Finite Group Databasebeta

← #13148733

Subgroups — #13148733

Order 1728.

1585 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88676C211yesmaximal, characteristic
2C22×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic, complemented
3C2×C4×((C3⋊D3)⋊C3)⋊C2C211yesmaximal, characteristic, complemented
4#11721737C211yesmaximal, characteristic, complemented
5#64090⋊C3C211yesmaximal, characteristic, complemented
6C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
7#11721315C211yesmaximal, characteristic, complemented
8#11721293C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721138C211yesmaximal, characteristic, complemented
11#11721124C211yesmaximal, characteristic, complemented
12#11721123C211yesmaximal, characteristic, complemented
13#11721122C211yesmaximal, characteristic, complemented
14#11721119C211yesmaximal, characteristic, complemented
15C4×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic, complemented
16#10594255—31nomaximal
17D3×#67⋊C4—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C2×#6235C2211yescharacteristic
21C22×#1084C2211yescharacteristic, complemented
22C2×C4×#272C2211yescharacteristic, complemented
23C2×#638⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
28#88676C418yescomplemented
29C2×#6200C2211yescharacteristic
30C2×#6199C2211yescharacteristic, complemented
31C2×#6198C2211yescharacteristic
32C2×((C3⋊D3)⋊C3)⋊C4—24no—
33C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
34C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
35C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
37C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
38C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
39C4×((C3⋊D3)⋊C3)⋊C2—24no—
40C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
41#88542C2211yescharacteristic, complemented
42#88540C2211yescharacteristic, complemented
43C4×#1084C2211yescharacteristic, complemented
44#3757⋊C3C2211yescharacteristic, complemented
45#3752⋊C3C2211yescharacteristic, complemented
46#3752⋊C3C2211yescharacteristic, complemented
47#3752⋊C3C2211yescharacteristic, complemented
48#3750⋊C3C2211yescharacteristic, complemented
49C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
50#88451C2211yescharacteristic, complemented
51#88450C2211yescharacteristic, complemented
52#88449C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55#88447C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C22×#624—31no—
59C22×D3×Dic3—31no—
60C2×C4×D32—31no—
61C2×C4×D32—31no—
62#64090D311yescharacteristic, complemented
63C22⋊C4×C3⋊D3D311yescharacteristic, complemented
64C3×#67⋊C4—31no—
65C3×#67⋊C4—31no—
66C3×#67⋊C4—31no—
67C3×#67⋊C4—61no—
68C3×D3×C22⋊C4—31no—
69#67⋊Dic3—31no—
70Dic3×#67—31no—
71Dic3×#67—31no—
72#63952—31no—
73#63921—31no—
74D3×(C2×D3)⋊C4—31no—
75#63904—31no—
