Finite Group Databasebeta

← #11904420

Subgroups — #11904420

Order 1152.

3569 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C3×#5804C211yesmaximal, characteristic, complemented
4C2×C3×#935C211yesmaximal, characteristic, complemented
5#10595519C211yesmaximal, characteristic, complemented
6#10595510C211yesmaximal, characteristic, complemented
7#10595500C214yesmaximal, complemented
8C2×#63966C211yesmaximal, characteristic, complemented
9#10595271C212yesmaximal, complemented
10#10595242C212yesmaximal, complemented
11#10595169C212yesmaximal, complemented
12#10595163C214yesmaximal, complemented
13#10595162C214yesmaximal, complemented
14#10595160C212yesmaximal, complemented
15#10594917C214yesmaximal, complemented
16#86296—31nomaximal
17#86012—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2212yescomplemented
22#64361—28no—
23C2×#3830C2212yes—
24C2×#3830C2212yescomplemented
25C2×D4×C3⋊D3C2212yes—
26C2×D4×C3⋊D3C2212yescomplemented
27C2×#3828C2212yescomplemented
28C22×C3×#67C2211yescharacteristic, complemented
29C23×C3×Dic3C2211yescharacteristic, complemented
30C22×#627C2211yescharacteristic, complemented
31C22×#626C2211yescharacteristic, complemented
32C22×#624C2211yescharacteristic, complemented
33C2×#3804—28no—
34C2×#3804C2214yescomplemented
35C2×#3804C2214yescomplemented
36C22×D3×Dic3C2211yescharacteristic, complemented
37C3×#953C2212yescomplemented
38C2×C3×#217C2212yescomplemented
39C2×C3×#217C2211yescharacteristic, complemented
40C2×C3×#217C2211yescharacteristic, complemented
41C3×#939C2214yescomplemented
42C3×#937C2212yescomplemented
43C3×#935C2212yescomplemented
44C3×#935C2214yescomplemented
45C3×#935C2212yescomplemented
46C3×#935C2212yescomplemented
47C3×#929C2212yescomplemented
48C2×C3×Dic3⋊C4C2212yescomplemented
49#63982C2214yescomplemented
50#63981C2212yescomplemented
51#63981C2214yescomplemented
52#63978C2214yescomplemented
53#63977C2212yescomplemented
54#63975C2214yescomplemented
55#63974C2214yescomplemented
56#63974C2212yescomplemented
57#67⋊Dic3C2214yescomplemented
58#63971C2214yescomplemented
59#63966C2212yescomplemented
60#63966C2212yescomplemented
61#63966C2214yescomplemented
62#63966C2212yescomplemented
63C2×Dic3⋊Dic3C2212yescomplemented
64C2×#3722C2212yescomplemented
65#63962C2212yescomplemented
66#63958C2214yescomplemented
67#63957C2212yescomplemented
68#63953C2214yescomplemented
69#63952C2214yescomplemented
70#63952C2214yescomplemented
71#63910C2214yescomplemented
72#63897C2214yescomplemented
73#63896C2214yescomplemented
74#63883C2214yescomplemented
75#63881C2214yescomplemented
76#63865C2214yescomplemented
77#63853C2214yescomplemented
78#63840C2214yescomplemented
79C2×#1004—31no—
80C2×#1004—31no—
81C2×#1004—61no—
82C22×#237—31no—
83C22×#235—31no—
84C3×#534—31no—
85C2×C3×#123—31no—
86#5804—31no—
87#5804D311yescharacteristic, complemented
88C2×#935D311yescharacteristic, complemented
89C2×#929—31no—
90#5656—32no—
91#5655—34no—
92#5655—34no—
93#5654—34no—
94#5653—32no—
95D3×#123—32no—
