Finite Group Databasebeta

← #13148647

Subgroups — #13148647

Order 1728.

1628 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88677C211yesmaximal, characteristic, complemented
2C2×#88676C211yesmaximal, characteristic, complemented
3C22×#6200C211yesmaximal, characteristic, complemented
4C2×#88654C211yesmaximal, characteristic, complemented
5#11721738C211yesmaximal, characteristic, complemented
6#64091⋊C3C211yesmaximal, characteristic, complemented
7#64090⋊C3C211yesmaximal, characteristic, complemented
8#11721322C211yesmaximal, characteristic, complemented
9#11721163C211yesmaximal, characteristic, complemented
10#11721162C211yesmaximal, characteristic, complemented
11#11721158C211yesmaximal, characteristic, complemented
12#11721157C211yesmaximal, characteristic, complemented
13#11721140C211yesmaximal, characteristic, complemented
14#11721127C211yesmaximal, characteristic, complemented
15#11721123C211yesmaximal, characteristic, complemented
16#10594277—31nomaximal
17#10594271—31nomaximal
18C23×#272C2211yescharacteristic, complemented
19C23×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
20C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic, complemented
21C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic, complemented
22C2×#6235C2211yescharacteristic, complemented
23C2×C4⋊#272C2211yescharacteristic, complemented
24C2×C4⋊#272C2211yescharacteristic, complemented
25C2×#638⋊C3C2211yescharacteristic
26C2×#638⋊C3C2211yescharacteristic, complemented
27C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
28C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
29C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
30C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
31#88677—24no—
32#88676—24no—
33C2×#6200—24no—
34C2×#6200C2211yescharacteristic
35C2×#6200C2211yescharacteristic, complemented
36C2×#6200C2211yescharacteristic, complemented
37C2×#6200C2211yescharacteristic, complemented
38C2×#6200C2211yescharacteristic, complemented
39C2×#6200C2211yescharacteristic, complemented
40C2×#6200C2211yescharacteristic, complemented
41C2×#6200C2211yescharacteristic, complemented
42C2×#6199C2211yescharacteristic, complemented
43C2×#6198C2211yescharacteristic, complemented
44C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
45#88654—24no—
46C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
47#88542C2211yescharacteristic, complemented
48#88542C2211yescharacteristic, complemented
49#3752⋊C3C2211yescharacteristic, complemented
50#3752⋊C3C2211yescharacteristic, complemented
51#3752⋊C3C2211yescharacteristic, complemented
52#3750⋊C3C2211yescharacteristic, complemented
53C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
54#88451C2211yescharacteristic, complemented
55#88450C2211yescharacteristic, complemented
56#88448C2211yescharacteristic, complemented
57C2×#3811—31no—
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C2×D3×#67—31no—
61C22×#626—31no—
62C22×#625—31no—
63C2×#3802—31no—
64C2×D3×D12—31no—
65#64091D311yescharacteristic, complemented
66#64090D311yescharacteristic, complemented
67C3×#882—31no—
68C3×#882—31no—
69C3×#882—31no—
70C3×#882—61no—