76#63904—31no—
77#63902—31no—
78#63883—31no—
79C4×#624—31no—
80#63881—31no—
81#63880—31no—
82#63880—31no—
83#63880—31no—
84#63879—31no—
85D3×Dic3⋊C4—31no—
86C4×D3×Dic3—31no—
87C23×H(3,𝔽3)C2311yescharacteristic
88C22×#272C2311yescharacteristic
89C22×(C3⋊D3)⋊C3—22no—
90C22×(C3⋊D3)⋊C3—22no—
91C22×(C3⋊D3)⋊C3C2×C414yescomplemented
92C22×(C3⋊D3)⋊C3C2311yescharacteristic
93C22×(C3⋊D3)⋊C3C2311yescharacteristic
94C22×(C3⋊D3)⋊C3C2311yescharacteristic
95C2×((C3⋊D3)⋊C3)⋊C2—22no—
96C2×((C3⋊D3)⋊C3)⋊C2—22no—
97C2×((C3⋊D3)⋊C3)⋊C2C2×C414yescomplemented
98C2×C4×H(3,𝔽3)C2311yescharacteristic
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100#6235C2×C414yescomplemented
101C2×#1084—22no—
102C2×#1084C2311yescharacteristic
103C2×#1084C2311yescharacteristic
104C2×#1084C2311yescharacteristic
105C4×#272—22no—
106#638⋊C3C2×C414yescomplemented
107C2×(C3⋊Dic3)⋊C3—22no—
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C4×(C3⋊D3)⋊C3—22no—
114C4×(C3⋊D3)⋊C3—22no—
115C4×(C3⋊D3)⋊C3—22no—
116#6200C2×C414yescomplemented
117#6199—22no—
118#6198C2×C414yescomplemented
119((C3⋊D3)⋊C3)⋊C4—22no—
120((C3⋊D3)⋊C3)⋊C4—22no—
121((C3⋊D3)⋊C3)⋊C4—22no—
122((C3⋊D3)⋊C3)⋊C4—22no—
123((C3⋊D3)⋊C3)⋊C4C2×C414yescomplemented
124((C3⋊D3)⋊C3)⋊C4D414yescomplemented
125C4×D3×D4—91no—
126C4×D3×D4—91no—
127C2×#67⋊C4—91no—
128C23×C3⋊D3C2×D311yescharacteristic
129C23×C3×D3—31no—
130C22×D32—31no—
131C22×D32—31no—
132C2×#638C2×D311yescharacteristic
133C22×C3⋊Dic3C2×D311yescharacteristic, complemented
134C2×C4×C3⋊D3C2×D311yescharacteristic
135C2×C4×C3⋊D3C2×D311yescharacteristic
136C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—61no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—61no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—61no—
151#3811—38no—
152D3×#67—38no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#625—31no—
157C2×#624—31no—
158C2×#624—31no—
159C2×#624—31no—
160C2×#624—31no—
161C2×#624—31no—
162C2×#624—31no—
163C2×#624—64no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—64no—
173C4×D32—64no—
174C4×D32—64no—
175C32×C22⋊C4—21no—
176C32×C22⋊C4C2×D311yescharacteristic, complemented
177C32×C22⋊C4C2×D311yescharacteristic, complemented
178#3757C2×D311yescharacteristic, complemented
179#3752C2×D311yescharacteristic, complemented
180#3752C2×D311yescharacteristic, complemented
181#3752C2×D311yescharacteristic, complemented
182#3750C2×D311yescharacteristic, complemented
183C4×C3⋊Dic3C2×D311yescharacteristic, complemented
184C3×#217—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—61no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—61no—
195C3×C4×Dic3—31no—
196C3×C4×Dic3—31no—
197C3×C4×Dic3—31no—
198C3×C4×Dic3—61no—
199#3724—31no—
200Dic3⋊Dic3—31no—
201Dic3⋊Dic3—31no—
202Dic3⋊Dic3—31no—
203#3722—31no—
204(C2×D3)⋊Dic3—31no—
205(C2×D3)⋊Dic3—31no—
206(C2×D3)⋊Dic3—31no—
