Finite Group Databasebeta

← #13147899

Subgroups — #13147899

Order 1728.

1249 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×((C3⋊D3)⋊C3)⋊C2C211yesmaximal, characteristic, complemented
2C2×#88650C211yesmaximal, characteristic, complemented
3C4×C4⋊#272C211yesmaximal, characteristic, complemented
4C4×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
5#64081⋊C3C211yesmaximal, characteristic, complemented
6#11721163C211yesmaximal, characteristic, complemented
7#11721162C211yesmaximal, characteristic, complemented
8#11721157C211yesmaximal, characteristic, complemented
9C4×#6200C211yesmaximal, characteristic, complemented
10C4×#6200C211yesmaximal, characteristic, complemented
11#11721150C211yesmaximal, characteristic, complemented
12#11721133C211yesmaximal, characteristic, complemented
13#11721131C211yesmaximal, characteristic, complemented
14#11721130C211yesmaximal, characteristic, complemented
15#11721127C211yesmaximal, characteristic, complemented
16#10594006—31nomaximal
17#10593997—31nomaximal
18C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
19C2×C4⋊#272C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×C4×#272C2211yescharacteristic, complemented
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
26C2×#6200C2211yescharacteristic
27C2×#6200C2211yescharacteristic
28C2×#6200C2211yescharacteristic
29C2×#6200C2211yescharacteristic, complemented
30C2×#6199C2211yescharacteristic
31C2×#6198C2211yescharacteristic
32C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
33C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
34C2×#6196C2211yescharacteristic, complemented
35C4×((C3⋊D3)⋊C3)⋊C2—24no—
36#88650—24no—
37C42×H(3,𝔽3)C2211yescharacteristic, complemented
38#88542C2211yescharacteristic
39#88542C2211yescharacteristic, complemented
40C4⋊#1084C2211yescharacteristic, complemented
41#3752⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44#3752⋊C3C2211yescharacteristic, complemented
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47#3750⋊C3C2211yescharacteristic, complemented
48C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
49#88451C2211yescharacteristic
50#88451C2211yescharacteristic, complemented
51#88450C2211yescharacteristic
52#88450C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88448C2211yescharacteristic, complemented
55C2×C4×D32—31no—
56C2×C4×D32—31no—
57C2×#3798—31no—
58C2×#3798—31no—
59C4×C4⋊(C3⋊D3)D311yescharacteristic, complemented
60#64081D311yescharacteristic, complemented
61C3×C4×D12—31no—
62C3×C4×D12—31no—
63C3×C4×D12—31no—
64C3×C4×D12—61no—
65C3×#872—31no—
66#63923—31no—
67#63922—31no—
68#63922—31no—
69#63922—31no—
70#63910—31no—
71C4×#626—31no—
72C4×#626—31no—
73C4×#625—31no—
74C4×#625—31no—
75#63899—31no—
76#63899—31no—
77#63895—31no—
78#63893—31no—
79#63891—31no—
80#63890—31no—
81#63886—31no—
