Finite Group Databasebeta

← #13152062

Subgroups — #13152062

Order 1728.

1405 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6235C211yesmaximal, characteristic, complemented
2C2×#88671C211yesmaximal, characteristic, complemented
3#11721702C211yesmaximal, characteristic, complemented
4C2×#3757⋊C3C211yesmaximal, characteristic, complemented
5#11721323C211yesmaximal, characteristic, complemented
6#11721322C211yesmaximal, characteristic, complemented
7#11721320C211yesmaximal, characteristic, complemented
8#11721319C211yesmaximal, characteristic, complemented
9#11721315C211yesmaximal, characteristic, complemented
10#11721312C211yesmaximal, characteristic, complemented
11#11721309C211yesmaximal, characteristic, complemented
12#11721303C211yesmaximal, characteristic, complemented
13#11721301C211yesmaximal, characteristic, complemented
14#11721294C211yesmaximal, characteristic, complemented
15#11721293C211yesmaximal, characteristic, complemented
16#10595494—31nomaximal
17#10595493—31nomaximal
18C24×H(3,𝔽3)C2211yescharacteristic
19C23×#272C2211yescharacteristic
20C2×#6235—24no—
21C2×#6235C2211yescharacteristic
22C2×#6235C2211yescharacteristic
23C2×#6235C2211yescharacteristic
24C2×#6235C2211yescharacteristic
25C22×#1084C2211yescharacteristic
26C2×#638⋊C3C2211yescharacteristic
27C2×#638⋊C3C2211yescharacteristic, complemented
28C2×#638⋊C3C2211yescharacteristic, complemented
29C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
30C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
31C2×#6200C2211yescharacteristic, complemented
32C2×#6200C2211yescharacteristic, complemented
33C2×#6199C2211yescharacteristic, complemented
34C2×#6199C2211yescharacteristic, complemented
35#88671—24no—
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
37C2×#6196C2211yescharacteristic, complemented
38#3757⋊C3C2211yescharacteristic
39#3757⋊C3C2211yescharacteristic
40#3757⋊C3C2211yescharacteristic
41#3757⋊C3C2211yescharacteristic, complemented
42#3757⋊C3C2211yescharacteristic, complemented
43#3757⋊C3C2211yescharacteristic, complemented
44#3757⋊C3C2211yescharacteristic, complemented
45#88451C2211yescharacteristic, complemented
46#88451C2211yescharacteristic, complemented
47#88451C2211yescharacteristic, complemented
48#88451C2211yescharacteristic, complemented
49#88450C2211yescharacteristic, complemented
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88448C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55C22×C3×#67—31no—
56C22×C3×#67—31no—
57C22×C3×#67—61no—
58C2×#3805—31no—
59C2×#3804—31no—
60#64162D311yescharacteristic, complemented
61C2×#3757D311yescharacteristic, complemented
62C3×#953—31no—
63C2×C3×#217—31no—
64#63980—31no—
65#63978—31no—
66#63977—31no—
67#63976—31no—
68#67⋊Dic3—31no—
69Dic3×#67—31no—
70Dic3×#67—31no—
71#63971—31no—
72#63970—31no—
73#63970—31no—
74#63969—31no—
75#63969—31no—
76D3×#217—31no—
77D3×#217—31no—
78#63964—31no—
79#63964—31no—
80#63962—31no—
81#63961—31no—
82#63959—31no—
83#63959—31no—
84#63958—31no—