71C3×#67⋊C4—31no—
72#63980—31no—
73#63978—31no—
74#63923—31no—
75#63922—31no—
76#63922—31no—
77#63922—31no—
78#63914—31no—
79#63912—31no—
80#63911—31no—
81#63910—31no—
82#63906—31no—
83#63902—31no—
84#63886—31no—
85#63885—31no—
86#63885—31no—
87#63880—31no—
88C23×H(3,𝔽3)C2311yescharacteristic
89C22×#272—22no—
90C22×#272—22no—
91C22×#272—41no—
92C22×#272C2311yescharacteristic
93C22×#272C2311yescharacteristic
94C22×#272C2311yescharacteristic
95C22×(C3⋊D3)⋊C3—22no—
96C22×(C3⋊D3)⋊C3—22no—
97C22×(C3⋊D3)⋊C3—41no—
98C22×(C3⋊D3)⋊C3C2311yescharacteristic
99C22×(C3⋊D3)⋊C3C2311yescharacteristic
100C22×(C3⋊D3)⋊C3C2311yescharacteristic
101C22×(C3⋊D3)⋊C3C2311yescharacteristic
102C2×((C3⋊D3)⋊C3)⋊C2—22no—
103C2×((C3⋊D3)⋊C3)⋊C2—22no—
104C2×((C3⋊D3)⋊C3)⋊C2—22no—
105C2×((C3⋊D3)⋊C3)⋊C2—22no—
106C2×((C3⋊D3)⋊C3)⋊C2—41no—
107C2×((C3⋊D3)⋊C3)⋊C2—41no—
108C2×C4×H(3,𝔽3)C2311yescharacteristic
109C2×C4×H(3,𝔽3)C2311yescharacteristic
110#6235—22no—
111C2×#1084C2311yescharacteristic
112C4⋊#272—22no—
113C4⋊#272—41no—
114#638⋊C3—22no—
115#638⋊C3D414yescomplemented
116C2×(C3⋊Dic3)⋊C3—22no—
117C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
118C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
119C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
120C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
121C4⋊((C3⋊D3)⋊C3)—22no—
122C4⋊((C3⋊D3)⋊C3)—41no—
123C4×(C3⋊D3)⋊C3—22no—
124#6200—22no—
125#6200—22no—
126#6200—22no—
127#6200—22no—
128#6200—22no—
129#6200—22no—
130#6200—22no—
131#6200D414yescomplemented
132#6199—22no—
133#6198—22no—
134((C3⋊D3)⋊C3)⋊C4—22no—
135#5590—91no—
136#5590—91no—
137D4×D12—91no—
138C23×C3⋊D3C2×D311yescharacteristic, complemented
139C23×C3×D3—31no—
140C23×C3×D3—31no—
141C23×C3×D3—31no—
142C23×C3×D3—61no—
143C22×D32—31no—
144C22×D32—31no—
145C22×D32—31no—
146C22×D32—31no—
147C2×#638C2×D311yescharacteristic
148C2×#638C2×D311yescharacteristic, complemented
149C22×C3⋊Dic3C2×D311yescharacteristic, complemented
150C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
151C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
152C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—61no—
158C22×C3×Dic3—31no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—31no—
162C2×C3×D12—31no—
163C2×C3×D12—31no—
164C2×C3×D12—31no—
165C2×C3×D12—61no—
166C2×C3×D12—61no—
167C2×C3×C4×D3—31no—
168#3811—64no—
169D3×#67—64no—
170D3×#67—64no—
171D3×#67—64no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—64no—
183C2×#625—31no—
184C2×#625—31no—
185C2×#625—31no—
186C2×#625—31no—
187C2×#625—31no—
188C2×#625—31no—
189C2×#625—31no—
190C2×#625—31no—
191C2×#625—64no—
192C2×#624—31no—
193C2×D3×Dic3—31no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—31no—
196#3802—64no—
197D3×D12—64no—
198C32×C22⋊C4—21no—
199C32×C22⋊C4C2×D311yescharacteristic, complemented
200C32×C22⋊C4C2×D311yescharacteristic, complemented
201#3752C2×D311yescharacteristic, complemented
202#3752C2×D311yescharacteristic, complemented
203#3752C2×D311yescharacteristic, complemented
204#3750C2×D311yescharacteristic, complemented
205C4×C3⋊Dic3C2×D311yescharacteristic, complemented
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—61no—