96D3×#123—32no—
97#5648—32no—
98#5648—32no—
99#5611—34no—
100#5610—34no—
101#5591—34no—
102#5589—32no—
103#5586—32no—
104#5507—34no—
105#5493—31no—
106C2×#886—31no—
107#5490—34no—
108#5486—31no—
109#5486—31no—
110C24×C32C2311yescharacteristic
111C24×C32C2311yescharacteristic
112C23×C3⋊D3C2312yes—
113C23×C3⋊D3C2311yescharacteristic
114C23×C3⋊D3C2311yescharacteristic
115C23×C3×D3C2311yescharacteristic
116C2×C32×D4—24no—
117C2×C32×D4C2312yes—
118C2×C32×D4C2312yes—
119C22×C32×C4C2311yescharacteristic
120C2×#638—24no—
121C2×#638—28no—
122C2×#638D418yescomplemented
123C2×#638C2312yes—
124C2×#638C2312yes—
125C2×#638C2312yes—
126C2×#638C2312yes—
127C2×#638C2312yes—
128C2×#638C2312yes—
129C22×C3⋊Dic3C2312yes—
130C22×C3⋊Dic3C2311yescharacteristic
131C22×C3⋊Dic3C2311yescharacteristic
132#3830—28no—
133#3830—28no—
134D4×C3⋊D3—28no—
135D4×C3⋊D3—28no—
136#3828—28no—
137C2×C4⋊(C3⋊D3)C2312yes—
138C2×C4×C3⋊D3C2312yes—
139C2×C4×C3⋊D3C2312yes—
140C2×#634C2312yes—
141C2×C3×#67—24no—
142C2×C3×#67C2312yes—
143C2×C3×#67C2312yes—
144C2×C3×#67C2314yes—
145C22×C3×Dic3—24no—
146C22×C3×Dic3C2312yes—
147C22×C3×Dic3C2311yescharacteristic
148C22×C3×Dic3C2312yes—
149C22×C3×Dic3C2311yescharacteristic
150C22×C3×Dic3C2311yescharacteristic
151C22×C3×Dic3C2312yes—
152C22×C3×Dic3C2312yes—
153C2×#627—24no—
154C2×#627C2314yes—
155C2×#626—24no—
156C2×#626C2314yes—
157C2×#626C2314yes—
158C2×#624—24no—
159C2×#624C2314yes—
160C2×#624C2314yes—
161#3804—216no—
162#3804—216no—
163C2×D3×Dic3—24no—
164C2×D3×Dic3C2314yes—
165C3×#217C2312yes—
166C3×#217C2312yes—
167C3×#217C2314yes—
168C3×#217C2312yes—
169C3×#217C2314yes—
170C3×#217C2312yes—
171C3×#217C2314yes—
172C3×(C2×D3)⋊C4C2314yes—
173C3×Dic3⋊C4C2314yes—
174C3×Dic3⋊C4C2314yes—
175C3×Dic3⋊C4C2314yes—
176#3724C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180#3722C2314yes—
181#3722C2314yes—
182#3722C2314yes—
183#3722C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185Dic32C2314yes—
186#3485—91noSylow
187C22×C3×D4—21no—
188C22×C3×D4—31no—
189C22×C3×D4C2×D311yescharacteristic
190C22×C3×D4C2×D311yescharacteristic
191C23×C3×C4—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—32no—
197C22×#67—32no—
198C22×#67—31no—
199C22×#67—61no—
200C22×#67—61no—
201C22×#67—62no—
202C22×#67C2×D311yescharacteristic, complemented
203C23×Dic3—31no—
204C23×Dic3C2×D311yescharacteristic, complemented
205#1004—68no—
206#1004—68no—
207#1004—616no—
208C2×#237—32no—
209C2×#237—32no—
210C2×#237—32no—
211C2×#237—32no—
212C2×#237—34no—
213C2×#237—34no—
214C2×#237—62no—
215C2×#237—62no—
216C2×#237—68no—
217C2×D3×D4—32no—
218C2×D3×D4—32no—
219C2×D3×D4—32no—
220C2×D3×D4—32no—
221C2×D3×D4—62no—
222C2×D3×D4—62no—
223C2×#235—32no—
224C2×#235—32no—
225C2×#235—34no—
226C2×#235—34no—
227C2×#235—62no—
228C2×#235—68no—
229C22×D12—31no—
230C22×C4×D3—31no—
231C22×C4×D3—31no—
232C22×C4×D3—31no—
233C22×Dic6—31no—
234C22×Dic6—31no—
235C3×#123—32no—
236C3×#123—32no—
237C3×#123—32no—
238C3×#123—34no—
239C3×#123—32no—
240C3×#121—34no—
241C3×#120—32no—