85#63952—31no—
86C23×H(3,𝔽3)—22no—
87C23×H(3,𝔽3)—22no—
88C23×H(3,𝔽3)—41no—
89C23×H(3,𝔽3)C2311yescharacteristic
90C23×H(3,𝔽3)C2311yescharacteristic
91C23×H(3,𝔽3)C2311yescharacteristic
92C22×#272—22no—
93C22×#272—22no—
94C22×#272—41no—
95C22×#272C2311yescharacteristic
96C22×#272C2311yescharacteristic
97C22×(C3⋊D3)⋊C3C2311yescharacteristic
98#6235—22no—
99#6235—22no—
100#6235—22no—
101#6235D414yescomplemented
102C2×#1084—22no—
103C2×#1084C2311yescharacteristic
104C2×#1084C2311yescharacteristic
105#638⋊C3—22no—
106#638⋊C3—22no—
107#638⋊C3—41no—
108C2×(C3⋊Dic3)⋊C3—22no—
109C2×(C3⋊Dic3)⋊C3—41no—
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
114C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
115C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
116C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
117#6200—22no—
118#6200—41no—
119#6199—22no—
120#6199—41no—
121((C3⋊D3)⋊C3)⋊C4—22no—
122#6196—22no—
123#5806—91no—
124#5591—91no—
125#5490—91no—
126C24×C32—21no—
127C24×C32C2×D311yescharacteristic
128C24×C32C2×D311yescharacteristic
129C23×C3×D3—31no—
130C23×C3×D3—31no—
131C23×C3×D3—61no—
132C2×#638C2×D311yescharacteristic
133C2×#638C2×D311yescharacteristic, complemented
134C2×#638C2×D311yescharacteristic, complemented
135C22×C3⋊Dic3C2×D311yescharacteristic, complemented
136C22×C3⋊Dic3C2×D311yescharacteristic, complemented
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—64no—
149C2×C3×#67—64no—
150C2×C3×#67—61no—
151C2×C3×#67—61no—
152C2×C3×#67—61no—
153C2×C3×#67—61no—
154C2×C3×#67—68no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—61no—
160C2×#627—31no—
161C2×#627—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#625—31no—
165C2×#625—31no—
166C2×#624—31no—
167#3805—64no—
168#3804—64no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C2×D3×Dic3—31no—
174#3757C2×D311yescharacteristic
175#3757C2×D311yescharacteristic
176#3757C2×D311yescharacteristic
177#3757C2×D311yescharacteristic, complemented
178#3757C2×D311yescharacteristic, complemented
179#3757C2×D311yescharacteristic, complemented
180#3757C2×D311yescharacteristic, complemented
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—31no—
188#3724—31no—
189#3724—31no—
190#3724—31no—
191Dic3⋊Dic3—31no—
192Dic3⋊Dic3—31no—
193Dic3⋊Dic3—31no—
194Dic3⋊Dic3—31no—
195Dic3⋊Dic3—31no—
196#3722—31no—
197(C2×D3)⋊Dic3—31no—
198(C2×D3)⋊Dic3—31no—
199(C2×D3)⋊Dic3—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—31no—
204(C2×D3)⋊Dic3—31no—
205(C2×D3)⋊Dic3—31no—
206Dic32—31no—
207Dic32—31no—
208C22×H(3,𝔽3)—21no—
209C22×H(3,𝔽3)—21no—
210C22×H(3,𝔽3)—21no—
211C22×H(3,𝔽3)—21no—
212C22×H(3,𝔽3)—21no—
213C22×H(3,𝔽3)—21no—
214C22×H(3,𝔽3)—21no—
215C22×H(3,𝔽3)—44no—
216C22×H(3,𝔽3)C2×D412yes—
217C22×H(3,𝔽3)#4112yescomplemented
218C22×H(3,𝔽3)C2411yescharacteristic
219C2×#272—21no—
220C2×#272—21no—
221C2×#272—21no—
222C2×#272—21no—
223C2×#272—21no—
224C2×#272—44no—
225C2×#272C2×D412yes—
226C2×(C3⋊D3)⋊C3—21no—
227C2×(C3⋊D3)⋊C3—21no—
228C2×(C3⋊D3)⋊C3—21no—
229#1084—21no—
