Finite Group Databasebeta

← #13168574

Subgroups — #13168574

Order 1728.

1088 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723686C211yesmaximal, characteristic
2Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
3#11723409C211yesmaximal, characteristic, complemented
4#11723400C211yesmaximal, characteristic, complemented
5C3×#63897C211yesmaximal, characteristic
6C3×#63867C211yesmaximal, characteristic, complemented
7C3×#63837C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723023C211yesmaximal, characteristic, complemented
10#11722974C211yesmaximal, characteristic, complemented
11#11722974C211yesmaximal, characteristic, complemented
12#11722922C211yesmaximal, characteristic, complemented
13#11722921C211yesmaximal, characteristic, complemented
14#11722915C211yesmaximal, characteristic, complemented
15#11722911C211yesmaximal, characteristic, complemented
16#10594431—31nomaximal
17#10594420—31nomaximal
18#10593947—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×Dic3×C3⋊D3C2211yescharacteristic
22C2×Dic3×C3⋊D3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#624C2211yescharacteristic
25C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
26C3×#3750C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C32×Dic3⋊C4C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31#88814C2211yescharacteristic
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88807C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64099—31no—
55#64098—31no—
56C4×C4⋊(C3⋊D3)—31no—
57C3×#894—31no—
58C3×#894—31no—
59C3×#889—31no—
60C3×#887—31no—
61C3×#870—31no—
62C3×C4×Dic6—31no—
63#63900—31no—
64#63897—31no—
65#63897D311yescharacteristic
66#63893—31no—
67#63893—31no—
68Dic3×D12—31no—
69Dic3×D12—31no—
70Dic3×D12—61no—
71#63887—31no—
72#63887—31no—
73#63884—31no—
74#63884—31no—
75#63878—31no—
76#63878—31no—
77#63878—31no—
78#63877—31no—
79D3×Dic3⋊C4—31no—
80D3×Dic3⋊C4—31no—
81#63871—31no—
82#63871—31no—
83#63868—31no—
84#63868—31no—
85#63867D311yescharacteristic, complemented
86#63861—31no—
87#63859—31no—
88#63859—31no—
89#63858—31no—
90#63855—31no—
91#63849—31no—
92#63845—31no—
93#63845—31no—
94#63845—31no—
95#63845—31no—
96#63845—61no—
97#63845—61no—
98#63841—31no—
99#63837D311yescharacteristic, complemented
100#63836—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C3×C4⋊(C3⋊D3)—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6294—22no—
119Dic3×C3⋊D3—22no—
120Dic3×C3⋊D3—22no—
121C3×#627—22no—
122C3×#624—22no—
123#5694—91no—
124#5650—91no—
125#5581—91no—
126C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C3×D12—31no—
130C2×C3×D12—31no—
131C2×C3×D12—61no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×#627C2×D311yescharacteristic
137C2×#624—31no—
138C2×#624C2×D311yescharacteristic
139C2×D3×Dic3—31no—
140C2×D3×Dic3—31no—
141C2×D3×Dic3—31no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—61no—
146C2×D3×Dic3—61no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C42—31no—
150#3752—31no—
151#3752—31no—
152C4⋊(C3⋊Dic3)—31no—
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—31no—
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—61no—
158C4⋊(C3⋊Dic3)—61no—
159C4⋊(C3⋊Dic3)—61no—
160C4⋊(C3⋊Dic3)—121no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750C2×D311yescharacteristic
166#3750C2×D311yescharacteristic
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×Dic3⋊C4—21no—
180C3×Dic3⋊C4—21no—
181C3×Dic3⋊C4—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—61no—
192C3×Dic3⋊C4—61no—
193C3×Dic3⋊C4C2×D311yescharacteristic
194C3×Dic3⋊C4C2×D311yescharacteristic
195C3×Dic3⋊C4C2×D311yescharacteristic
196C3×Dic3⋊C4C2×D311yescharacteristic
197C3×C4×Dic3—21no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3C2×D311yescharacteristic
203C3×C4×Dic3C2×D311yescharacteristic
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—61no—