242C3×#120—32no—
243C2×C3×C4⋊C4—32no—
244C2×C3×C22⋊C4—31no—
245C2×C3×C22⋊C4—31no—
246C2×C3×C22⋊C4—32no—
247#953—32no—
248#953C2×D312yescomplemented
249C2×#217C2×D311yescharacteristic, complemented
250C2×#217C2×D311yescharacteristic, complemented
251C2×#217C2×D312yescomplemented
252#939—34no—
253#939—34no—
254#939C2×D314yescomplemented
255#938—34no—
256#937—32no—
257#937—34no—
258#937C2×D312yescomplemented
259#935—32no—
260#935C2×D312yescomplemented
261#935C2×D312yescomplemented
262#935C2×D312yescomplemented
263#935C2×D314yescomplemented
264D4×Dic3—34no—
265#930—34no—
266#929—32no—
267#929—32no—
268#929—32no—
269#929—34no—
270#929C2×D312yescomplemented
271C4×#67—34no—
272C4×#67—34no—
273C2×(C2×D3)⋊C4—32no—
274C2×(C2×D3)⋊C4—32no—
275C2×C4⋊Dic3—32no—
276C2×Dic3⋊C4—32no—
277C2×Dic3⋊C4C2×D312yescomplemented
278#896—34no—
279#896—34no—
280#896—34no—
281#895—34no—
282#894—34no—
283#894—34no—
284#894—34no—
285#893—34no—
286D3×C4⋊C4—34no—
287D3×C4⋊C4—34no—
288#888—34no—
289#888—34no—
290#886—32no—
291#886—32no—
292#886—32no—
293#886—32no—
294#886—34no—
295#885—34no—
296#885—34no—
297#884—34no—
298#884—34no—
299#884—34no—
300#883—34no—
301#883—34no—
302#883—34no—
303#882—32no—
304#882—34no—
305#882—32no—
306#67⋊C4—34no—
307#67⋊C4—34no—
308#67⋊C4—34no—
309#67⋊C4—34no—
310D3×C22⋊C4—32no—
311D3×C22⋊C4—34no—
312D3×C22⋊C4—32no—
313D3×C22⋊C4—34no—
314#878—34no—
315#878—34no—
316#878—34no—
317#877—32no—
318#877—32no—
319C23×C32—22no—
320C23×C32—42no—
321C23×C32—42no—
322C23×C32C2×D414yes—
323C23×C32C2412yes—
324C23×C32C2411yescharacteristic
325C23×C32C2411yescharacteristic
326C23×C32C2411yescharacteristic
327C22×C3⋊D3—22no—
328C22×C3⋊D3—24no—
329C22×C3⋊D3—42no—
330C22×C3⋊D3—44no—
331C22×C3⋊D3—42no—
332C22×C3⋊D3C2×D414yes—
333C22×C3⋊D3C2412yes—
334C22×C3⋊D3C2412yes—
335C22×C3×D3—22no—
336C22×C3×D3—42no—
337C22×C3×D3C2412yes—
338C32×D4—24no—
339C32×D4—24no—
340C2×C32×C4—22no—
341C2×C32×C4C2412yes—
342#638—24no—
343#638—24no—
344#638—24no—
345#638—24no—
346#638C2×D418yes—
347#638C2×D418yes—
348C2×C3⋊Dic3—22no—
349C2×C3⋊Dic3—24no—
350C2×C3⋊Dic3C2×D414yes—
351C2×C3⋊Dic3C2412yes—
352C2×C3⋊Dic3C2412yes—
353C4⋊(C3⋊D3)—24no—
354C4×C3⋊D3—24no—
355C4×C3⋊D3—24no—
356#634—24no—
357C3×#67—24no—
358C3×#67—24no—
359C3×#67—44no—
360C2×C3×Dic3—22no—
361C2×C3×Dic3—24no—
362C2×C3×Dic3—24no—
363C2×C3×Dic3—22no—
364C2×C3×Dic3—22no—
365C2×C3×Dic3—42no—
366C2×C3×Dic3—42no—
367C2×C3×Dic3C2414yes—
368C2×C3×Dic3C2414yes—
369C2×C3×Dic3C2412yes—
370C2×C3×Dic3C2412yes—
371C2×C3×Dic3C2412yes—
372#627—28no—
373#626—28no—
374#626—44no—
375#624—28no—
376#624—44no—
377D3×Dic3—28no—
378C2×H(5,𝔽2)—91no—
379C22×#41—91no—
380#547—94no—
381#547—94no—
382#546—94no—
383#546—94no—
384#536—92no—
385#534—31no—
386#534—91no—
387#534—92no—
388#525—92no—
389C2×#123—31no—
390C2×#123—91no—
391C2×#123—92no—
392#518—91no—
393C24×C3—21no—
394C24×C3—21no—
395C24×C3—31no—
396C24×C3C22×D311yescharacteristic
397C24×C3C22×D311yescharacteristic
398C24×C3C22×D311yescharacteristic