230#1084C2×D412yes—
231(C3⋊Dic3)⋊C3—21no—
232(C3⋊Dic3)⋊C3—21no—
233(C3⋊Dic3)⋊C3—21no—
234(C3⋊Dic3)⋊C3—21no—
235(C3⋊Dic3)⋊C3—21no—
236(C3⋊Dic3)⋊C3—21no—
237(C3⋊Dic3)⋊C3—21no—
238C22×C3×D4—91no—
239C22×#67—31no—
240C22×#67—31no—
241C22×#67—61no—
242C2×#237—91no—
243C2×#237—91no—
244C2×#235—91no—
245C3×#120—91no—
246C2×C3×C22⋊C4—91no—
247#953—31no—
248#953—91no—
249#953—91no—
250C2×#217—31no—
251C2×#217—91no—
252C2×#217—91no—
253#939—91no—
254#939—91no—
255#939—91no—
256#939—91no—
257#938—91no—
258#938—91no—
259#937—91no—
260#936—91no—
261#935—91no—
262#935—91no—
263D4×Dic3—91no—
264D4×Dic3—91no—
265#930—91no—
266#929—91no—
267C4×#67—91no—
268C4×#67—91no—
269#924—91no—
270#886—91no—
271#885—91no—
272#885—91no—
273#884—91no—
274#884—91no—
275#883—91no—
276#883—91no—
277#882—91no—
278#67⋊C4—91no—
279#67⋊C4—91no—
280D3×C22⋊C4—91no—
281D3×C22⋊C4—91no—
282#878—91no—
283#878—91no—
284C23×C32—24no—
285C23×C32—22no—
286C23×C32—22no—
287C23×C32—22no—
288C23×C32—22no—
289C23×C32—21no—
290C23×C32—21no—
291C23×C32—21no—
292C23×C32—42no—
293C23×C32—41no—
294C23×C32—41no—
295C23×C32—42no—
296C23×C32C22×D311yescharacteristic
297C23×C32C22×D311yescharacteristic
298C23×C32C22×D311yescharacteristic
299C23×C32C22×D311yescharacteristic
300C23×C32C22×D311yescharacteristic
301C23×C32C22×D311yescharacteristic
302C22×C3⋊D3C22×D311yescharacteristic
303C22×C3×D3—31no—
304C22×C3×D3—31no—
305C22×C3×D3—31no—
306C22×C3×D3—31no—
307C22×C3×D3—31no—
308C22×C3×D3—61no—
309C22×C3×D3—61no—
310C22×C3×D3—62no—
311C22×C3×D3—62no—
312C22×C3×D3—64no—
313C22×C3×D3—62no—
314C22×C3×D3—62no—
315C22×C3×D3—122no—
316C22×C3×D3—121no—
317C22×C3×D3—121no—
318C22×C3×D3—122no—
319#638—22no—
320#638—22no—
321#638—41no—
322C2×C3⋊Dic3—22no—
323C2×C3⋊Dic3—41no—
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D311yescharacteristic
326C2×C3⋊Dic3C22×D311yescharacteristic
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C2×C3⋊Dic3C22×D311yescharacteristic
331C3×#67—34no—
332C3×#67—34no—
333C3×#67—64no—
334C3×#67—62no—
335C3×#67—62no—
336C3×#67—62no—
337C3×#67—62no—
338C3×#67—64no—
339C3×#67—64no—
340C3×#67—64no—
341C3×#67—62no—
342C3×#67—62no—
343C3×#67—62no—
344C3×#67—62no—
345C3×#67—121no—
346C2×C3×Dic3—31no—
347C2×C3×Dic3—31no—
348C2×C3×Dic3—31no—
349C2×C3×Dic3—31no—
350C2×C3×Dic3—31no—
351C2×C3×Dic3—31no—
352C2×C3×Dic3—31no—
353C2×C3×Dic3—31no—
354C2×C3×Dic3—31no—
355C2×C3×Dic3—31no—
356C2×C3×Dic3—31no—
357C2×C3×Dic3—61no—
358C2×C3×Dic3—61no—
359C2×C3×Dic3—62no—
360C2×C3×Dic3—62no—
361C2×C3×Dic3—64no—
362C2×C3×Dic3—62no—
363C2×C3×Dic3—121no—
364#627—62no—
365#627—62no—
366#626—62no—
367#626—121no—
368#625—62no—
369#625—121no—
370#624—62no—
371D3×Dic3—62no—
372D3×Dic3—62no—
373D3×Dic3—62no—
374D3×Dic3—121no—
375D3×Dic3—121no—
376#546—271noSylow
377C2×H(3,𝔽3)—22no—
378C2×H(3,𝔽3)—22no—
379C2×H(3,𝔽3)—41no—
380C2×H(3,𝔽3)C22×D411yescharacteristic
381C2×H(3,𝔽3)C2×#4111yescharacteristic
382C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
383#272—22no—
384#272—41no—