207Dic32—31no—
208Dic32—31no—
209Dic32—31no—
210Dic32—31no—
211C22×H(3,𝔽3)—21no—
212C22×H(3,𝔽3)—21no—
213C22×H(3,𝔽3)C22×C412yescomplemented
214C22×H(3,𝔽3)C2411yescharacteristic
215C2×#272—21no—
216C2×#272—21no—
217C2×#272C22×C412yescomplemented
218C2×(C3⋊D3)⋊C3—21no—
219C2×(C3⋊D3)⋊C3—21no—
220C2×(C3⋊D3)⋊C3—21no—
221C2×(C3⋊D3)⋊C3—21no—
222C2×(C3⋊D3)⋊C3—28no—
223C2×(C3⋊D3)⋊C3C22×C412yes—
224C2×(C3⋊D3)⋊C3C22×C412yescomplemented
225C2×(C3⋊D3)⋊C3C22×C412yescomplemented
226C2×(C3⋊D3)⋊C3C2×D412yes—
227C2×(C3⋊D3)⋊C3#4112yes—
228((C3⋊D3)⋊C3)⋊C2—28no—
229C4×H(3,𝔽3)—21no—
230C4×H(3,𝔽3)—21no—
231#1084—21no—
232#1084C22×C412yescomplemented
233#1084C2×D412yescomplemented
234(C3⋊Dic3)⋊C3—21no—
235(C3⋊Dic3)⋊C3—21no—
236(C3⋊Dic3)⋊C3—21no—
237(C3⋊Dic3)⋊C3C22×C412yescomplemented
238(C3⋊Dic3)⋊C3C2×D412yescomplemented
239C22×#67—91no—
240C23×Dic3—91no—
241C2×D3×D4—91no—
242C2×D3×D4—91no—
243C22×C4×D3—91no—
244C22×C4×D3—91no—
245C22×C4×D3—91no—
246C22×C4×D3—91no—
247C22×C4×D3—91no—
248C3×C4×D4—91no—
249C3×C4×D4—91no—
250C2×C3×C22⋊C4—91no—
251D4×Dic3—91no—
252D4×Dic3—91no—
253C4×#67—91no—
254C4×#67—91no—
255C4×#67—91no—
256C4×#67—91no—
257C2×(C2×D3)⋊C4—91no—
258C2×Dic3⋊C4—91no—
259C2×C4×Dic3—91no—
260#893—91no—
261#893—91no—
262D3×C4⋊C4—91no—
263D3×C4⋊C4—91no—
264#67⋊C4—31no—
265#67⋊C4—31no—
266#67⋊C4—31no—
267#67⋊C4—61no—
268#67⋊C4—91no—
269#67⋊C4—91no—
270#67⋊C4—91no—
271#67⋊C4—91no—
272#67⋊C4—91no—
273#67⋊C4—91no—
274#67⋊C4—91no—
275#67⋊C4—91no—
276#67⋊C4—91no—
277D3×C22⋊C4—31no—
278D3×C22⋊C4—91no—
279D3×C22⋊C4—91no—
280D3×C22⋊C4—91no—
281C4×D12—91no—
282C4×D12—91no—
283C42×D3—91no—
284C42×D3—91no—
285C23×C32—21no—
286C23×C32C22×D311yescharacteristic
287C23×C32C22×D311yescharacteristic
288C22×C3⋊D3—22no—
289C22×C3⋊D3—22no—
290C22×C3⋊D3C4×D314yescomplemented
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3⋊D3C22×D311yescharacteristic
294C22×C3×D3—31no—
295C22×C3×D3—34no—
296C22×C3×D3—31no—
297C22×C3×D3—31no—
298C22×C3×D3—31no—
299C22×C3×D3—31no—
300C22×C3×D3—61no—
301C22×C3×D3—62no—
302C22×C3×D3—62no—
303C2×D32—34no—
304C2×D32—34no—
305C2×D32—62no—
306C2×D32—62no—
307C2×D32—62no—
308C2×D32—62no—
309C2×C32×C4—21no—
310C2×C32×C4—21no—
311C2×C32×C4C22×D311yescharacteristic
312C2×C32×C4C22×D311yescharacteristic
313C2×C32×C4C22×D311yescharacteristic
314C2×C32×C4C22×D311yescharacteristic
315#638C4×D314yescomplemented
316C2×C3⋊Dic3—22no—
317C2×C3⋊Dic3C22×D311yescharacteristic
318C2×C3⋊Dic3C22×D311yescharacteristic
319C2×C3⋊Dic3C22×D311yescharacteristic
320C2×C3⋊Dic3C22×D311yescharacteristic
321C2×C3⋊Dic3C22×D311yescharacteristic
322C4×C3⋊D3—22no—
323C4×C3⋊D3—22no—
324C4×C3⋊D3—22no—
325C3×#67—34no—
326C3×#67—34no—
327C3×#67—34no—
328C3×#67—64no—
329C2×C3×Dic3—31no—
330C2×C3×Dic3—31no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—31no—
333C2×C3×Dic3—31no—