399C24×C3C22×D311yescharacteristic
400C23×D3—31no—
401C23×D3—31no—
402C23×D3—32no—
403C23×D3—32no—
404C23×D3—31no—
405C23×D3—31no—
406C23×D3—61no—
407C23×D3—62no—
408C23×D3—61no—
409C23×D3C22×D311yescharacteristic
410C2×C3×D4—28no—
411C2×C3×D4—24no—
412C2×C3×D4—24no—
413C2×C3×D4—22no—
414C2×C3×D4—22no—
415C2×C3×D4—32no—
416C2×C3×D4—32no—
417C2×C3×D4—34no—
418C2×C3×D4—64no—
419C2×C3×D4C22×D312yes—
420C2×C3×D4C22×D312yes—
421C2×C3×D4C22×D312yes—
422C2×C3×D4C22×D312yes—
423C22×C3×C4—21no—
424C22×C3×C4—32no—
425C22×C3×C4—32no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—31no—
429C22×C3×C4—32no—
430C22×C3×C4—32no—
431C22×C3×C4—64no—
432C22×C3×C4C22×D311yescharacteristic
433C22×C3×C4C22×D311yescharacteristic
434C2×#67—24no—
435C2×#67—38no—
436C2×#67—38no—
437C2×#67—32no—
438C2×#67—32no—
439C2×#67—32no—
440C2×#67—32no—
441C2×#67—32no—
442C2×#67—32no—
443C2×#67—32no—
444C2×#67—32no—
445C2×#67—32no—
446C2×#67—32no—
447C2×#67—32no—
448C2×#67—32no—
449C2×#67—34no—
450C2×#67—34no—
451C2×#67—62no—
452C2×#67—62no—
453C2×#67—62no—
454C2×#67—62no—
455C2×#67—62no—
456C2×#67—62no—
457C2×#67—68no—
458C2×#67—64no—
459C2×#67—68no—
460C2×#67—68no—
461C2×#67—616no—
462C2×#67—68no—
463C2×#67—64no—
464C2×#67—64no—
465C2×#67C22×D312yes—
466C2×#67C22×D312yes—
467C2×#67C22×D314yes—
468C22×Dic3—24no—
469C22×Dic3—31no—
470C22×Dic3—31no—
471C22×Dic3—32no—
472C22×Dic3—32no—
473C22×Dic3—31no—
474C22×Dic3—31no—
475C22×Dic3—34no—
476C22×Dic3—61no—
477C22×Dic3—61no—
478C22×Dic3—62no—
479C22×Dic3—64no—
480C22×Dic3C22×D312yes—
481C22×Dic3C22×D311yescharacteristic
482C22×Dic3C22×D311yescharacteristic
483C22×Dic3C22×D311yescharacteristic
484C22×Dic3C22×D312yes—
485C22×Dic3C22×D312yes—
486C22×Dic3C22×D312yes—
487#237—616no—
488#237—616no—
489#237—68no—
490#237—68no—
491#237—68no—
492#237—68no—
493#237—616no—
494#237—616no—
495D3×D4—68no—
496D3×D4—68no—
497D3×D4—68no—
498D3×D4—68no—
499D3×D4—616no—
500D3×D4—616no—
501#235—616no—
502#235—616no—
503#235—68no—
504#235—68no—
505#235—616no—
506C2×D12—34no—
507C2×D12—32no—
508C2×D12—32no—
509C2×D12—34no—
510C2×D12—62no—
511C2×D12—64no—
512C2×C4×D3—34no—
513C2×C4×D3—32no—
514C2×C4×D3—32no—
515C2×C4×D3—32no—
516C2×C4×D3—32no—
517C2×C4×D3—34no—
518C2×C4×D3—34no—
519C2×C4×D3—34no—
520C2×C4×D3—34no—
521C2×C4×D3—62no—
522C2×C4×D3—62no—
523C2×C4×D3—64no—
524C2×C4×D3—64no—
525C2×C4×D3—64no—
526C2×Dic6—32no—
527C2×Dic6—32no—
528C2×Dic6—34no—
529C2×Dic6—34no—
530C2×Dic6—62no—
531C2×Dic6—64no—
532C2×Dic6—64no—
533C3×C4⋊C4—34no—
534C3×C4⋊C4—34no—
535C3×C4⋊C4—34no—
536C3×C22⋊C4—32no—
537C3×C22⋊C4—32no—
538C3×C22⋊C4—34no—
539C3×C22⋊C4—34no—
540C3×C22⋊C4—34no—
541C3×C22⋊C4—32no—
542C3×C22⋊C4—32no—
543C3×C22⋊C4—34no—
544#217—34no—
545#217C22×D312yes—
546#217C22×D312yes—
547#217C22×D314yes—
548#217C22×D314yes—
549#217C22×D314yes—
550#217C22×D312yes—
551#217C22×D312yes—
552(C2×D3)⋊C4—34no—
553(C2×D3)⋊C4—34no—
554(C2×D3)⋊C4—34no—
555(C2×D3)⋊C4—34no—
556(C2×D3)⋊C4—34no—
557(C2×D3)⋊C4—34no—
558(C2×D3)⋊C4—34no—
559(C2×D3)⋊C4—34no—