385(C3⋊D3)⋊C3—41no—
386C24×C3—31no—
387C24×C3—31no—
388C24×C3—61no—
389C24×C3—91no—
390C24×C3D3211yescharacteristic
391C23×D3—31no—
392C23×D3—31no—
393C23×D3—61no—
394C2×C3×D4—91no—
395C2×C3×D4—91no—
396C2×C3×D4—91no—
397C2×C3×D4—91no—
398C2×C3×D4—91no—
399C2×C3×D4—91no—
400C2×C3×D4—91no—
401C2×C3×D4—184no—
402C22×C3×C4—91no—
403C22×C3×C4—91no—
404C22×C3×C4—91no—
405C2×#67—31no—
406C2×#67—31no—
407C2×#67—31no—
408C2×#67—31no—
409C2×#67—31no—
410C2×#67—31no—
411C2×#67—31no—
412C2×#67—31no—
413C2×#67—31no—
414C2×#67—31no—
415C2×#67—31no—
416C2×#67—61no—
417C2×#67—61no—
418C2×#67—61no—
419C2×#67—61no—
420C2×#67—64no—
421C2×#67—64no—
422C2×#67—68no—
423C2×#67—91no—
424C2×#67—91no—
425C2×#67—91no—
426C2×#67—91no—
427C2×#67—91no—
428C2×#67—91no—
429C2×#67—91no—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—61no—
435C22×Dic3—91no—
436C22×Dic3—91no—
437C22×Dic3—91no—
438C22×Dic3—91no—
439C22×Dic3—91no—
440#237—184no—
441#237—184no—
442#235—184no—
443C2×D12—91no—
444C2×D12—91no—
445C2×C4×D3—91no—
446C2×C4×D3—91no—
447C2×C4×D3—91no—
448C2×C4×D3—91no—
449C2×C4×D3—91no—
450C2×C4×D3—91no—
451C2×Dic6—91no—
452C2×Dic6—91no—
453C2×Dic6—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C22⋊C4—91no—
459C3×C22⋊C4—91no—
460C3×C22⋊C4—91no—
461#217—31no—
462#217—31no—
463#217—31no—
464#217—31no—
465#217—31no—
466#217—31no—
467#217—31no—
468#217—91no—
469#217—91no—
470#217—91no—
471#217—91no—
472#217—91no—
473#217—91no—
474#217—91no—
475#217—91no—
476#217—91no—
477#217—91no—
478#217—91no—
479#217—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487(C2×D3)⋊C4—91no—
488(C2×D3)⋊C4—91no—
489(C2×D3)⋊C4—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494Dic3⋊C4—91no—
495Dic3⋊C4—91no—
496Dic3⋊C4—91no—
497Dic3⋊C4—91no—
498Dic3⋊C4—91no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502C4×Dic3—91no—
503C4×Dic3—91no—
504C4×Dic3—91no—
505C22×C32—22no—
506C22×C32—22no—
507C22×C32—21no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32—21no—
515C22×C32—22no—
516C22×C32—21no—
517C22×C32—21no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—21no—
521C22×C32—21no—
522C22×C32—21no—
523C22×C32—22no—
524C22×C32—22no—
525C22×C32—41no—
526C22×C32—41no—
527C22×C32—41no—
528C22×C32—41no—
529C22×C32—44no—
530C22×C32—44no—
531C22×C32—48no—
532C22×C32#23512yescomplemented
533C22×C32D3×D412yes—
534C22×C32D3×D412yes—
535C22×C32#23712yescomplemented
536C22×C32C23×D311yescharacteristic
537C22×C32C23×D311yescharacteristic
538C2×C3⋊D3—21no—
539C2×C3⋊D3—21no—
540C2×C3⋊D3—21no—
541C2×C3×D3—32no—
542C2×C3×D3—32no—
543C2×C3×D3—62no—
544C2×C3×D3—61no—
545C2×C3×D3—61no—
546C2×C3×D3—61no—
547C2×C3×D3—61no—
548C2×C3×D3—62no—
549C2×C3×D3—61no—
550C2×C3×D3—61no—
551C2×C3×D3—61no—
552C2×C3×D3—61no—
553C2×C3×D3—61no—
554C2×C3×D3—61no—
555C2×C3×D3—61no—
556C2×C3×D3—61no—
557C2×C3×D3—61no—
558C2×C3×D3—121no—
559C2×C3×D3—121no—
560C2×C3×D3—121no—
561C2×C3×D3—121no—
562C2×C3×D3—124no—
563C2×C3×D3—124no—
564C2×C3×D3—128no—
565C3⋊Dic3—21no—
566C3⋊Dic3—21no—