214C3×(C2×D3)⋊C4—61no—
215C3×Dic3⋊C4—31no—
216C3×C4×Dic3—31no—
217#3724—31no—
218Dic3⋊Dic3—31no—
219#3722—31no—
220(C2×D3)⋊Dic3—31no—
221(C2×D3)⋊Dic3—31no—
222(C2×D3)⋊Dic3—31no—
223C22×H(3,𝔽3)—21no—
224C22×H(3,𝔽3)—21no—
225C22×H(3,𝔽3)C2×D412yescomplemented
226C22×H(3,𝔽3)C2411yescharacteristic
227C2×#272—21no—
228C2×#272—21no—
229C2×#272—21no—
230C2×#272—21no—
231C2×#272—21no—
232C2×#272—21no—
233C2×#272—21no—
234C2×#272—21no—
235C2×#272—44no—
236C2×#272C2×D412yescomplemented
237C2×(C3⋊D3)⋊C3—21no—
238C2×(C3⋊D3)⋊C3—21no—
239C2×(C3⋊D3)⋊C3—21no—
240C2×(C3⋊D3)⋊C3—21no—
241C2×(C3⋊D3)⋊C3—21no—
242C2×(C3⋊D3)⋊C3—21no—
243C2×(C3⋊D3)⋊C3—21no—
244C2×(C3⋊D3)⋊C3—21no—
245C2×(C3⋊D3)⋊C3—21no—
246C2×(C3⋊D3)⋊C3—21no—
247C2×(C3⋊D3)⋊C3—44no—
248C2×(C3⋊D3)⋊C3C2×D412yescomplemented
249C2×(C3⋊D3)⋊C3C2×D412yescomplemented
250((C3⋊D3)⋊C3)⋊C2—44no—
251((C3⋊D3)⋊C3)⋊C2—44no—
252C4×H(3,𝔽3)—21no—
253C4×H(3,𝔽3)—21no—
254#1084—21no—
255(C3⋊Dic3)⋊C3—21no—
256(C3⋊Dic3)⋊C3—21no—
257(C3⋊Dic3)⋊C3C2×D412yescomplemented
258(C3⋊Dic3)⋊C3C2×D412yescomplemented
259C22×#67—91no—
260C22×#67—91no—
261C22×#67—91no—
262C22×#67—91no—
263C2×D3×D4—91no—
264C2×D3×D4—91no—
265C2×D3×D4—91no—
266C2×D3×D4—91no—
267C2×D3×D4—91no—
268C2×D3×D4—91no—
269C22×D12—91no—
270C22×D12—91no—
271C3×#120—91no—
272C3×#120—91no—
273C3×C4×D4—91no—
274#940—91no—
275#940—91no—
276#939—91no—
277#939—91no—
278#939—91no—
279#939—91no—
280#937—91no—
281#937—91no—
282#930—91no—
283#930—91no—
284#895—91no—
285#895—91no—
286#884—91no—
287#884—91no—
288#884—91no—
289#884—91no—
290#882—31no—
291#882—31no—
292#882—31no—
293#882—61no—
294#882—91no—
295#882—91no—
296#882—91no—
297#882—91no—
298#882—91no—
299#67⋊C4—31no—
300#67⋊C4—91no—
301#67⋊C4—91no—
302#67⋊C4—91no—
303#874—91no—
304C4×D12—91no—
305C23×C32—21no—
306C23×C32C22×D311yescharacteristic
307C23×C32C22×D311yescharacteristic
308C22×C3⋊D3—22no—
309C22×C3⋊D3—22no—
310C22×C3⋊D3—41no—
311C22×C3⋊D3C22×D311yescharacteristic
312C22×C3⋊D3C22×D311yescharacteristic
313C22×C3⋊D3C22×D311yescharacteristic
314C22×C3⋊D3C22×D311yescharacteristic
315C22×C3×D3—31no—
316C22×C3×D3—31no—
317C22×C3×D3—31no—
318C22×C3×D3—31no—
319C22×C3×D3—31no—
320C22×C3×D3—31no—
321C22×C3×D3—31no—
322C22×C3×D3—31no—
323C22×C3×D3—31no—
324C22×C3×D3—31no—
325C22×C3×D3—61no—
326C22×C3×D3—61no—
327C22×C3×D3—61no—
328C22×C3×D3—62no—
329C22×C3×D3—62no—
330C22×C3×D3—62no—
331C22×C3×D3—62no—
332C22×C3×D3—62no—
333C22×C3×D3—62no—
334C22×C3×D3—122no—
335C22×C3×D3—122no—
336C22×C3×D3—121no—
337C22×C3×D3—121no—
338C22×C3×D3—121no—
339C22×C3×D3—122no—
340C2×D32—62no—
341C2×D32—62no—
342C2×D32—62no—
343C2×D32—62no—
344C2×D32—62no—
345C2×D32—62no—
346C2×D32—62no—
347C2×D32—62no—
348C2×D32—121no—
349C2×D32—121no—
350C2×D32—121no—
351C2×D32—121no—
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4C22×D311yescharacteristic
355C2×C32×C4C22×D311yescharacteristic
356C2×C32×C4C22×D311yescharacteristic
357C2×C32×C4C22×D311yescharacteristic
358#638—22no—
359#638D1214yescomplemented
360C2×C3⋊Dic3—22no—
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C4⋊(C3⋊D3)—22no—
366C4⋊(C3⋊D3)—41no—
367C4×C3⋊D3—22no—
368C3×#67—34no—
369C3×#67—62no—
370C3×#67—62no—
