2×D3×#2152
D3×#9182
C2×#638112
C2×#638012
C2×D3×#2042
C2×D3×ΓL(1,𝔽25)2
C2×D3×#1373
C22×#9183