567C3⋊Dic3—21no—
568C3⋊Dic3—21no—
569C3⋊Dic3—21no—
570C3⋊Dic3—21no—
571C3⋊Dic3—21no—
572C3×Dic3—32no—
573C3×Dic3—32no—
574C3×Dic3—62no—
575C3×Dic3—62no—
576C3×Dic3—61no—
577C3×Dic3—61no—
578C3×Dic3—61no—
579C3×Dic3—61no—
580C3×Dic3—61no—
581C3×Dic3—61no—
582C3×Dic3—61no—
583C3×Dic3—61no—
584C3×Dic3—61no—
585C2×#41—271no—
586C22×D4—91no—
587#124—271no—
588#123—271no—
589#123—271no—
590C22⋊Q8—271no—
591#121—271no—
592#121—271no—
593#121—271no—
594#120—91no—
595#120—271no—
596C4×D4—271no—
597C4×D4—271no—
598C2×C22⋊C4—91no—
599C2×C22⋊C4—271no—
600H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—31no—
604C23×C3—31no—
605C23×C3—31no—
606C23×C3—31no—
607C23×C3—31no—
608C23×C3—31no—
609C23×C3—41no—
610C23×C3—62no—
611C23×C3—62no—
612C23×C3—62no—
613C23×C3—62no—
614C23×C3—64no—
615C23×C3—61no—
616C23×C3—61no—
617C23×C3—61no—
618C23×C3—91no—
619C23×C3—91no—
620C23×C3—91no—
621C23×C3—122no—
622C23×C3—121no—
623C23×C3—121no—
624C23×C3—122no—
625C23×C3—182no—
626C23×C3—182no—
627C23×C3—361no—
628C23×C3C2×D3211yescharacteristic
629C23×C3C2×D3211yescharacteristic
630C23×C3C2×D3211yescharacteristic
631C22×D3—31no—
632C22×D3—31no—
633C22×D3—31no—
634C22×D3—31no—
635C22×D3—31no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—62no—
641C22×D3—62no—
642C22×D3—64no—
643C22×D3—91no—
644C22×D3—122no—
645C22×D3—121no—
646C22×D3—121no—
647C22×D3—122no—
648C3×D4—94no—
649C3×D4—182no—
650C3×D4—182no—
651C3×D4—182no—
652C3×D4—182no—
653C3×D4—182no—
654C3×D4—361no—
655C2×C3×C4—91no—
656C2×C3×C4—91no—
657C2×C3×C4—91no—
658C2×C3×C4—91no—
659C2×C3×C4—91no—
660C2×C3×C4—91no—
661C2×C3×C4—91no—
662C2×C3×C4—91no—
663C2×C3×C4—91no—
664C2×C3×C4—182no—
665C2×C3×C4—182no—
666C2×C3×C4—361no—
667#67—34no—
668#67—34no—
669#67—64no—
670#67—62no—
671#67—62no—
672#67—62no—
673#67—62no—
674#67—62no—
675#67—62no—
676#67—64no—
677#67—64no—
678#67—64no—
679#67—62no—
680#67—62no—
681#67—121no—
682#67—182no—
683#67—182no—
684#67—182no—
685#67—182no—
686#67—361no—
687#67—361no—
688#67—361no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—62no—
703C2×Dic3—62no—
704C2×Dic3—64no—
705C2×Dic3—62no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—91no—
711C2×Dic3—91no—
712C2×Dic3—91no—
713C2×Dic3—121no—
714C2×Dic3—182no—
715C2×Dic3—182no—
716C2×Dic3—182no—
717C2×Dic3—361no—
718C2×Dic3—361no—
719D12—182no—
720D12—361no—
721C4×D3—182no—
722C4×D3—182no—
723C4×D3—182no—
724C4×D3—182no—
725C4×D3—361no—
726C4×D3—361no—
727Dic6—182no—
728Dic6—182no—
729Dic6—182no—
730C2×C32—24no—
731C2×C32—22no—
732C2×C32—22no—
733C2×C32—22no—
734C2×C32—22no—
735C2×C32—21no—
736C2×C32—21no—
737C2×C32—21no—
738C2×C32—42no—
739C2×C32—42no—
740C2×C32—41no—
741C2×C32—41no—
742C2×C32C2×#23511yescharacteristic
743C2×C32C2×D3×D411yescharacteristic
744C2×C32C2×D3×D411yescharacteristic
745C2×C32C2×#23711yescharacteristic
746C2×C32#100411yescharacteristic
747C2×C32#100411yescharacteristic
748C3⋊D3—41no—
749C3×D3—62no—
750C3×D3—62no—
751C3×D3—122no—
752C3×D3—122no—
753C3×D3—121no—
754C3×D3—121no—