82#63885—31no—
83#63885—31no—
84#63854—31no—
85#63854—31no—
86C22×#272C2311yescharacteristic
87C22×#272C2311yescharacteristic
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C2×((C3⋊D3)⋊C3)⋊C2—22no—
92C2×((C3⋊D3)⋊C3)⋊C2—22no—
93C2×((C3⋊D3)⋊C3)⋊C2—22no—
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95C2×C4×H(3,𝔽3)C2311yescharacteristic
96C2×C4×H(3,𝔽3)C2311yescharacteristic
97C2×#1084C2311yescharacteristic
98C2×#1084C2311yescharacteristic
99C4⋊#272—22no—
100C4×#272—22no—
101C4×#272—22no—
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C4⋊((C3⋊D3)⋊C3)—22no—
108C4×(C3⋊D3)⋊C3—22no—
109C4×(C3⋊D3)⋊C3—22no—
110C4×(C3⋊D3)⋊C3D414yescomplemented
111#6200—22no—
112#6200—22no—
113#6200—22no—
114#6200—22no—
115#6199—22no—
116#6198—22no—
117((C3⋊D3)⋊C3)⋊C4—22no—
118((C3⋊D3)⋊C3)⋊C4—22no—
119#6196—22no—
120#5547—91no—
121#5547—91no—
122#5524—91no—
123C22×D32—31no—
124C22×D32—31no—
125C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
126C2×C4×C3⋊D3C2×D311yescharacteristic
127C2×C4×C3⋊D3C2×D311yescharacteristic
128C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
129C2×C3×D12—31no—
130C2×C3×D12—31no—
131C2×C3×D12—31no—
132C2×C3×D12—61no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—61no—
141C2×C3×C4×D3—61no—
142C2×#627—31no—
143C2×#627—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#626—31no—
148C2×#626—31no—
149C2×#626—31no—
150C2×#625—31no—
151C2×#625—31no—
152C2×#625—31no—
153C2×#625—31no—
154C2×#624—31no—
155C2×#624—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C4×D32—64no—
161C4×D32—64no—
162#3798—64no—
163#3798—64no—
164C32×C42—21no—
165C32×C42C2×D311yescharacteristic, complemented
166C32×C42C2×D311yescharacteristic, complemented
167#3752C2×D311yescharacteristic
168#3752C2×D311yescharacteristic
169#3752C2×D311yescharacteristic
170#3752C2×D311yescharacteristic, complemented
171C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
172#3750C2×D311yescharacteristic, complemented
173#3750C2×D311yescharacteristic, complemented
174C4×C3⋊Dic3C2×D311yescharacteristic, complemented
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—61no—
184C3×(C2×D3)⋊C4—61no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—61no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×C4×Dic3—31no—
192#3724—31no—
193#3724—31no—
194Dic3⋊Dic3—31no—
195Dic3⋊Dic3—31no—
196#3722—31no—
197#3722—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—
204C22×H(3,𝔽3)C2411yescharacteristic
205C2×#272—21no—
206C2×#272—21no—
207C2×#272—21no—
208C2×#272—21no—
209C2×#272—21no—
210C2×#272#4112yescomplemented
211C2×(C3⋊D3)⋊C3—21no—
212C2×(C3⋊D3)⋊C3—21no—
213C2×(C3⋊D3)⋊C3—21no—
214C2×(C3⋊D3)⋊C3—21no—
215C2×(C3⋊D3)⋊C3—21no—
216C2×(C3⋊D3)⋊C3—21no—
217C2×(C3⋊D3)⋊C3—21no—
218C2×(C3⋊D3)⋊C3C2×D412yes—
219C2×(C3⋊D3)⋊C3#4112yescomplemented
220((C3⋊D3)⋊C3)⋊C2—28no—