209#3724—61no—
210#3724C2×D311yescharacteristic
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—61no—
220Dic3⋊Dic3—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3C2×D311yescharacteristic
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226Dic3⋊Dic3C2×D311yescharacteristic
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722C2×D311yescharacteristic
231#3722C2×D311yescharacteristic
232#3722C2×D311yescharacteristic
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—61no—
244(C2×D3)⋊Dic3—61no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—61no—
250Dic32—61no—
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3×C3⋊D3—21no—
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3#4112yes—
260C33×C4—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3⋊(C3⋊Dic3)—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3#4112yes—
273C3×#125—91no—
274C3×#123—91no—
275C3×C4×Q8—91no—
276#946—91no—
277#946—91no—
278#935—91no—
279D4×Dic3—91no—
280#926—91no—
281C2×Dic3⋊C4—91no—
282#898—91no—
283#898—91no—
284#897—91no—
285#897—91no—
286#894—31no—
287#894—31no—
288#894—91no—
289#894—91no—
290#892—91no—
291#892—91no—
292#892—91no—
293#892—91no—
294D3×C4⋊C4—91no—
295D3×C4⋊C4—91no—
296#890—91no—
297#890—91no—
298#890—91no—
299#890—181no—
300#889—31no—
301#889—91no—
302#889—91no—
303#889—91no—
304#889—181no—
305#887—31no—
306#879—91no—
307#879—91no—
308#878—91no—
309#878—91no—
310#877—91no—
311#877—91no—
312#876—91no—
313#876—91no—
314C4×D12—91no—
315C4×D12—91no—
316C4×D12—181no—
317#872—91no—
318#872—91no—
319#870—31no—
320C4×Dic6—31no—
321C22×C3⋊D3C22×D311yescharacteristic
322C22×C3⋊D3C22×D311yescharacteristic
323C22×C3×D3—31no—
324C22×C3×D3—31no—
325C22×C3×D3—31no—
326C22×C3×D3—31no—
327C22×C3×D3—61no—
328C22×C3×D3—61no—
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—41no—
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C32×C4C22×D311yescharacteristic
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—31no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—61no—
354C2×C3⋊Dic3—121no—
355C2×C3⋊Dic3—121no—
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C4⋊(C3⋊D3)—22no—
361C4×C3⋊D3—62no—
362C4×C3⋊D3—62no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C3×D12—62no—
394C3×D12—62no—
395C3×D12—64no—
396C3×C4×D3—62no—
397C3×C4×D3—62no—
398C3×Dic6—62no—
399C3×Dic6—62no—
400#627—22no—
401#624—22no—
402#624—62no—
403D3×Dic3—62no—
404D3×Dic3—62no—
405D3×Dic3—62no—
406D3×Dic3—62no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—122no—
410D3×Dic3—122no—
411#552—271noSylow
412C2×C33C2×#4111yescharacteristic
413C2×C33C2×#4111yescharacteristic
414C2×C332−1+411yescharacteristic
415C3×C3⋊D3—22no—
416C3×C3⋊D3—41no—
417C2×C3×Q8—91no—
418C2×C3×D4—91no—
419C22×C3×C4—91no—
420C22×Dic3—91no—
421C22×Dic3—91no—
422C22×Dic3—91no—
423C2×D12—31no—
424C2×D12—31no—
425C2×D12—61no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
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—181no—
435C2×C4×D3—181no—
436C2×Dic6—31no—
437C2×Dic6—31no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—61no—
443C3×C4⋊C4—61no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C42—31no—
455C3×C42—31no—
456C3×C42—61no—
457C3×C42—91no—
458C3×C42—91no—
459#217—91no—
460#217—91no—
461#217—91no—
462#217—91no—
463#217—91no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—31no—
469(C2×D3)⋊C4—31no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
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—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—181no—
481(C2×D3)⋊C4—181no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—181no—
496C4⋊Dic3—181no—
497C4⋊Dic3—181no—
498C4⋊Dic3—181no—
499C4⋊Dic3—181no—
500C4⋊Dic3—361no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—31no—
511Dic3⋊C4—61no—
512Dic3⋊C4—61no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—181no—