755C3×D3—121no—
756C24—91no—
757C24((C3⋊D3)⋊C3)⋊C211yescharacteristic
758#41—544no—
759C2×Q8—271no—
760C2×D4—91no—
761C2×D4—91no—
762C2×D4—91no—
763C2×D4—91no—
764C2×D4—91no—
765C2×D4—91no—
766C2×D4—91no—
767C2×D4—184no—
768C2×D4—271no—
769C2×D4—271no—
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—271no—
774C22×C4—271no—
775C22×C4—271no—
776C4⋊C4—271no—
777C4⋊C4—271no—
778C4⋊C4—271no—
779C4⋊C4—271no—
780C22⋊C4—91no—
781C22⋊C4—91no—
782C22⋊C4—91no—
783C22⋊C4—91no—
784C22⋊C4—91no—
785C22⋊C4—91no—
786C22⋊C4—91no—
787C22⋊C4—271no—
788C22⋊C4—271no—
789C22⋊C4—271no—
790C22⋊C4—271no—
791C22⋊C4—271no—
792C42—271no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—31no—
801C22×C3—31no—
802C22×C3—32no—
803C22×C3—32no—
804C22×C3—32no—
805C22×C3—32no—
806C22×C3—44no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—61no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—92no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—124no—
833C22×C3—124no—
834C22×C3—128no—
835C22×C3—181no—
836C22×C3—181no—
837C22×C3—181no—
838C22×C3—181no—
839C22×C3—181no—
840C22×C3—181no—
841C22×C3—181no—
842C22×C3—181no—
843C22×C3—364no—
844C22×C3#380412yes—
845C22×C3#381112yes—
846C22×C3C22×D3211yescharacteristic
847C2×D3—32no—
848C2×D3—32no—
849C2×D3—62no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—61no—
853C2×D3—61no—
854C2×D3—61no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—61no—
858C2×D3—61no—
859C2×D3—61no—
860C2×D3—62no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—124no—
869C2×D3—124no—
870C2×D3—128no—
871C2×D3—181no—
872C2×D3—181no—
873C2×D3—181no—
874C3×C4—92no—
875C3×C4—181no—
876C3×C4—181no—
877C3×C4—181no—
878C3×C4—181no—
879C3×C4—181no—
880C3×C4—181no—
881C3×C4—181no—
882C3×C4—181no—
883Dic3—32no—
884Dic3—32no—
885Dic3—62no—
886Dic3—61no—
887Dic3—61no—
888Dic3—62no—
889Dic3—61no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—181no—
897Dic3—181no—
898Dic3—181no—
899Dic3—181no—
900Dic3—181no—
901Dic3—181no—
902Dic3—181no—
903C32—21no—
904C32#549011yescharacteristic, complemented
905C32#559111yescharacteristic, complemented
906C23—22no—
907C23—22no—
908C23—41no—
909C23—91no—
910C23—91no—
911C23—91no—
912C23—182no—
913C23—182no—
914C23—361no—
915C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
916C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
917C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
918Q8—542no—
919D4—94no—
920D4—182no—
921D4—182no—
922D4—182no—
923D4—182no—
924D4—182no—
925D4—361no—
926D4—542no—
927D4—1081no—
928C2×C4—91no—
929C2×C4—91no—
930C2×C4—91no—
931C2×C4—91no—
932C2×C4—91no—
933C2×C4—91no—
934C2×C4—91no—
935C2×C4—91no—
936C2×C4—91no—
937C2×C4—182no—
938C2×C4—182no—
939C2×C4—361no—
940C2×C4—542no—
941C2×C4—542no—
942C2×C4—1081no—
943C2×C3—22no—
944C2×C3—22no—
945C2×C3—31no—
946C2×C3—31no—
947C2×C3—31no—
948C2×C3—31no—
949C2×C3—31no—
950C2×C3—31no—
951C2×C3—41no—
952C2×C3—62no—
953C2×C3—62no—
954C2×C3—62no—
955C2×C3—62no—
956C2×C3—64no—
957C2×C3—61no—
958C2×C3—61no—