221C4×H(3,𝔽3)—21no—
222C4×H(3,𝔽3)—21no—
223C4×H(3,𝔽3)C2×D412yes—
224#1084—21no—
225#1084—21no—
226(C3⋊Dic3)⋊C3—21no—
227(C3⋊Dic3)⋊C3—21no—
228(C3⋊Dic3)⋊C3—21no—
229(C3⋊Dic3)⋊C3—21no—
230(C3⋊Dic3)⋊C3C2×D412yes—
231C2×#235—91no—
232C2×#235—91no—
233C2×#235—91no—
234C22×C4×D3—91no—
235C22×C4×D3—91no—
236C22×C4×D3—91no—
237C3×C4×D4—91no—
238C3×C4×D4—91no—
239C3×#117—91no—
240#939—91no—
241#939—91no—
242#937—91no—
243#937—91no—
244C4×#67—91no—
245C4×#67—91no—
246C4×#67—91no—
247C4×#67—91no—
248#897—91no—
249#897—91no—
250#896—91no—
251#896—91no—
252#895—91no—
253#895—91no—
254#894—91no—
255#894—91no—
256#886—91no—
257#886—91no—
258#884—91no—
259#884—91no—
260#883—91no—
261#883—91no—
262#882—91no—
263#882—91no—
264#882—91no—
265#882—91no—
266#878—91no—
267#878—91no—
268C4×D12—31no—
269C4×D12—31no—
270C4×D12—31no—
271C4×D12—61no—
272C4×D12—91no—
273C4×D12—91no—
274C4×D12—91no—
275#872—31no—
276#872—91no—
277C22×C3⋊D3C22×D311yescharacteristic
278C22×C3⋊D3C22×D311yescharacteristic
279C22×C3⋊D3C22×D311yescharacteristic
280C22×C3×D3—31no—
281C22×C3×D3—31no—
282C22×C3×D3—31no—
283C22×C3×D3—31no—
284C22×C3×D3—31no—
285C22×C3×D3—31no—
286C22×C3×D3—31no—
287C22×C3×D3—61no—
288C22×C3×D3—61no—
289C2×D32—62no—
290C2×D32—62no—
291C2×D32—62no—
292C2×D32—62no—
293C2×D32—62no—
294C2×D32—62no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4—21no—
298C2×C32×C4C22×D311yescharacteristic
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C22×D311yescharacteristic
301C2×C32×C4C22×D311yescharacteristic
302C2×C32×C4C22×D311yescharacteristic
303C2×C32×C4C22×D311yescharacteristic
304C2×C3⋊Dic3C22×D311yescharacteristic
305C2×C3⋊Dic3C22×D311yescharacteristic
306C2×C3⋊Dic3C22×D311yescharacteristic
307C2×C3⋊Dic3C22×D311yescharacteristic
308C2×C3⋊Dic3C22×D311yescharacteristic
309C4⋊(C3⋊D3)—22no—
310C4×C3⋊D3—22no—
311C4×C3⋊D3—22no—
312C4×C3⋊D3D1214yescomplemented
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C3×D12—62no—
325C3×D12—62no—
326C3×D12—62no—
327C3×D12—64no—
328C3×C4×D3—34no—
329C3×C4×D3—62no—
330C3×C4×D3—62no—
331C3×C4×D3—62no—
332C3×C4×D3—62no—
333C3×C4×D3—62no—
334C3×C4×D3—62no—
335C3×C4×D3—122no—
336C3×C4×D3—122no—
337#627—62no—
338#627—62no—
339#626—62no—
340#626—62no—
341#626—62no—
342#626—62no—
343#626—62no—
344#626—62no—
345#625—62no—
346#625—62no—
347#625—62no—
348#625—62no—
349#624—62no—
350#624—62no—
351D3×Dic3—62no—
352D3×Dic3—62no—
353D3×Dic3—62no—
354D3×Dic3—62no—
355#525—271noSylow
356C2×H(3,𝔽3)C22×D411yescharacteristic
357C2×H(3,𝔽3)C2×#4111yescharacteristic
358C2×H(3,𝔽3)C2×#4111yescharacteristic
359#272—22no—
360#272—41no—
361(C3⋊D3)⋊C3—22no—
362(C3⋊D3)⋊C3—22no—
363(C3⋊D3)⋊C3—41no—
364C23×D3—91no—
365C23×D3—91no—
366C23×D3—91no—
367C2×C3×D4—91no—
368C2×C3×D4—91no—
369C22×C3×C4—91no—