371C3×#67—62no—
372C3×#67—122no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—62no—
381C3×D12—62no—
382C3×D12—62no—
383C3×D12—62no—
384C3×D12—122no—
385C3×D12—121no—
386C3×D12—121no—
387C3×D12—121no—
388C3×D12—122no—
389C3×C4×D3—62no—
390#626—34no—
391#626—62no—
392#626—62no—
393#626—62no—
394#626—62no—
395#626—62no—
396#626—62no—
397#626—62no—
398#626—62no—
399#626—62no—
400#625—34no—
401#625—62no—
402#625—62no—
403#625—62no—
404#625—62no—
405#625—62no—
406#625—62no—
407#625—62no—
408#624—62no—
409D3×Dic3—62no—
410D3×Dic3—62no—
411D3×Dic3—62no—
412D42—271noSylow
413C2×H(3,𝔽3)—22no—
414C2×H(3,𝔽3)C22×D411yescharacteristic
415C2×H(3,𝔽3)C22×D411yescharacteristic
416C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
417#272—22no—
418#272—41no—
419#272—41no—
420(C3⋊D3)⋊C3—22no—
421(C3⋊D3)⋊C3—22no—
422(C3⋊D3)⋊C3—41no—
423(C3⋊D3)⋊C3—41no—
424C24×C3—91no—
425C24×C3—91no—
426C23×D3—31no—
427C23×D3—31no—
428C23×D3—31no—
429C23×D3—61no—
430C23×D3—91no—
431C23×D3—91no—
432C23×D3—91no—
433C23×D3—91no—
434C23×D3—91no—
435C23×D3—91no—
436C23×D3—91no—
437C2×C3×D4—91no—
438C2×C3×D4—91no—
439C2×C3×D4—91no—
440C2×C3×D4—91no—
441C2×C3×D4—91no—
442C2×C3×D4—91no—
443C2×C3×D4—91no—
444C22×C3×C4—91no—
445C22×C3×C4—91no—
446C2×#67—31no—
447C2×#67—31no—
448C2×#67—31no—
449C2×#67—31no—
450C2×#67—61no—
451C2×#67—91no—
452C2×#67—91no—
453C2×#67—91no—
454C2×#67—91no—
455C2×#67—91no—
456C2×#67—91no—
457C2×#67—91no—
458C2×#67—91no—
459C2×#67—91no—
460C2×#67—91no—
461C2×#67—91no—
462C2×#67—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—91no—
468C2×#67—91no—
469C2×#67—91no—
470C2×#67—91no—
471C2×#67—184no—
472C2×#67—184no—
473C2×#67—184no—
474C2×#67—184no—
475C22×Dic3—31no—
476C22×Dic3—91no—
477C22×Dic3—91no—
478C22×Dic3—91no—
479D3×D4—184no—
480D3×D4—184no—
481D3×D4—184no—
482D3×D4—184no—
483D3×D4—184no—
484D3×D4—184no—
485C2×D12—31no—
486C2×D12—31no—
487C2×D12—31no—
488C2×D12—31no—
489C2×D12—31no—
490C2×D12—31no—
491C2×D12—61no—
492C2×D12—61no—
493C2×D12—91no—
494C2×D12—91no—
495C2×D12—91no—
496C2×D12—91no—
497C2×D12—91no—
498C2×D12—91no—
499C2×D12—91no—
500C2×D12—91no—
501C2×D12—91no—
502C2×D12—91no—
503C2×D12—91no—
504C2×D12—184no—
505C2×D12—184no—
506C2×C4×D3—31no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×C4×D3—91no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C3×C4⋊C4—91no—
513C3×C22⋊C4—31no—
514C3×C22⋊C4—31no—
515C3×C22⋊C4—61no—
516C3×C22⋊C4—91no—
517C3×C22⋊C4—91no—
518C3×C22⋊C4—91no—
519C3×C22⋊C4—91no—
520C3×C22⋊C4—91no—
521C3×C22⋊C4D3211yescharacteristic
522C3×C42—91no—
523#217—91no—
524#217—91no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—61no—
533(C2×D3)⋊C4—61no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541C4⋊Dic3—91no—
542Dic3⋊C4—31no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546C4×Dic3—31no—
547C4×Dic3—91no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—22no—
554C22×C32—41no—
555C22×C32—41no—
556C22×C32C2×D1212yescomplemented
557C22×C32D3×D412yescomplemented
558C22×C32C23×D311yescharacteristic
559C22×C32C23×D311yescharacteristic
560C2×C3⋊D3—21no—
561C2×C3⋊D3—21no—
562C2×C3⋊D3—21no—
563C2×C3⋊D3—21no—
564C2×C3⋊D3—21no—
565C2×C3⋊D3—21no—