959C2×C3—61no—
960C2×C3—122no—
961C2×C3—121no—
962C2×C3—121no—
963C2×C3—122no—
964C2×C3—182no—
965C2×C3—361no—
966C2×C3—361no—
967C2×C3C2×#380411yescharacteristic
968C2×C3C2×#381111yescharacteristic
969C2×C3#6433011yescharacteristic
970D3—62no—
971D3—62no—
972D3—122no—
973D3—121no—
974D3—121no—
975D3—122no—
976D3—121no—
977D3—361no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—44no—
986C22—92no—
987C22—181no—
988C22—181no—
989C22—181no—
990C22—181no—
991C22—181no—
992C22—181no—
993C22—181no—
994C22—181no—
995C22—364no—
996C22#8867112yescomplemented
997C22#8867712yes—
998C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
999C4—92no—
1000C4—181no—
1001C4—181no—
1002C4—181no—
1003C4—181no—
1004C4—181no—
1005C4—181no—
1006C4—181no—
1007C4—181no—
1008C3—31no—
1009C3—31no—
1010C3—61no—
1011C3#1059550011yescharacteristic
1012C2—22no—
1013C2—22no—
1014C2—41no—
1015C2—182no—
1016C2—361no—
1017C2—361no—
1018C2C2×#8867111yescharacteristic
1019C2C2×#8867711yescharacteristic
1020C2#1172254511yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC24×H(3,𝔽3)C22
hypercenterC24((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#546
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#6235C2semidirect
2. C2×#88671C2semidirect
3. #11721702C2semidirect
4. C2×#3757⋊C3C2semidirect
5. #11721323C2semidirect
6. #11721322C2semidirect
7. #11721320C2semidirect
8. #11721319C2semidirect
9. #11721315C2semidirect
10. #11721312C2semidirect
11. #11721309C2semidirect
12. #11721303C2semidirect
13. #11721301C2semidirect
14. #11721294C2semidirect
15. #11721293C2semidirect
27. C2×#638⋊C3C22semidirect
28. C2×#638⋊C3C22semidirect
29. C22×(C3⋊Dic3)⋊C3C22semidirect
30. C22×(C3⋊Dic3)⋊C3C22semidirect
31. C2×#6200C22semidirect
32. C2×#6200C22semidirect
33. C2×#6199C22semidirect
34. C2×#6199C22semidirect
36. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
37. C2×#6196C22semidirect
41. #3757⋊C3C22semidirect
42. #3757⋊C3C22semidirect
43. #3757⋊C3C22semidirect
44. #3757⋊C3C22semidirect
45. #88451C22semidirect
46. #88451C22semidirect
47. #88451C22semidirect
48. #88451C22semidirect
49. #88450C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88448C22semidirect
53. #88448C22semidirect
54. #88447C22semidirect
60. #64162D3semidirect
61. C2×#3757D3semidirect
101. #6235D4semidirect
133. C2×#638C2×D3semidirect
134. C2×#638C2×D3semidirect
135. C22×C3⋊Dic3C2×D3semidirect
136. C22×C3⋊Dic3C2×D3semidirect
177. #3757C2×D3semidirect
178. #3757C2×D3semidirect
179. #3757C2×D3semidirect
180. #3757C2×D3semidirect
217. C22×H(3,𝔽3)#41semidirect
532. C22×C32#235semidirect
535. C22×C32#237semidirect
600. H(3,𝔽3)#546semidirect
904. C32#5490semidirect
905. C32#5591semidirect
996. C22#88671semidirect

Maximal subgroups

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

subgroupindex
C22×#62352
C2×#886712
#117217022
C2×#3757⋊C32
#117213232
#117213222
#117213202
#117213192
#117213152
#117213122
#117213092
#117213032
#117213012
#117212942
#117212932
#105954943
#105954933