370C22×C3×C4—91no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C22×C3×C4—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C22×Dic3—91no—
385C22×Dic3—91no—
386C22×Dic3—91no—
387#235—184no—
388#235—184no—
389#235—184no—
390C2×D12—31no—
391C2×D12—31no—
392C2×D12—31no—
393C2×D12—61no—
394C2×D12—91no—
395C2×D12—91no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12—91no—
399C2×D12—91no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—31no—
405C2×C4×D3—31no—
406C2×C4×D3—31no—
407C2×C4×D3—61no—
408C2×C4×D3—61no—
409C2×C4×D3—91no—
410C2×C4×D3—91no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C2×C4×D3—91no—
414C2×C4×D3—91no—
415C2×C4×D3—91no—
416C2×C4×D3—91no—
417C2×C4×D3—91no—
418C2×C4×D3—184no—
419C2×C4×D3—184no—
420C2×C4×D3—184no—
421C2×Dic6—91no—
422C2×Dic6—91no—
423C2×Dic6—91no—
424C3×C4⋊C4—91no—
425C3×C4⋊C4—91no—
426C3×C4⋊C4—91no—
427C3×C4⋊C4—91no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4—91no—
432C3×C22⋊C4—91no—
433C3×C22⋊C4—91no—
434C3×C42—31no—
435C3×C42—31no—
436C3×C42—61no—
437C3×C42—91no—
438C3×C42D3211yescharacteristic
439#217—91no—
440#217—91no—
441#217—91no—
442#217—91no—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—31no—
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—31no—
447(C2×D3)⋊C4—31no—
448(C2×D3)⋊C4—31no—
449(C2×D3)⋊C4—31no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—91no—
454(C2×D3)⋊C4—91no—
455(C2×D3)⋊C4—91no—
456(C2×D3)⋊C4—91no—
457(C2×D3)⋊C4—91no—
458(C2×D3)⋊C4—91no—
459(C2×D3)⋊C4—91no—
460(C2×D3)⋊C4—91no—
461(C2×D3)⋊C4—91no—
462(C2×D3)⋊C4—91no—
463(C2×D3)⋊C4—91no—
464(C2×D3)⋊C4—91no—
465C4⋊Dic3—31no—
466C4⋊Dic3—31no—
467C4⋊Dic3—31no—
468C4⋊Dic3—61no—
469C4⋊Dic3—91no—
470C4⋊Dic3—91no—
471C4⋊Dic3—91no—
472Dic3⋊C4—31no—
473Dic3⋊C4—31no—
474Dic3⋊C4—91no—
475Dic3⋊C4—91no—
476Dic3⋊C4—91no—
477Dic3⋊C4—91no—
478Dic3⋊C4—91no—
479Dic3⋊C4—91no—
480C4×Dic3—31no—
481C4×Dic3—91no—
482C22×C32—21no—
483C22×C32C23×D311yescharacteristic
484C22×C32C23×D311yescharacteristic
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3—21no—
490C2×C3⋊D3—21no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3C2×D1212yes—
493C2×C3⋊D3#23512yescomplemented
494C2×C3×D3—32no—
495C2×C3×D3—32no—
496C2×C3×D3—32no—
497C2×C3×D3—32no—
498C2×C3×D3—62no—
499C2×C3×D3—61no—
500C2×C3×D3—61no—
501C2×C3×D3—61no—
502C2×C3×D3—61no—
503C2×C3×D3—61no—
504C2×C3×D3—61no—
505C2×C3×D3—61no—
506C2×C3×D3—61no—
507C2×C3×D3—62no—
508C2×C3×D3—61no—
509C2×C3×D3—61no—
510C2×C3×D3—61no—
511C2×C3×D3—61no—
512C2×C3×D3—61no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—61no—
516C2×C3×D3—61no—
517C2×C3×D3—121no—
518C2×C3×D3—121no—
519C2×C3×D3—121no—
520C2×C3×D3—121no—
521D32—68no—
522D32—68no—
523C32×C4—22no—
524C32×C4—21no—
525C32×C4—21no—
526C32×C4—21no—
527C32×C4—21no—
528C32×C4—22no—
529C32×C4—41no—
530C32×C4C2×D1212yes—
531C32×C4D3×D412yes—
532C3⋊Dic3—21no—
533C3⋊Dic3—21no—
534C3⋊Dic3—21no—