566C2×C3⋊D3—21no—
567C2×C3⋊D3—21no—
568C2×C3⋊D3—21no—
569C2×C3⋊D3—21no—
570C2×C3⋊D3—44no—
571C2×C3⋊D3C2×D1212yescomplemented
572C2×C3⋊D3D3×D412yescomplemented
573C2×C3×D3—32no—
574C2×C3×D3—32no—
575C2×C3×D3—32no—
576C2×C3×D3—32no—
577C2×C3×D3—62no—
578C2×C3×D3—61no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—61no—
583C2×C3×D3—61no—
584C2×C3×D3—61no—
585C2×C3×D3—61no—
586C2×C3×D3—62no—
587C2×C3×D3—61no—
588C2×C3×D3—61no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—61no—
594C2×C3×D3—61no—
595C2×C3×D3—61no—
596C2×C3×D3—61no—
597C2×C3×D3—61no—
598C2×C3×D3—61no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—61no—
604C2×C3×D3—61no—
605C2×C3×D3—121no—
606C2×C3×D3—121no—
607C2×C3×D3—121no—
608C2×C3×D3—121no—
609C2×C3×D3—121no—
610C2×C3×D3—121no—
611C2×C3×D3—121no—
612C2×C3×D3—124no—
613C2×C3×D3—124no—
614C2×C3×D3—124no—
615C2×C3×D3—128no—
616D32—124no—
617D32—124no—
618D32—124no—
619D32—124no—
620C32×C4—21no—
621C32×C4—21no—
622C32×C4—21no—
623C32×C4—21no—
624C32×C4—41no—
625C32×C4—41no—
626C3⋊Dic3—21no—
627C3⋊Dic3—21no—
628C3⋊Dic3C2×D1212yescomplemented
629C3⋊Dic3D3×D412yescomplemented
630C3×Dic3—32no—
631C3×Dic3—32no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—121no—
637C22×D4—271no—
638C22×D4—271no—
639C22×D4—271no—
640C22×D4—271no—
641#127—271no—
642#121—271no—
643#121—271no—
644#121—271no—
645#121—271no—
646#120—91no—
647#120—91no—
648#120—271no—
649#120—271no—
650C4×D4—91no—
651C4×D4—271no—
652H(3,𝔽3)D4211yescharacteristic, complemented, Sylow
653C23×C3—31no—
654C23×C3—31no—
655C23×C3—61no—
656C23×C3—91no—
657C23×C3—91no—
658C23×C3—91no—
659C23×C3—91no—
660C23×C3—91no—
661C23×C3—91no—
662C23×C3—91no—
663C23×C3—182no—
664C23×C3—182no—
665C23×C3—182no—
666C23×C3—182no—
667C23×C3—361no—
668C23×C3—361no—
669C23×C3C2×D3211yescharacteristic
670C22×D3—31no—
671C22×D3—31no—
672C22×D3—31no—
673C22×D3—31no—
674C22×D3—31no—
675C22×D3—31no—
676C22×D3—31no—
677C22×D3—31no—
678C22×D3—31no—
679C22×D3—31no—
680C22×D3—61no—
681C22×D3—61no—
682C22×D3—61no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—62no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—91no—
690C22×D3—91no—
691C22×D3—91no—
692C22×D3—91no—
693C22×D3—122no—
694C22×D3—122no—
695C22×D3—121no—
696C22×D3—121no—
697C22×D3—121no—
698C22×D3—122no—
699C22×D3—182no—
700C22×D3—182no—
701C22×D3—182no—
702C22×D3—182no—
703C22×D3—182no—
704C22×D3—182no—
705C22×D3—182no—
706C22×D3—182no—
707C22×D3—182no—
708C22×D3—182no—
709C22×D3—182no—
710C22×D3—182no—
711C22×D3—182no—
712C22×D3—182no—
713C22×D3—361no—
714C22×D3—361no—
715C22×D3—361no—
716C22×D3—361no—
717C22×D3—361no—
718C22×D3—361no—
719C22×D3—361no—
720C3×D4—94no—
721C3×D4—182no—
722C3×D4—182no—
723C3×D4—182no—
724C3×D4—182no—
725C3×D4—361no—
726C3×D4—361no—
727C2×C3×C4—31no—
728C2×C3×C4—31no—
729C2×C3×C4—31no—
730C2×C3×C4—31no—
731C2×C3×C4—61no—
732C2×C3×C4—61no—
733C2×C3×C4—91no—
734C2×C3×C4—91no—
735C2×C3×C4—91no—
736C2×C3×C4—91no—
737C2×C3×C4—91no—
738C2×C3×C4—182no—
739C2×C3×C4—182no—
740C2×C3×C4C2×D3211yescharacteristic
741C2×C3×C4C2×D3211yescharacteristic
742#67—34no—
743#67—62no—
744#67—62no—
745#67—62no—
746#67—94no—
747#67—94no—
748#67—94no—