334C2×C3×Dic3—31no—
335C2×C3×Dic3—31no—
336C2×C3×Dic3—31no—
337C2×C3×Dic3—31no—
338C2×C3×Dic3—31no—
339C2×C3×Dic3—31no—
340C2×C3×Dic3—61no—
341C2×C3×Dic3—61no—
342C2×C3×Dic3—61no—
343C2×C3×Dic3—62no—
344C2×C3×Dic3—62no—
345C2×C3×Dic3—62no—
346C2×C3×Dic3—122no—
347C3×C4×D3—62no—
348C3×C4×D3—62no—
349C3×C4×D3—62no—
350C3×C4×D3—62no—
351C3×C4×D3—62no—
352C3×C4×D3—122no—
353#626—34no—
354#626—34no—
355#626—34no—
356#625—34no—
357#624—34no—
358#624—34no—
359#624—62no—
360#624—62no—
361#624—62no—
362#624—62no—
363D3×Dic3—34no—
364D3×Dic3—34no—
365D3×Dic3—62no—
366D3×Dic3—62no—
367D3×Dic3—62no—
368D3×Dic3—62no—
369D3×Dic3—62no—
370D3×Dic3—62no—
371C2×C4×D4—271noSylow
372C2×H(3,𝔽3)—22no—
373C2×H(3,𝔽3)C23×C411yescharacteristic
374C2×H(3,𝔽3)C22×D411yescharacteristic
375C2×H(3,𝔽3)C2×#4111yescharacteristic
376#272—22no—
377(C3⋊D3)⋊C3—22no—
378(C3⋊D3)⋊C3—22no—
379(C3⋊D3)⋊C3C4×D414yescomplemented
380C24×C3—91no—
381C23×D3—31no—
382C23×D3—91no—
383C23×D3—91no—
384C23×D3—91no—
385C23×D3—91no—
386C2×C3×D4—91no—
387C2×C3×D4—91no—
388C22×C3×C4—91no—
389C22×C3×C4—91no—
390C22×C3×C4—91no—
391C22×C3×C4—91no—
392C22×C3×C4—91no—
393C22×C3×C4—91no—
394C2×#67—31no—
395C2×#67—31no—
396C2×#67—31no—
397C2×#67—61no—
398C2×#67—91no—
399C2×#67—91no—
400C2×#67—91no—
401C2×#67—91no—
402C2×#67—98no—
403C2×#67—91no—
404C22×Dic3—31no—
405C22×Dic3—31no—
406C22×Dic3—31no—
407C22×Dic3—61no—
408C22×Dic3—91no—
409C22×Dic3—91no—
410C22×Dic3—91no—
411C22×Dic3—91no—
412C22×Dic3—91no—
413C22×Dic3—91no—
414C22×Dic3—91no—
415C22×Dic3—91no—
416C22×Dic3—184no—
417D3×D4—98no—
418D3×D4—98no—
419C2×D12—91no—
420C2×D12—91no—
421C2×C4×D3—31no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—61no—
427C2×C4×D3—91no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×C4×D3—91no—
440C2×C4×D3—91no—
441C2×C4×D3—91no—
442C2×C4×D3—91no—
443C2×C4×D3—91no—
444C2×C4×D3—184no—
445C2×C4×D3—184no—
446C2×C4×D3—184no—
447C2×C4×D3—184no—
448C2×C4×D3—184no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C22⋊C4—31no—
452C3×C22⋊C4—31no—
453C3×C22⋊C4—61no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C22⋊C4—91no—
459C3×C22⋊C4D3211yescharacteristic
460C3×C42—91no—
461C3×C42—91no—
462#217—31no—
463#217—91no—
464#217—91no—
465#217—91no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—31no—
469(C2×D3)⋊C4—31no—
470(C2×D3)⋊C4—31no—
471(C2×D3)⋊C4—61no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479C4⋊Dic3—91no—
480C4⋊Dic3—91no—
481Dic3⋊C4—31no—
482Dic3⋊C4—31no—
483Dic3⋊C4—31no—
484Dic3⋊C4—61no—
485Dic3⋊C4—91no—
486Dic3⋊C4—91no—
487Dic3⋊C4—91no—
488Dic3⋊C4—91no—
489Dic3⋊C4—91no—
490C4×Dic3—31no—
491C4×Dic3—31no—
492C4×Dic3—31no—
493C4×Dic3—61no—
494C4×Dic3—91no—
495C4×Dic3—91no—
496C4×Dic3—91no—
497C4×Dic3—91no—
498C4×Dic3—91no—
499C4×Dic3—91no—
500C4×Dic3—91no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—21no—