535C3⋊Dic3—21no—
536C3⋊Dic3C2×D1212yes—
537C3×Dic3—32no—
538C3×Dic3—61no—
539C3×Dic3—61no—
540C3×Dic3—61no—
541C3×Dic3—61no—
542C3×Dic3—61no—
543C3×Dic3—61no—
544C3×Dic3—61no—
545C3×Dic3—61no—
546C3×Dic3—121no—
547C3×Dic3—121no—
548C2×#41—271no—
549C23×C4—271no—
550#123—271no—
551#123—271no—
552C22⋊Q8—271no—
553C22⋊Q8—271no—
554#121—271no—
555#121—271no—
556#120—271no—
557#120—271no—
558C4×D4—91no—
559C4×D4—91no—
560C4×D4—271no—
561C4×D4—271no—
562#117—91no—
563H(3,𝔽3)#52511yescharacteristic, complemented, Sylow
564C23×C3—91no—
565C23×C3—91no—
566C23×C3—91no—
567C23×C3—91no—
568C23×C3—91no—
569C22×D3—31no—
570C22×D3—31no—
571C22×D3—31no—
572C22×D3—31no—
573C22×D3—31no—
574C22×D3—31no—
575C22×D3—31no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—91no—
579C22×D3—91no—
580C22×D3—91no—
581C22×D3—182no—
582C22×D3—182no—
583C22×D3—182no—
584C22×D3—182no—
585C22×D3—182no—
586C22×D3—182no—
587C22×D3—182no—
588C22×D3—182no—
589C22×D3—182no—
590C3×D4—182no—
591C3×D4—182no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—94no—
602C2×C3×C4—91no—
603C2×C3×C4—91no—
604C2×C3×C4—91no—
605C2×C3×C4—91no—
606C2×C3×C4—91no—
607C2×C3×C4—91no—
608C2×C3×C4—91no—
609C2×C3×C4—182no—
610C2×C3×C4—182no—
611C2×C3×C4—182no—
612C2×C3×C4—182no—
613C2×C3×C4C2×D3211yescharacteristic
614C2×C3×C4C2×D3211yescharacteristic
615C2×C3×C4C2×D3211yescharacteristic
616#67—182no—
617#67—182no—
618#67—182no—
619#67—182no—
620#67—182no—
621#67—182no—
622#67—182no—
623#67—182no—
624#67—182no—
625#67—182no—
626C2×Dic3—31no—
627C2×Dic3—31no—
628C2×Dic3—31no—
629C2×Dic3—31no—
630C2×Dic3—31no—
631C2×Dic3—31no—
632C2×Dic3—31no—
633C2×Dic3—31no—
634C2×Dic3—31no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—91no—
638C2×Dic3—91no—
639C2×Dic3—91no—
640C2×Dic3—91no—
641C2×Dic3—91no—
642C2×Dic3—182no—
643C2×Dic3—182no—
644C2×Dic3—182no—
645D12—62no—
646D12—62no—
647D12—62no—
648D12—64no—
649D12—182no—
650D12—182no—
651D12—182no—
652D12—182no—
653D12—182no—
654D12—182no—
655C4×D3—34no—
656C4×D3—62no—
657C4×D3—62no—
658C4×D3—62no—
659C4×D3—62no—
660C4×D3—62no—
661C4×D3—62no—
662C4×D3—94no—
663C4×D3—122no—
664C4×D3—122no—
665C4×D3—182no—
666C4×D3—182no—
667C4×D3—182no—
668C4×D3—182no—
669C4×D3—182no—
670C4×D3—182no—
671C4×D3—182no—
672C4×D3—182no—
673Dic6—182no—
674Dic6—182no—
675Dic6—182no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32C22×D1211yescharacteristic
680C2×C32C2×#23511yescharacteristic
681C2×C32C2×D3×D411yescharacteristic
682C2×C32D3×#4111yescharacteristic
683C2×C32D3×#4111yescharacteristic
684C2×C32D3×#4111yescharacteristic
685C3⋊D3—22no—
686C3⋊D3—22no—
687C3⋊D3—41no—
688C3×D3—62no—
689C3×D3—62no—
690C3×D3—62no—
691C3×D3—62no—
692C3×D3—122no—
693C3×D3—122no—
694C3×D3—121no—
695C3×D3—121no—
696C3×D3—121no—
697C24—271no—
698#41—544no—
699C2×Q8—271no—
700C2×D4—91no—
701C2×D4—91no—