749#67—122no—
750#67—182no—
751#67—182no—
752#67—182no—
753#67—182no—
754#67—182no—
755#67—182no—
756#67—182no—
757#67—182no—
758#67—182no—
759#67—182no—
760#67—182no—
761#67—182no—
762#67—182no—
763#67—182no—
764#67—182no—
765#67—182no—
766#67—182no—
767C2×Dic3—31no—
768C2×Dic3—31no—
769C2×Dic3—31no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—61no—
774C2×Dic3—62no—
775C2×Dic3—91no—
776C2×Dic3—91no—
777C2×Dic3—91no—
778C2×Dic3—91no—
779C2×Dic3—182no—
780C2×Dic3—182no—
781C2×Dic3—182no—
782D12—62no—
783D12—62no—
784D12—62no—
785D12—94no—
786D12—122no—
787D12—121no—
788D12—121no—
789D12—121no—
790D12—122no—
791D12—182no—
792D12—182no—
793D12—182no—
794D12—182no—
795D12—182no—
796D12—182no—
797D12—182no—
798D12—182no—
799D12—182no—
800D12—361no—
801C4×D3—62no—
802C4×D3—182no—
803C4×D3—182no—
804C4×D3—182no—
805C4×D3—182no—
806C4×D3—182no—
807C2×C32—22no—
808C2×C32—22no—
809C2×C32—21no—
810C2×C32—21no—
811C2×C32—21no—
812C2×C32—42no—
813C2×C32C22×D1211yescharacteristic
814C2×C32C2×D3×D411yescharacteristic
815C2×C32C2×D3×D411yescharacteristic
816C2×C32C2×D3×D411yescharacteristic
817C2×C32#100411yescharacteristic
818C2×C32#100911yescharacteristic
819C3⋊D3—22no—
820C3⋊D3—22no—
821C3⋊D3—41no—
822C3⋊D3—41no—
823C3×D3—62no—
824C3×D3—62no—
825C3×D3—62no—
826C3×D3—62no—
827C3×D3—122no—
828C3×D3—122no—
829C3×D3—121no—
830C3×D3—121no—
831C3×D3—121no—
832C3×D3—121no—
833C3×D3—121no—
834C3×D3—121no—
835C3×D3—241no—
836C24—91no—
837C24—91no—
838C24—271no—
839C24—271no—
840C2×D4—91no—
841C2×D4—91no—
842C2×D4—91no—
843C2×D4—91no—
844C2×D4—91no—
845C2×D4—91no—
846C2×D4—91no—
847C2×D4—271no—
848C2×D4—271no—
849C2×D4—271no—
850C2×D4—271no—
851C2×D4—271no—
852C2×D4—271no—
853C2×D4—271no—
854C2×D4—271no—
855C2×D4—271no—
856C2×D4—544no—
857C2×D4—544no—
858C2×D4—544no—
859C2×D4—544no—
860C22×C4—91no—
861C22×C4—91no—
862C22×C4—271no—
863C22×C4—271no—
864C4⋊C4—91no—
865C4⋊C4—271no—
866C22⋊C4—91no—
867C22⋊C4—91no—
868C22⋊C4—91no—
869C22⋊C4—91no—
870C22⋊C4—91no—
871C22⋊C4—271no—
872C22⋊C4—271no—
873C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
874C42—91no—
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—31no—
878C22×C3—31no—
879C22×C3—32no—
880C22×C3—32no—
881C22×C3—61no—
882C22×C3—61no—
883C22×C3—61no—
884C22×C3—61no—
885C22×C3—61no—
886C22×C3—62no—
887C22×C3—92no—
888C22×C3—92no—
889C22×C3—92no—
890C22×C3—121no—
891C22×C3—121no—
892C22×C3—181no—
893C22×C3—181no—
894C22×C3—181no—
895C22×C3—181no—
896C22×C3—181no—
897C22×C3—181no—
898C22×C3—181no—
899C22×C3—181no—
900C22×C3—181no—
901C22×C3—181no—
902C22×C3—181no—
903C22×C3—181no—
904C22×C3—181no—
905C22×C3—181no—
906C22×C3—181no—
907C22×C3—181no—
908C22×C3—181no—
909C22×C3—181no—
910C22×C3—364no—
911C22×C3—364no—
912C22×C3D3×D1212yes—
913C22×C3C22×D3211yescharacteristic
914C2×D3—32no—
915C2×D3—32no—
916C2×D3—32no—
917C2×D3—32no—
918C2×D3—62no—
919C2×D3—61no—
920C2×D3—61no—
921C2×D3—61no—
922C2×D3—61no—
923C2×D3—61no—
924C2×D3—61no—
925C2×D3—61no—
926C2×D3—61no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—61no—
930C2×D3—61no—
931C2×D3—61no—
932C2×D3—61no—
933C2×D3—61no—
934C2×D3—61no—
935C2×D3—61no—
936C2×D3—61no—