506C22×C32—22no—
507C22×C32—41no—
508C22×C32—41no—
509C22×C32C2×C4×D312yescomplemented
510C22×C32C2×C4×D312yescomplemented
511C22×C32C23×D311yescharacteristic
512C22×C32C23×D311yescharacteristic
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3—28no—
518C2×C3⋊D3C2×C4×D312yes—
519C2×C3⋊D3C2×C4×D312yescomplemented
520C2×C3⋊D3C2×C4×D312yescomplemented
521C2×C3⋊D3D3×D412yes—
522C2×C3⋊D3#23712yes—
523C2×C3×D3—32no—
524C2×C3×D3—32no—
525C2×C3×D3—32no—
526C2×C3×D3—32no—
527C2×C3×D3—32no—
528C2×C3×D3—32no—
529C2×C3×D3—32no—
530C2×C3×D3—62no—
531C2×C3×D3—68no—
532C2×C3×D3—61no—
533C2×C3×D3—61no—
534C2×C3×D3—61no—
535C2×C3×D3—61no—
536C2×C3×D3—61no—
537C2×C3×D3—61no—
538C2×C3×D3—61no—
539C2×C3×D3—61no—
540C2×C3×D3—121no—
541C2×C3×D3—121no—
542D32—68no—
543D32—68no—
544C32×C4—21no—
545C32×C4—21no—
546C32×C4—21no—
547C32×C4—21no—
548C32×C4—41no—
549C32×C4—41no—
550C3⋊Dic3—21no—
551C3⋊Dic3—21no—
552C3⋊Dic3—21no—
553C3⋊Dic3C2×C4×D312yescomplemented
554C3⋊Dic3D3×D412yescomplemented
555C3×Dic3—32no—
556C3×Dic3—32no—
557C3×Dic3—32no—
558C3×Dic3—32no—
559C3×Dic3—32no—
560C3×Dic3—32no—
561C3×Dic3—62no—
562C3×Dic3—62no—
563C3×Dic3—61no—
564C3×Dic3—61no—
565C3×Dic3—61no—
566C3×Dic3—61no—
567C3×Dic3—61no—
568C3×Dic3—121no—
569C22×D4—271no—
570C23×C4—271no—
571C23×C4—271no—
572C4×D4—91no—
573C4×D4—91no—
574C4×D4—271no—
575C4×D4—271no—
576C4×D4—271no—
577C4×D4—271no—
578C4×D4—271no—
579C4×D4—271no—
580C2×C4⋊C4—271no—
581C2×C22⋊C4—91no—
582C2×C22⋊C4—271no—
583C2×C42—271no—
584H(3,𝔽3)C2×C4×D411yescharacteristic, complemented, Sylow
585C23×C3—31no—
586C23×C3—31no—
587C23×C3—61no—
588C23×C3—91no—
589C23×C3—91no—
590C23×C3—91no—
591C23×C3—94no—
592C23×C3—91no—
593C23×C3—182no—
594C23×C3—182no—
595C23×C3C2×D3211yescharacteristic
596C22×D3—31no—
597C22×D3—31no—
598C22×D3—31no—
599C22×D3—31no—
600C22×D3—31no—
601C22×D3—34no—
602C22×D3—61no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—91no—
606C22×D3—94no—
607C22×D3—91no—
608C22×D3—91no—
609C22×D3—94no—
610C22×D3—94no—
611C22×D3—94no—
612C22×D3—182no—
613C22×D3—182no—
614C22×D3—182no—
615C22×D3—182no—
616C22×D3—182no—
617C22×D3—182no—
618C22×D3—182no—
619C22×D3—182no—
620C3×D4—94no—
621C3×D4—94no—
622C2×C3×C4—31no—
623C2×C3×C4—31no—
624C2×C3×C4—31no—
625C2×C3×C4—31no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—91no—
629C2×C3×C4—91no—
630C2×C3×C4—91no—
631C2×C3×C4—91no—
632C2×C3×C4—91no—
633C2×C3×C4—91no—
634C2×C3×C4—91no—
635C2×C3×C4—91no—
636C2×C3×C4—182no—
637C2×C3×C4—182no—
638C2×C3×C4—182no—
639C2×C3×C4—182no—
640C2×C3×C4—182no—
641C2×C3×C4—182no—
642C2×C3×C4C2×D3211yescharacteristic
643C2×C3×C4C2×D3211yescharacteristic
644#67—34no—
645#67—34no—
646#67—34no—
647#67—64no—
648#67—94no—
649#67—94no—
650#67—94no—
651#67—94no—
652#67—94no—
653C2×Dic3—31no—
654C2×Dic3—31no—