702C2×D4—271no—
703C2×D4—271no—
704C2×D4—271no—
705C2×D4—271no—
706C2×D4—271no—
707C22×C4—91no—
708C22×C4—91no—
709C22×C4—91no—
710C22×C4—91no—
711C22×C4—91no—
712C22×C4—271no—
713C22×C4—271no—
714C22×C4—271no—
715C22×C4—544no—
716C4⋊C4—91no—
717C4⋊C4—91no—
718C4⋊C4—91no—
719C4⋊C4—91no—
720C4⋊C4—271no—
721C4⋊C4—271no—
722C22⋊C4—91no—
723C22⋊C4—91no—
724C22⋊C4—91no—
725C22⋊C4—91no—
726C22⋊C4—91no—
727C22⋊C4—91no—
728C22⋊C4—271no—
729C22⋊C4—271no—
730C22⋊C4—271no—
731C22⋊C4—271no—
732C42—91no—
733C42((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
734C22×C3—31no—
735C22×C3—31no—
736C22×C3—61no—
737C22×C3—92no—
738C22×C3—92no—
739C22×C3—92no—
740C22×C3—181no—
741C22×C3—181no—
742C22×C3—181no—
743C22×C3—181no—
744C22×C3—181no—
745C22×C3—181no—
746C22×C3—181no—
747C22×C3—181no—
748C22×C3—181no—
749C22×C3—181no—
750C22×C3—181no—
751C22×C3—181no—
752C22×C3C22×D3211yescharacteristic
753C2×D3—32no—
754C2×D3—32no—
755C2×D3—32no—
756C2×D3—32no—
757C2×D3—62no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—62no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—92no—
777C2×D3—92no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—181no—
783C2×D3—181no—
784C2×D3—181no—
785C2×D3—181no—
786C2×D3—181no—
787C2×D3—181no—
788C2×D3—181no—
789C2×D3—188no—
790C2×D3—188no—
791C2×D3—188no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—32no—
795C3×C4—32no—
796C3×C4—61no—
797C3×C4—61no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—62no—
801C3×C4—62no—
802C3×C4—92no—
803C3×C4—121no—
804C3×C4—181no—
805C3×C4—181no—
806C3×C4—181no—
807C3×C4—181no—
808C3×C4—181no—
809C3×C4—181no—
810C3×C4D3×D1212yes—
811Dic3—32no—
812Dic3—61no—
813Dic3—61no—
814Dic3—61no—
815Dic3—61no—
816Dic3—61no—
817Dic3—61no—
818Dic3—61no—
819Dic3—61no—
820Dic3—92no—
821Dic3—121no—
822Dic3—121no—
823Dic3—181no—
824Dic3—181no—
825Dic3—181no—
826Dic3—181no—
827C32—21no—
828C32#552411yescharacteristic, complemented
829C32#554711yescharacteristic, complemented
830C23—91no—
831C23—91no—
832C23—91no—
833C23—91no—
834C23—91no—
835C23—542no—
836C23—542no—
837C23—542no—
838Q8—542no—
839D4—182no—
840D4—182no—
841D4—542no—
842D4—542no—
843D4—542no—
844D4—542no—
845D4—542no—
846C2×C4—91no—
847C2×C4—94no—
848C2×C4—91no—
849C2×C4—91no—
850C2×C4—91no—
851C2×C4—91no—
852C2×C4—91no—
853C2×C4—91no—
854C2×C4—182no—
855C2×C4—182no—
856C2×C4—182no—
857C2×C4—182no—
858C2×C4—542no—
859C2×C4—542no—
860C2×C4—542no—
861C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
862C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
863C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
864C2×C3—31no—
865C2×C3—31no—
866C2×C3—31no—
867C2×C3—31no—
868C2×C3—31no—
869C2×C3—31no—
870C2×C3—61no—
871C2×C3—61no—
872C2×C3—61no—
873C2×C3—182no—
874C2×C3—182no—
875C2×C3—182no—
876C2×C3—361no—
877C2×C3—361no—