937C2×D3—61no—
938C2×D3—61no—
939C2×D3—62no—
940C2×D3—61no—
941C2×D3—61no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—61no—
945C2×D3—61no—
946C2×D3—92no—
947C2×D3—92no—
948C2×D3—121no—
949C2×D3—121no—
950C2×D3—121no—
951C2×D3—121no—
952C2×D3—121no—
953C2×D3—121no—
954C2×D3—121no—
955C2×D3—124no—
956C2×D3—124no—
957C2×D3—124no—
958C2×D3—128no—
959C2×D3—181no—
960C2×D3—181no—
961C2×D3—181no—
962C2×D3—181no—
963C2×D3—181no—
964C2×D3—181no—
965C2×D3—181no—
966C2×D3—181no—
967C2×D3—181no—
968C2×D3—181no—
969C2×D3—364no—
970C2×D3—364no—
971C2×D3—364no—
972C2×D3—364no—
973C2×D3—364no—
974C2×D3—364no—
975C2×D3—364no—
976C3×C4—21no—
977C3×C4—21no—
978C3×C4—61no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—61no—
982C3×C4—92no—
983C3×C4—92no—
984C3×C4—121no—
985C3×C4—121no—
986C3×C4—181no—
987C3×C4—181no—
988C3×C4—181no—
989Dic3—32no—
990Dic3—32no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—92no—
996Dic3—92no—
997Dic3—121no—
998Dic3—181no—
999Dic3—181no—
1000C32—21no—
1001C32D4×D1211yescharacteristic, complemented
1002C32#559011yescharacteristic, complemented
1003C23—91no—
1004C23—91no—
1005C23—91no—
1006C23—91no—
1007C23—91no—
1008C23—91no—
1009C23—91no—
1010C23—182no—
1011C23—182no—
1012C23—182no—
1013C23—182no—
1014C23—361no—
1015C23—361no—
1016C23—542no—
1017C23—542no—
1018C23—542no—
1019C23—542no—
1020C23—1081no—
1021C23—1081no—
1022C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1023D4—94no—
1024D4—182no—
1025D4—182no—
1026D4—182no—
1027D4—182no—
1028D4—274no—
1029D4—361no—
1030D4—361no—
1031D4—542no—
1032D4—542no—
1033D4—542no—
1034D4—542no—
1035D4—542no—
1036D4—542no—
1037D4—542no—
1038D4—542no—
1039C2×C4—91no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—91no—
1044C2×C4—182no—
1045C2×C4—182no—
1046C2×C4—542no—
1047C2×C4—542no—
1048C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1049C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1050C2×C3—22no—
1051C2×C3—31no—
1052C2×C3—31no—
1053C2×C3—31no—
1054C2×C3—31no—
1055C2×C3—31no—
1056C2×C3—31no—
1057C2×C3—62no—
1058C2×C3—62no—
1059C2×C3—61no—
1060C2×C3—61no—
1061C2×C3—61no—
1062C2×C3—122no—
1063C2×C3—182no—
1064C2×C3—182no—
1065C2×C3—182no—
1066C2×C3—361no—
1067C2×C3—361no—
1068C2×C3—361no—
1069C2×C3—361no—
1070C2×C3C2×D3×D1211yescharacteristic
1071C2×C3D32×D411yescharacteristic
1072C2×C3#6431411yescharacteristic
1073D3—62no—
1074D3—62no—
1075D3—62no—
1076D3—62no—
1077D3—122no—
1078D3—121no—
1079D3—121no—
1080D3—121no—
1081D3—121no—
1082D3—122no—
1083D3—121no—
1084D3—121no—
1085D3—182no—
1086D3—182no—
1087D3—241no—
1088D3—361no—
1089D3—361no—
1090C22—21no—
1091C22—21no—
1092C22—92no—
1093C22—92no—
1094C22—92no—
1095C22—181no—
1096C22—181no—
1097C22—181no—
1098C22—181no—
1099C22—181no—
1100C22—181no—
1101C22—181no—
1102C22—181no—
1103C22—181no—
1104C22—181no—
1105C22—181no—
1106C22—181no—
1107C22—181no—
1108C22—181no—
1109C22—181no—
1110C22—181no—
1111C22—181no—
1112C22—181no—
1113C22—364no—
1114C22—364no—
1115C22—1084no—
1116C22—1084no—
1117C22#8865412yescomplemented
1118C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1119C4—21no—
1120C4—21no—
1121C4—92no—
1122C4—92no—
1123C4—181no—