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—31no—
660C2×Dic3—31no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—91no—
671C2×Dic3—91no—
672C2×Dic3—91no—
673C2×Dic3—91no—
674C2×Dic3—91no—
675C2×Dic3—94no—
676C2×Dic3—94no—
677C2×Dic3—122no—
678C2×Dic3—182no—
679C2×Dic3—182no—
680C2×Dic3—182no—
681C2×Dic3—182no—
682C2×Dic3—182no—
683C2×Dic3—182no—
684D12—94no—
685D12—94no—
686C4×D3—62no—
687C4×D3—62no—
688C4×D3—62no—
689C4×D3—62no—
690C4×D3—62no—
691C4×D3—94no—
692C4×D3—94no—
693C4×D3—94no—
694C4×D3—94no—
695C4×D3—122no—
696C4×D3—182no—
697C4×D3—182no—
698C4×D3—182no—
699C4×D3—182no—
700C4×D3—182no—
701C4×D3—182no—
702C4×D3—182no—
703C4×D3—182no—
704C4×D3—182no—
705C4×D3—182no—
706C4×D3—182no—
707C4×D3—182no—
708C4×D3—182no—
709C2×C32—22no—
710C2×C32—22no—
711C2×C32—21no—
712C2×C32—21no—
713C2×C32—21no—
714C2×C32—42no—
715C2×C32C22×C4×D311yescharacteristic
716C2×C32C22×C4×D311yescharacteristic
717C2×C32C2×D3×D411yescharacteristic
718C2×C32C2×D3×D411yescharacteristic
719C2×C32C2×#23711yescharacteristic
720C2×C32D3×#4111yescharacteristic
721C3⋊D3—22no—
722C3⋊D3—22no—
723C3⋊D3#67⋊C414yescomplemented
724C3×D3—34no—
725C3×D3—62no—
726C3×D3—62no—
727C3×D3—62no—
728C3×D3—62no—
729C3×D3—122no—
730C24—91no—
731C24—271no—
732C2×D4—91no—
733C2×D4—91no—
734C2×D4—271no—
735C2×D4—271no—
736C2×D4—278no—
737C22×C4—91no—
738C22×C4—91no—
739C22×C4—91no—
740C22×C4—91no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—271no—
744C22×C4—271no—
745C22×C4—271no—
746C22×C4—271no—
747C22×C4—271no—
748C22×C4—271no—
749C22×C4—271no—
750C22×C4—544no—
751C22×C4—544no—
752C4⋊C4—91no—
753C4⋊C4—91no—
754C4⋊C4—271no—
755C4⋊C4—271no—
756C22⋊C4—91no—
757C22⋊C4—91no—
758C22⋊C4—91no—
759C22⋊C4—91no—
760C22⋊C4—91no—
761C22⋊C4—271no—
762C22⋊C4—271no—
763C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
764C42—91no—
765C42—91no—
766C42—271no—
767C42—271no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—31no—
771C22×C3—31no—
772C22×C3—32no—
773C22×C3—32no—
774C22×C3—61no—
775C22×C3—61no—
776C22×C3—61no—
777C22×C3—61no—
778C22×C3—61no—
779C22×C3—62no—
780C22×C3—92no—
781C22×C3—92no—
782C22×C3—92no—
783C22×C3—92no—
784C22×C3—92no—
785C22×C3—92no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—181no—
789C22×C3—181no—
790C22×C3—181no—
791C22×C3—181no—
792C22×C3—188no—
793C22×C3—181no—
794C22×C3—181no—
795C22×C3C4×D3212yes—
796C22×C3C22×D3211yescharacteristic
797C2×D3—32no—
798C2×D3—32no—
799C2×D3—32no—
800C2×D3—32no—
801C2×D3—32no—
802C2×D3—32no—
803C2×D3—32no—
804C2×D3—62no—
805C2×D3—68no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—61no—
814C2×D3—92no—
815C2×D3—92no—
816C2×D3—92no—
817C2×D3—92no—
818C2×D3—92no—
819C2×D3—121no—
820C2×D3—121no—
821C2×D3—188no—
822C2×D3—181no—
823C2×D3—181no—
824C2×D3—181no—
825C2×D3—181no—
826C2×D3—188no—