878C2×C3C2×D3×D1211yescharacteristic
879C2×C3D3×#23511yescharacteristic
880C2×C3#6430611yescharacteristic
881D3—62no—
882D3—62no—
883D3—62no—
884D3—62no—
885D3—122no—
886D3—121no—
887D3—121no—
888D3—122no—
889D3—121no—
890D3—182no—
891D3—182no—
892D3—361no—
893C22—92no—
894C22—92no—
895C22—92no—
896C22—181no—
897C22—181no—
898C22—181no—
899C22—181no—
900C22—181no—
901C22—181no—
902C22—181no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—181no—
907C22—181no—
908C22—548no—
909C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
910C4—21no—
911C4—21no—
912C4—92no—
913C4—181no—
914C4—181no—
915C4—181no—
916C4—181no—
917C4—181no—
918C4—181no—
919C4#8865412yes—
920C3—31no—
921C3—31no—
922C3—61no—
923C3#1059399711yescharacteristic
924C2—182no—
925C2—182no—
926C2—182no—
927C2—361no—
928C2—361no—
929C2C2×#8865411yescharacteristic
930C2#1172249011yescharacteristic
931C2#1172249111yescharacteristic
subgroupG/H
centerC2×C4C2×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC42×H(3,𝔽3)C22
hypercenterC42((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#525
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×((C3⋊D3)⋊C3)⋊C2C2semidirect
2. C2×#88650C2semidirect
3. C4×C4⋊#272C2semidirect
4. C4×C4⋊((C3⋊D3)⋊C3)C2semidirect
5. #64081⋊C3C2semidirect
6. #11721163C2semidirect
7. #11721162C2semidirect
8. #11721157C2semidirect
9. C4×#6200C2semidirect
10. C4×#6200C2semidirect
11. #11721150C2semidirect
12. #11721133C2semidirect
13. #11721131C2semidirect
14. #11721130C2semidirect
15. #11721127C2semidirect
21. C2×C4×#272C22semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
29. C2×#6200C22semidirect
34. C2×#6196C22semidirect
37. C42×H(3,𝔽3)C22semidirect
39. #88542C22semidirect
40. C4⋊#1084C22semidirect
44. #3752⋊C3C22semidirect
45. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
46. #3750⋊C3C22semidirect
47. #3750⋊C3C22semidirect
48. C4×(C3⋊Dic3)⋊C3C22semidirect
50. #88451C22semidirect
52. #88450C22semidirect
53. #88448C22semidirect
54. #88448C22semidirect
59. C4×C4⋊(C3⋊D3)D3semidirect
60. #64081D3semidirect
110. C4×(C3⋊D3)⋊C3D4semidirect
128. C2×C4×C3⋊D3C2×D3semidirect
165. C32×C42C2×D3semidirect
166. C32×C42C2×D3semidirect
170. #3752C2×D3semidirect
171. C4⋊(C3⋊Dic3)C2×D3semidirect
172. #3750C2×D3semidirect
173. #3750C2×D3semidirect
174. C4×C3⋊Dic3C2×D3semidirect
210. C2×#272#41semidirect
219. C2×(C3⋊D3)⋊C3#41semidirect
312. C4×C3⋊D3D12semidirect
493. C2×C3⋊D3#235semidirect
563. H(3,𝔽3)#525semidirect
733. C42((C3⋊D3)⋊C3)⋊C2semidirect
828. C32#5524semidirect
829. C32#5547semidirect

Maximal subgroups

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

subgroupindex
C2×C4×((C3⋊D3)⋊C3)⋊C22
C2×#886502
C4×C4⋊#2722
C4×C4⋊((C3⋊D3)⋊C3)2
#64081⋊C32
#117211632
#117211622
#117211572
C4×#62002
#117211502
#117211332
#117211312
#117211302
#117211272
#105940063
#105939973