560(C2×D3)⋊C4—34no—
561(C2×D3)⋊C4C22×D314yes—
562C4⋊Dic3—34no—
563C4⋊Dic3—34no—
564C4⋊Dic3—34no—
565Dic3⋊C4—34no—
566Dic3⋊C4—34no—
567Dic3⋊C4—34no—
568Dic3⋊C4—34no—
569Dic3⋊C4—34no—
570Dic3⋊C4C22×D314yes—
571Dic3⋊C4C22×D314yes—
572Dic3⋊C4C22×D314yes—
573C4×Dic3—34no—
574C4×Dic3—34no—
575C22×C32—22no—
576C22×C32—22no—
577C22×C32—22no—
578C22×C32—22no—
579C22×C32—24no—
580C22×C32—44no—
581C22×C32—82no—
582C22×C32C22×D412yes—
583C22×C32C22×D412yes—
584C22×C32C22×D412yes—
585C22×C32C2511yescharacteristic
586C2×C3⋊D3—22no—
587C2×C3⋊D3—24no—
588C2×C3⋊D3—24no—
589C2×C3⋊D3—44no—
590C2×C3⋊D3—84no—
591C2×C3⋊D3—82no—
592C2×C3⋊D3C22×D414yes—
593C2×C3×D3—22no—
594C2×C3×D3—24no—
595C2×C3×D3—44no—
596C32×C4—22no—
597C3⋊Dic3—22no—
598C3⋊Dic3C22×D414yes—
599C3×Dic3—22no—
600C3×Dic3—22no—
601C3×Dic3—22no—
602C3×Dic3—24no—
603C3×Dic3—24no—
604H(5,𝔽2)—188no—
605C2×#41—94no—
606C2×#41—94no—
607C2×#41—92no—
608C2×#41—92no—
609C2×#41—92no—
610C2×#41—188no—
611C22×Q8—91no—
612C22×D4—31no—
613C22×D4—91no—
614C22×D4—91no—
615C22×D4—91no—
616C22×D4—92no—
617C22×D4—92no—
618C22×D4—92no—
619C22×D4D3211yescharacteristic
620C23×C4—31no—
621C23×C4—91no—
622C23×C4—91no—
623C4⋊Q8—94no—
624#124—94no—
625#123—32no—
626#123—32no—
627#123—34no—
628#123—32no—
629#123—32no—
630#123—94no—
631#123—94no—
632#123—92no—
633#123—92no—
634#123—92no—
635#123—94no—
636#123—92no—
637#123—94no—
638C22⋊Q8—94no—
639C22⋊Q8—94no—
640C22⋊Q8—94no—
641#121—34no—
642#121—94no—
643#121—94no—
644#121—94no—
645#121—94no—
646#120—32no—
647#120—32no—
648#120—92no—
649#120—94no—
650#120—92no—
651C4×D4—94no—
652C4×D4—94no—
653C4×D4—94no—
654C4×D4—94no—
655#117—92no—
656C2×C4⋊C4—32no—
657C2×C4⋊C4—94no—
658C2×C4⋊C4—92no—
659C2×C22⋊C4—31no—
660C2×C22⋊C4—31no—
661C2×C22⋊C4—32no—
662C2×C22⋊C4—92no—
663C2×C22⋊C4—94no—
664C2×C22⋊C4—92no—
665C23×C3—24no—
666C23×C3—22no—
667C23×C3—22no—
668C23×C3—22no—
669C23×C3—21no—
670C23×C3—21no—
671C23×C3—21no—
672C23×C3—24no—
673C23×C3—32no—
674C23×C3—42no—
675C23×C3—42no—
676C23×C3—42no—
677C23×C3—42no—
678C23×C3—62no—
679C23×C3—82no—
680C23×C3—82no—
681C23×C3—122no—
682C23×C3D3×D414yes—
683C23×C3D3×D414yes—
684C23×C3C23×D312yes—
685C23×C3C23×D312yes—
686C23×C3C23×D311yescharacteristic
687C23×C3C23×D311yescharacteristic
688C23×C3C23×D311yescharacteristic
689C23×C3C23×D311yescharacteristic
690C23×C3C23×D311yescharacteristic
691C23×C3C23×D311yescharacteristic
692C22×D3—22no—
693C22×D3—32no—
694C22×D3—32no—
695C22×D3—34no—
696C22×D3—34no—
697C22×D3—32no—
698C22×D3—32no—
699C22×D3—42no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—64no—
703C22×D3—64no—
704C22×D3—64no—
705C22×D3—68no—
706C22×D3—64no—
707C22×D3—62no—
708C22×D3—62no—
709C22×D3—122no—
710C22×D3—122no—
711C22×D3—124no—
712C22×D3—124no—
713C22×D3—122no—
714C22×D3—122no—
715C22×D3—242no—
716C22×D3—242no—
717C22×D3—244no—
718C22×D3C23×D312yes—
719C3×D4—28no—
720C3×D4—28no—
721C3×D4—24no—
722C3×D4—24no—
723C3×D4—24no—
724C3×D4—24no—
725C3×D4—64no—
726C3×D4—64no—
727C3×D4—124no—