526Dic3⋊C4—181no—
527Dic3⋊C4—181no—
528Dic3⋊C4—181no—
529Dic3⋊C4D3211yescharacteristic
530Dic3⋊C4D3211yescharacteristic
531C4×Dic3—31no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—181no—
542C4×Dic3—181no—
543C4×Dic3D3211yescharacteristic
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—41no—
548C22×C32C23×D311yescharacteristic
549C22×C32C23×D311yescharacteristic
550C22×C32C23×D311yescharacteristic
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3⋊D3—21no—
556C2×C3⋊D3#23712yes—
557C2×C3×D3—32no—
558C2×C3×D3—32no—
559C2×C3×D3—62no—
560C2×C3×D3—61no—
561C2×C3×D3—61no—
562C2×C3×D3—61no—
563C2×C3×D3—61no—
564C2×C3×D3—62no—
565C2×C3×D3—61no—
566C2×C3×D3—61no—
567C2×C3×D3—61no—
568C2×C3×D3—61no—
569C2×C3×D3—61no—
570C2×C3×D3—61no—
571C2×C3×D3—121no—
572C2×C3×D3—121no—
573C2×C3×D3—121no—
574C2×C3×D3—121no—
575C32×C4—21no—
576C32×C4—22no—
577C32×C4—21no—
578C32×C4—21no—
579C32×C4—32no—
580C32×C4—41no—
581C32×C4—41no—
582C32×C4—42no—
583C32×C4—61no—
584C32×C4—61no—
585C32×C4—61no—
586C32×C4—61no—
587C32×C4—61no—
588C3⋊Dic3—21no—
589C3⋊Dic3—21no—
590C3⋊Dic3—21no—
591C3⋊Dic3—21no—
592C3⋊Dic3—61no—
593C3⋊Dic3—61no—
594C3⋊Dic3—61no—
595C3⋊Dic3—61no—
596C3⋊Dic3—61no—
597C3⋊Dic3—61no—
598C3⋊Dic3—121no—
599C3⋊Dic3—121no—
600C3⋊Dic3—121no—
601C3⋊Dic3—121no—
602C3⋊Dic3—121no—
603C3⋊Dic3—121no—
604C3⋊Dic3—241no—
605C3⋊Dic3—241no—
606C3×Dic3—22no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—22no—
618C3×Dic3—41no—
619C3×Dic3—41no—
620C3×Dic3—41no—
621C3×Dic3—41no—
622C3×Dic3—62no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—121no—
632C3×Dic3—121no—
633C3×Dic3—121no—
634C3×Dic3#23512yes—
635C3×Dic3#23912yes—
636#126—271no—
637#126—271no—
638#125—91no—
639#125—271no—
640#125—271no—
641#123—91no—
642#123—271no—
643C22⋊Q8—271no—
644C22⋊Q8—271no—
645C4×Q8—91no—
646C4×D4—271no—
647#117—271no—
648#117—271no—
649#117—271no—
650C2×C4⋊C4—271no—
651C33#55211yescharacteristic, complemented, Sylow
652C23×C3—91no—
653C23×C3—91no—
654C22×D3—31no—
655C22×D3—31no—
656C22×D3—31no—
657C22×D3—31no—
658C22×D3—61no—
659C22×D3—61no—
660C3×Q8—182no—
661C3×D4—182no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—41no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—91no—
685C2×C3×C4—91no—
686C2×C3×C4—91no—
687C2×C3×C4—91no—
688C2×C3×C4—182no—
689C2×C3×C4C2×D3211yescharacteristic
690C2×C3×C4C2×D3211yescharacteristic
691C2×C3×C4C2×D3211yescharacteristic
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—61no—
703C2×Dic3—61no—
704C2×Dic3—91no—
705C2×Dic3—91no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—181no—
711C2×Dic3—181no—
712C2×Dic3—181no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—182no—
717C2×Dic3—182no—
718C2×Dic3—182no—
719C2×Dic3—361no—
720C2×Dic3—361no—
721C2×Dic3C2×D3211yescharacteristic
722C2×Dic3C2×D3211yescharacteristic
723C2×Dic3C2×D3211yescharacteristic
724C2×Dic3C2×D3211yescharacteristic
725C2×Dic3C2×D3211yescharacteristic
726C2×Dic3C2×D3211yescharacteristic
727D12—62no—
728D12—62no—
729D12—64no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—182no—
733C4×D3—182no—
734C4×D3—182no—
735C4×D3—182no—
736C4×D3—182no—
737C4×D3—182no—
738C4×D3—362no—
739C4×D3—362no—
740Dic6—62no—
741Dic6—62no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—41no—
752C2×C32—41no—
753C2×C32—41no—
754C2×C32C2×#23511yescharacteristic
755C2×C32C2×#23711yescharacteristic
756C2×C32C2×#23911yescharacteristic
757C2×C32#100711yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C2×C32D3×#4111yescharacteristic
761C2×C32#101011yescharacteristic
762C2×C32#101011yescharacteristic
763C3⋊D3—22no—
764C3⋊D3—41no—
765C3×D3—62no—
766C3×D3—62no—
767C3×D3—122no—
768C3×D3—122no—
769C3×D3—121no—
770C3×D3—121no—
771C2×Q8—91no—
772C2×D4—91no—
773C22×C4—91no—
774C22×C4—271no—
775C22×C4—271no—
776C22×C4—271no—
777C4⋊C4—31no—