827C2×D3—188no—
828C2×D3—188no—
829C3×C4—21no—
830C3×C4—21no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—61no—
835C3×C4—92no—
836C3×C4—92no—
837C3×C4—92no—
838C3×C4—92no—
839C3×C4—121no—
840C3×C4—121no—
841C3×C4—181no—
842C3×C4—181no—
843C3×C4—181no—
844C3×C4—181no—
845Dic3—32no—
846Dic3—32no—
847Dic3—32no—
848Dic3—32no—
849Dic3—32no—
850Dic3—32no—
851Dic3—62no—
852Dic3—62no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—92no—
859Dic3—92no—
860Dic3—121no—
861Dic3—181no—
862Dic3—181no—
863Dic3—181no—
864C32—21no—
865C32C2×#67⋊C411yescharacteristic, complemented
866C32C4×D3×D411yescharacteristic, complemented
867C23—91no—
868C23—91no—
869C23—91no—
870C23—91no—
871C23—94no—
872C23—182no—
873C23—182no—
874C23—274no—
875C23—542no—
876C23—542no—
877C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
878D4—94no—
879D4—94no—
880D4—274no—
881D4—274no—
882C2×C4—91no—
883C2×C4—91no—
884C2×C4—91no—
885C2×C4—91no—
886C2×C4—91no—
887C2×C4—91no—
888C2×C4—91no—
889C2×C4—91no—
890C2×C4—182no—
891C2×C4—182no—
892C2×C4—182no—
893C2×C4—182no—
894C2×C4—182no—
895C2×C4—182no—
896C2×C4—274no—
897C2×C4—274no—
898C2×C4—542no—
899C2×C4—542no—
900C2×C4—542no—
901C2×C4—542no—
902C2×C4—542no—
903C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
904C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
905C2×C3—22no—
906C2×C3—31no—
907C2×C3—31no—
908C2×C3—31no—
909C2×C3—31no—
910C2×C3—31no—
911C2×C3—31no—
912C2×C3—62no—
913C2×C3—62no—
914C2×C3—61no—
915C2×C3—61no—
916C2×C3—61no—
917C2×C3—94no—
918C2×C3—122no—
919C2×C3—182no—
920C2×C3—182no—
921C2×C3—182no—
922C2×C3C2×C4×D3211yescharacteristic
923C2×C3D32×D411yescharacteristic
924C2×C3D3×#23711yescharacteristic
925D3—34no—
926D3—62no—
927D3—62no—
928D3—62no—
929D3—62no—
930D3—94no—
931D3—122no—
932D3—182no—
933D3—182no—
934C22—21no—
935C22—21no—
936C22—92no—
937C22—92no—
938C22—92no—
939C22—92no—
940C22—92no—
941C22—92no—
942C22—188no—
943C22—181no—
944C22—181no—
945C22—181no—
946C22—181no—
947C22—181no—
948C22—181no—
949C22—548no—
950C22C4×((C3⋊D3)⋊C3)⋊C212yescomplemented
951C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
952C4—21no—
953C4—21no—
954C4—92no—
955C4—92no—
956C4—92no—
957C4—92no—
958C4—181no—
959C4—181no—
960C4—181no—
961C4—181no—
962C3—31no—
963C3—31no—
964C3—61no—
965C3D3×#67⋊C411yescharacteristic
966C2—22no—
967C2—94no—
968C2—182no—
969C2—182no—
970C2—182no—
971C2C2×C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
972C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
973C2#1172250411yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C23×C4
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
prime radicalC2×#88676C2
cosocleC22×H(3,𝔽3)C24
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×C4×D4
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×((C3⋊D3)⋊C3)⋊C4C2semidirect