728C2×C3×C4—24no—
729C2×C3×C4—22no—
730C2×C3×C4—22no—
731C2×C3×C4—22no—
732C2×C3×C4—34no—
733C2×C3×C4—34no—
734C2×C3×C4—32no—
735C2×C3×C4—32no—
736C2×C3×C4—32no—
737C2×C3×C4—62no—
738C2×C3×C4—62no—
739C2×C3×C4—62no—
740C2×C3×C4—64no—
741C2×C3×C4—64no—
742C2×C3×C4—122no—
743C2×C3×C4—122no—
744C2×C3×C4C23×D312yes—
745C2×C3×C4C23×D312yes—
746#67—24no—
747#67—24no—
748#67—38no—
749#67—38no—
750#67—38no—
751#67—38no—
752#67—44no—
753#67—68no—
754#67—68no—
755#67—68no—
756#67—64no—
757#67—64no—
758#67—64no—
759#67—64no—
760#67—68no—
761#67—68no—
762#67—68no—
763#67—68no—
764#67—64no—
765#67—64no—
766#67—64no—
767#67—64no—
768#67—124no—
769C2×Dic3—22no—
770C2×Dic3—22no—
771C2×Dic3—22no—
772C2×Dic3—24no—
773C2×Dic3—24no—
774C2×Dic3—34no—
775C2×Dic3—34no—
776C2×Dic3—32no—
777C2×Dic3—32no—
778C2×Dic3—32no—
779C2×Dic3—32no—
780C2×Dic3—42no—
781C2×Dic3—42no—
782C2×Dic3—64no—
783C2×Dic3—62no—
784C2×Dic3—62no—
785C2×Dic3—68no—
786C2×Dic3—64no—
787C2×Dic3—64no—
788C2×Dic3—68no—
789C2×Dic3—64no—
790C2×Dic3—62no—
791C2×Dic3—62no—
792C2×Dic3C23×D314yes—
793C2×Dic3C23×D314yes—
794C2×Dic3C23×D312yes—
795C2×Dic3C23×D312yes—
796C2×Dic3C23×D312yes—
797D12—64no—
798D12—64no—
799D12—68no—
800D12—68no—
801D12—124no—
802C4×D3—68no—
803C4×D3—68no—
804C4×D3—64no—
805C4×D3—64no—
806C4×D3—68no—
807C4×D3—64no—
808C4×D3—64no—
809C4×D3—68no—
810C4×D3—68no—
811C4×D3—124no—
812C4×D3—124no—
813Dic6—68no—
814Dic6—68no—
815Dic6—64no—
816Dic6—64no—
817Dic6—68no—
818C2×C32—22no—
819C2×C32—22no—
820C2×C32—22no—
821C2×C32—42no—
822C2×C32C23×D411yescharacteristic
823C2×C32#58512yes—
824C3⋊D3—24no—
825C3⋊D3—42no—
826C3×D3—42no—
827C24—31no—
828C24—91no—
829C24—92no—
830C24—91no—
831C24C2×D3211yescharacteristic
832C24C2×D3211yescharacteristic
833#41—188no—
834#41—1816no—
835#41—1816no—
836#41—188no—
837#41—188no—
838C2×Q8—94no—
839C2×Q8—92no—
840C2×Q8—184no—
841C2×D4—24no—
842C2×D4—32no—
843C2×D4—32no—
844C2×D4—34no—
845C2×D4—64no—
846C2×D4—94no—
847C2×D4—94no—
848C2×D4—92no—
849C2×D4—92no—
850C2×D4—98no—
851C2×D4—92no—
852C2×D4—92no—
853C2×D4—92no—
854C2×D4—92no—
855C2×D4—92no—
856C2×D4—184no—
857C2×D4—188no—
858C2×D4—188no—
859C2×D4—188no—
860C2×D4—184no—
861C2×D4C2×D3212yes—
862C2×D4C2×D3212yes—
863C22×C4—32no—
864C22×C4—32no—
865C22×C4—31no—
866C22×C4—31no—
867C22×C4—31no—
868C22×C4—32no—
869C22×C4—32no—
870C22×C4—64no—
871C22×C4—94no—
872C22×C4—94no—
873C22×C4—94no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—92no—
877C22×C4—92no—
878C22×C4—92no—
879C22×C4—184no—
880C22×C4—184no—
881C22×C4C2×D3211yescharacteristic
882C4⋊C4—34no—
883C4⋊C4—34no—
884C4⋊C4—34no—
885C4⋊C4—94no—
886C4⋊C4—94no—
887C4⋊C4—94no—
888C4⋊C4—94no—
889C22⋊C4—32no—
890C22⋊C4—32no—
891C22⋊C4—34no—
892C22⋊C4—32no—
893C22⋊C4—32no—
894C22⋊C4—34no—
895C22⋊C4—34no—
896C22⋊C4—34no—
897C22⋊C4—94no—
898C22⋊C4—94no—
899C22⋊C4—94no—
900C22⋊C4—94no—
901C22⋊C4—94no—
902C42—94no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—22no—
907C22×C3—22no—
908C22×C3—22no—
909C22×C3—24no—
910C22×C3—22no—