1124C4—181no—
1125C4—181no—
1126C3—31no—
1127C3—31no—
1128C3—61no—
1129C3#1059427711yescharacteristic
1130C2—22no—
1131C2—182no—
1132C2—182no—
1133C2—182no—
1134C2—361no—
1135C2—361no—
1136C2—361no—
1137C2—361no—
1138C2C2×#8865411yescharacteristic
1139C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1140C2#1172250711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)D42
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#88677C2semidirect
2. C2×#88676C2semidirect
3. C22×#6200C2semidirect
4. C2×#88654C2semidirect
5. #11721738C2semidirect
6. #64091⋊C3C2semidirect
7. #64090⋊C3C2semidirect
8. #11721322C2semidirect
9. #11721163C2semidirect
10. #11721162C2semidirect
11. #11721158C2semidirect
12. #11721157C2semidirect
13. #11721140C2semidirect
14. #11721127C2semidirect
15. #11721123C2semidirect
18. C23×#272C22semidirect
19. C23×(C3⋊D3)⋊C3C22semidirect
20. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
21. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
22. C2×#6235C22semidirect
23. C2×C4⋊#272C22semidirect
24. C2×C4⋊#272C22semidirect
26. C2×#638⋊C3C22semidirect
27. C22×(C3⋊Dic3)⋊C3C22semidirect
28. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
29. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
30. C2×C4×(C3⋊D3)⋊C3C22semidirect
35. C2×#6200C22semidirect
36. C2×#6200C22semidirect
37. C2×#6200C22semidirect
38. C2×#6200C22semidirect
39. C2×#6200C22semidirect
40. C2×#6200C22semidirect
41. C2×#6200C22semidirect
42. C2×#6199C22semidirect
43. C2×#6198C22semidirect
44. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
46. C22⋊C4×H(3,𝔽3)C22semidirect
47. #88542C22semidirect
48. #88542C22semidirect
49. #3752⋊C3C22semidirect
50. #3752⋊C3C22semidirect
51. #3752⋊C3C22semidirect
52. #3750⋊C3C22semidirect
53. C4×(C3⋊Dic3)⋊C3C22semidirect
54. #88451C22semidirect
55. #88450C22semidirect
56. #88448C22semidirect
65. #64091D3semidirect
66. #64090D3semidirect
115. #638⋊C3D4semidirect
131. #6200D4semidirect
138. C23×C3⋊D3C2×D3semidirect
148. C2×#638C2×D3semidirect
149. C22×C3⋊Dic3C2×D3semidirect
150. C2×C4⋊(C3⋊D3)C2×D3semidirect
151. C2×C4⋊(C3⋊D3)C2×D3semidirect
152. C2×C4×C3⋊D3C2×D3semidirect
199. C32×C22⋊C4C2×D3semidirect
200. C32×C22⋊C4C2×D3semidirect
201. #3752C2×D3semidirect
202. #3752C2×D3semidirect
203. #3752C2×D3semidirect
204. #3750C2×D3semidirect
205. C4×C3⋊Dic3C2×D3semidirect
225. C22×H(3,𝔽3)C2×D4semidirect
236. C2×#272C2×D4semidirect
248. C2×(C3⋊D3)⋊C3C2×D4semidirect
249. C2×(C3⋊D3)⋊C3C2×D4semidirect
257. (C3⋊Dic3)⋊C3C2×D4semidirect
258. (C3⋊Dic3)⋊C3C2×D4semidirect
359. #638D12semidirect
556. C22×C32C2×D12semidirect
557. C22×C32D3×D4semidirect
571. C2×C3⋊D3C2×D12semidirect
572. C2×C3⋊D3D3×D4semidirect
628. C3⋊Dic3C2×D12semidirect
629. C3⋊Dic3D3×D4semidirect
652. H(3,𝔽3)D42semidirect
873. C22⋊C4((C3⋊D3)⋊C3)⋊C2semidirect
1001. C32D4×D12semidirect
1002. C32#5590semidirect
1117. C22#88654semidirect

Maximal subgroups

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

subgroupindex
C2×#886772
C2×#886762
C22×#62002
C2×#886542
#117217382
#64091⋊C32
#64090⋊C32
#117213222
#117211632
#117211622
#117211582
#117211572
#117211402
#117211272
#117211232
#105942773
#105942713