3. C2×C4×((C3⋊D3)⋊C3)⋊C2C2semidirect
4. #11721737C2semidirect
5. #64090⋊C3C2semidirect
6. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
7. #11721315C2semidirect
8. #11721293C2semidirect
9. #11721160C2semidirect
10. #11721138C2semidirect
11. #11721124C2semidirect
12. #11721123C2semidirect
13. #11721122C2semidirect
14. #11721119C2semidirect
15. C4×((C3⋊D3)⋊C3)⋊C4C2semidirect
21. C22×#1084C22semidirect
22. C2×C4×#272C22semidirect
24. C22×(C3⋊Dic3)⋊C3C22semidirect
27. C2×C4×(C3⋊D3)⋊C3C22semidirect
28. #88676C4semidirect
30. C2×#6199C22semidirect
36. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
37. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
38. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
40. C22⋊C4×H(3,𝔽3)C22semidirect
41. #88542C22semidirect
42. #88540C22semidirect
43. C4×#1084C22semidirect
44. #3757⋊C3C22semidirect
45. #3752⋊C3C22semidirect
46. #3752⋊C3C22semidirect
47. #3752⋊C3C22semidirect
48. #3750⋊C3C22semidirect
49. C4×(C3⋊Dic3)⋊C3C22semidirect
50. #88451C22semidirect
51. #88450C22semidirect
52. #88449C22semidirect
53. #88448C22semidirect
54. #88447C22semidirect
55. #88447C22semidirect
62. #64090D3semidirect
63. C22⋊C4×C3⋊D3D3semidirect
91. C22×(C3⋊D3)⋊C3C2×C4semidirect
97. C2×((C3⋊D3)⋊C3)⋊C2C2×C4semidirect
100. #6235C2×C4semidirect
106. #638⋊C3C2×C4semidirect
116. #6200C2×C4semidirect
118. #6198C2×C4semidirect
123. ((C3⋊D3)⋊C3)⋊C4C2×C4semidirect
124. ((C3⋊D3)⋊C3)⋊C4D4semidirect
133. C22×C3⋊Dic3C2×D3semidirect
136. C2×C4×C3⋊D3C2×D3semidirect
176. C32×C22⋊C4C2×D3semidirect
177. C32×C22⋊C4C2×D3semidirect
178. #3757C2×D3semidirect
179. #3752C2×D3semidirect
180. #3752C2×D3semidirect
181. #3752C2×D3semidirect
182. #3750C2×D3semidirect
183. C4×C3⋊Dic3C2×D3semidirect
213. C22×H(3,𝔽3)C22×C4semidirect
217. C2×#272C22×C4semidirect
224. C2×(C3⋊D3)⋊C3C22×C4semidirect
225. C2×(C3⋊D3)⋊C3C22×C4semidirect
232. #1084C22×C4semidirect
233. #1084C2×D4semidirect
237. (C3⋊Dic3)⋊C3C22×C4semidirect
238. (C3⋊Dic3)⋊C3C2×D4semidirect
290. C22×C3⋊D3C4×D3semidirect
315. #638C4×D3semidirect
379. (C3⋊D3)⋊C3C4×D4semidirect
509. C22×C32C2×C4×D3semidirect
510. C22×C32C2×C4×D3semidirect
519. C2×C3⋊D3C2×C4×D3semidirect
520. C2×C3⋊D3C2×C4×D3semidirect
553. C3⋊Dic3C2×C4×D3semidirect
554. C3⋊Dic3D3×D4semidirect
584. H(3,𝔽3)C2×C4×D4semidirect
723. C3⋊D3#67⋊C4semidirect
763. C22⋊C4((C3⋊D3)⋊C3)⋊C2semidirect
865. C32C2×#67⋊C4semidirect
866. C32C4×D3×D4semidirect
950. C22C4×((C3⋊D3)⋊C3)⋊C2semidirect

Maximal subgroups

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

subgroupindex
C2×#886762
C22×((C3⋊D3)⋊C3)⋊C42
C2×C4×((C3⋊D3)⋊C3)⋊C22
#117217372
#64090⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#117213152
#117212932
#117211602
#117211382
#117211242
#117211232
#117211222
#117211192
C4×((C3⋊D3)⋊C3)⋊C42
#105942553
D3×#67⋊C43