911C22×C3—22no—
912C22×C3—24no—
913C22×C3—24no—
914C22×C3—22no—
915C22×C3—22no—
916C22×C3—22no—
917C22×C3—21no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—44no—
921C22×C3—42no—
922C22×C3—44no—
923C22×C3—44no—
924C22×C3—62no—
925C22×C3—64no—
926C22×C3—84no—
927C22×C3—82no—
928C22×C3—82no—
929C22×C3—84no—
930C22×C3—124no—
931C22×C3C2×D3×D412yes—
932C22×C3C2×D3×D412yes—
933C22×C3C2×D3×D412yes—
934C22×C3C2×D3×D412yes—
935C22×C3C2×D3×D412yes—
936C22×C3C2×D3×D412yes—
937C22×C3C24×D311yescharacteristic
938C22×C3C24×D311yescharacteristic
939C2×D3—22no—
940C2×D3—24no—
941C2×D3—34no—
942C2×D3—34no—
943C2×D3—44no—
944C2×D3—64no—
945C2×D3—64no—
946C2×D3—64no—
947C2×D3—64no—
948C2×D3—62no—
949C2×D3—62no—
950C2×D3—64no—
951C2×D3—64no—
952C2×D3—124no—
953C2×D3—124no—
954C2×D3—124no—
955C2×D3—124no—
956C2×D3—244no—
957C2×D3—244no—
958C2×D3—244no—
959C2×D3—242no—
960C2×D3—242no—
961C2×D3—244no—
962C2×D3—248no—
963C3×C4—24no—
964C3×C4—22no—
965C3×C4—22no—
966C3×C4—62no—
967C3×C4—62no—
968C3×C4—62no—
969C3×C4—64no—
970C3×C4—64no—
971Dic3—22no—
972Dic3—22no—
973Dic3—22no—
974Dic3—24no—
975Dic3—24no—
976Dic3—34no—
977Dic3—34no—
978Dic3—64no—
979Dic3—64no—
980Dic3—62no—
981Dic3—62no—
982C32#348511yescharacteristic, complemented, Sylow
983C23—22no—
984C23—32no—
985C23—42no—
986C23—42no—
987C23—62no—
988C23—92no—
989C23—94no—
990C23—92no—
991C23—122no—
992C23—184no—
993C23—182no—
994C23—362no—
995C23—362no—
996C23—364no—
997C23#381114yes—
998C23C22×D3212yes—
999C23C22×D3211yescharacteristic
1000C23C22×D3211yescharacteristic
1001C23C22×D3211yescharacteristic
1002Q8—184no—
1003Q8—188no—
1004D4—24no—
1005D4—24no—
1006D4—64no—
1007D4—64no—
1008D4—98no—
1009D4—98no—
1010D4—124no—
1011D4—184no—
1012D4—188no—
1013D4—184no—
1014D4—184no—
1015D4—184no—
1016D4—184no—
1017D4—364no—
1018C2×C4—22no—
1019C2×C4—34no—
1020C2×C4—34no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—32no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—64no—
1027C2×C4—64no—
1028C2×C4—62no—
1029C2×C4—94no—
1030C2×C4—92no—
1031C2×C4—92no—
1032C2×C4—122no—
1033C2×C4—122no—
1034C2×C4—184no—
1035C2×C4—184no—
1036C2×C4—188no—
1037C2×C4—188no—
1038C2×C4—184no—
1039C2×C4—182no—
1040C2×C4—364no—
1041C2×C4C22×D3212yes—
1042C2×C3—22no—
1043C2×C3—22no—
1044C2×C3—22no—
1045C2×C3—22no—
1046C2×C3—22no—
1047C2×C3—22no—
1048C2×C3—22no—
1049C2×C3—21no—
1050C2×C3—42no—
1051C2×C3—42no—
1052C2×C3—42no—
1053C2×C3—44no—
1054C2×C3—42no—
1055C2×C3—42no—
1056C2×C3—122no—
1057C2×C3C22×D3×D411yescharacteristic
1058C2×C3C22×D3×D411yescharacteristic
1059C2×C3#596412yes—
1060C2×C3#596612yes—
1061D3—42no—
1062D3—64no—
1063D3—64no—
1064D3—124no—
1065D3—124no—
1066D3—122no—
1067D3—122no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—24no—
1072C22—22no—
1073C22—44no—
1074C22—64no—
1075C22—62no—
1076C22—82no—
1077C22—94no—
1078C22—124no—
1079C22—184no—
1080C22—184no—
1081C22—182no—
1082C22—364no—
1083C22—722no—
1084C22—724no—
1085C22C2×#381112yes—
1086C22C2×#381112yes—
1087C22C2×#381112yes—
1088C22C23×D3211yescharacteristic
1089C4—22no—
1090C4—64no—
1091C4—64no—
1092C4—62no—
1093C4—62no—
1094C4—62no—
1095C4—94no—
1096C4—182no—
1097C3—21no—
1098C3#8601211yescharacteristic, complemented
1099C3#8629611yescharacteristic, complemented
1100C2—22no—
1101C2—22no—
1102C2—22no—
1103C2—42no—
1104C2—122no—
1105C2—184no—
1106C2—362no—
1107C2#1059667812yes—
1108C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64361C2semidirect
2. C22×#3804C2semidirect
3. C3×#5804C2semidirect
4. C2×C3×#935C2semidirect
5. #10595519C2semidirect
6. #10595510C2semidirect
7. #10595500C2semidirect
8. C2×#63966C2semidirect
9. #10595271C2semidirect
10. #10595242C2semidirect
11. #10595169C2semidirect
12. #10595163C2semidirect
13. #10595162C2semidirect
14. #10595160C2semidirect
15. #10594917C2semidirect
21. C22×#638C22semidirect
24. C2×#3830C22semidirect
26. C2×D4×C3⋊D3C22semidirect
27. C2×#3828C22semidirect
28. C22×C3×#67C22semidirect
29. C23×C3×Dic3C22semidirect
30. C22×#627C22semidirect
31. C22×#626C22semidirect
32. C22×#624C22semidirect
34. C2×#3804C22semidirect
35. C2×#3804C22semidirect
36. C22×D3×Dic3C22semidirect
37. C3×#953C22semidirect
38. C2×C3×#217C22semidirect
39. C2×C3×#217C22semidirect
40. C2×C3×#217C22semidirect
41. C3×#939C22semidirect
42. C3×#937C22semidirect
43. C3×#935C22semidirect
44. C3×#935C22semidirect
45. C3×#935C22semidirect
46. C3×#935C22semidirect
47. C3×#929C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. #63982C22semidirect
50. #63981C22semidirect
51. #63981C22semidirect
52. #63978C22semidirect
53. #63977C22semidirect
54. #63975C22semidirect
55. #63974C22semidirect
56. #63974C22semidirect
57. #67⋊Dic3C22semidirect
58. #63971C22semidirect
59. #63966C22semidirect
60. #63966C22semidirect
61. #63966C22semidirect
62. #63966C22semidirect
63. C2×Dic3⋊Dic3C22semidirect
64. C2×#3722C22semidirect
65. #63962C22semidirect
66. #63958C22semidirect
67. #63957C22semidirect
68. #63953C22semidirect
69. #63952C22semidirect
70. #63952C22semidirect
71. #63910C22semidirect
72. #63897C22semidirect
73. #63896C22semidirect
74. #63883C22semidirect
75. #63881C22semidirect
76. #63865C22semidirect
77. #63853C22semidirect
78. #63840C22semidirect
87. #5804D3semidirect
88. C2×#935D3semidirect
122. C2×#638D4semidirect
202. C22×#67C2×D3semidirect
204. C23×Dic3C2×D3semidirect
248. #953C2×D3semidirect
249. C2×#217C2×D3semidirect
250. C2×#217C2×D3semidirect
251. C2×#217C2×D3semidirect
254. #939C2×D3semidirect
258. #937C2×D3semidirect
260. #935C2×D3semidirect
261. #935C2×D3semidirect
262. #935C2×D3semidirect
263. #935C2×D3semidirect
270. #929C2×D3semidirect
277. C2×Dic3⋊C4C2×D3semidirect
982. C32#3485semidirect
1098. C3#86012semidirect
1099. C3#86296semidirect

Maximal subgroups

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

subgroupindex
C2×#643612
C22×#38042
C3×#58042
C2×C3×#9352
#105955192
#105955102
#105955002
C2×#639662
#105952712
#105952422
#105951692
#105951632
#105951622
#105951602
#105949172
#862963
#860123