778C4⋊C4—31no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4—91no—
786C4⋊C4—271no—
787C4⋊C4—271no—
788C4⋊C4—271no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C4⋊C4—271no—
792C4⋊C4—271no—
793C22⋊C4—91no—
794C22⋊C4—91no—
795C22⋊C4—91no—
796C22⋊C4—271no—
797C22⋊C4—271no—
798C22⋊C4—271no—
799C22⋊C4—271no—
800C22⋊C4—271no—
801C42—31no—
802C42—91no—
803C42—91no—
804C42—271no—
805C42—271no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—41no—
810C22×C3—92no—
811C22×C3—181no—
812C22×C3—181no—
813C22×C3—181no—
814C22×C3—181no—
815C22×C3—181no—
816C22×C3C22×D3211yescharacteristic
817C22×C3C22×D3211yescharacteristic
818C22×C3C22×D3211yescharacteristic
819C2×D3—32no—
820C2×D3—32no—
821C2×D3—62no—
822C2×D3—61no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—62no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—121no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—121no—
837C3×C4—22no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—21no—
841C3×C4—32no—
842C3×C4—32no—
843C3×C4—41no—
844C3×C4—41no—
845C3×C4—42no—
846C3×C4—62no—
847C3×C4—62no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—61no—
855C3×C4—61no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—121no—
859C3×C4—121no—
860C3×C4—121no—
861C3×C4—121no—
862C3×C4—181no—
863C3×C4—181no—
864C3×C4—181no—
865C3×C4—181no—
866Dic3—21no—
867Dic3—21no—
868Dic3—21no—
869Dic3—21no—
870Dic3—21no—
871Dic3—62no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—61no—
878Dic3—61no—
879Dic3—61no—
880Dic3—121no—
881Dic3—121no—
882Dic3—121no—
883Dic3—181no—
884Dic3—181no—
885Dic3—181no—
886Dic3—181no—
887Dic3—181no—
888Dic3—181no—
889Dic3—361no—
890Dic3—361no—
891Dic3—361no—
892Dic3—361no—
893Dic3—361no—
894Dic3—361no—
895Dic3—721no—
896Dic3—721no—
897Dic3#379912yes—
898C32—21no—
899C32—21no—
900C32—21no—
901C32—41no—
902C32#558111yescharacteristic, complemented
903C32#565011yescharacteristic, complemented
904C32#569411yescharacteristic, complemented
905C23—91no—
906C23—91no—
907Q8—182no—
908D4—182no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—31no—
913C2×C4—31no—
914C2×C4—31no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—91no—
918C2×C4—91no—
919C2×C4—182no—
920C2×C4—271no—
921C2×C4—271no—
922C2×C4—542no—
923C2×C4—542no—
924C2×C4—542no—
925C2×C4D3311yescharacteristic
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—41no—
936C2×C3—41no—
937C2×C3—41no—
938C2×C3—182no—
939C2×C3—361no—
940C2×C3#6429711yescharacteristic
941C2×C3#6429811yescharacteristic
942C2×C3C2×#379911yescharacteristic
943C2×C3D3×#23511yescharacteristic
944C2×C3#6430611yescharacteristic
945C2×C3D3×#23711yescharacteristic
946C2×C3D3×#23711yescharacteristic
947C2×C3#6431511yescharacteristic
948C2×C3D3×#23911yescharacteristic
949D3—62no—
950D3—62no—
951D3—122no—
952D3—122no—
953D3—121no—
954D3—121no—
955C22—92no—
956C22—181no—
957C22—181no—
958C22—181no—
959C22—181no—
960C22—181no—
961C22C2×D3311yescharacteristic
962C4—21no—
963C4—32no—
964C4—61no—
965C4—61no—
966C4—61no—
967C4—61no—
968C4—61no—
969C4—181no—
970C4—181no—
971C4—181no—
972C4—181no—
973C4—541no—
974C4—541no—
975C3—21no—
976C3—21no—
977C3—21no—
978C3—41no—
979C3#1059394711yescharacteristic, complemented
980C3#1059442011yescharacteristic, complemented
981C3#1059443111yescharacteristic, complemented
982C2—182no—
983C2—361no—
984C2D3×#379911yescharacteristic
985C2#1172439611yescharacteristic
986C2#1172440711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×C4⋊(C3⋊D3)C22
hypercenterC2×C4D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #11723409C2semidirect
4. #11723400C2semidirect
6. C3×#63867C2semidirect
7. C3×#63837C2semidirect
8. #11723024C2semidirect
9. #11723023C2semidirect
10. #11722974C2semidirect
11. #11722974C2semidirect
12. #11722922C2semidirect
13. #11722921C2semidirect
14. #11722915C2semidirect
15. #11722911C2semidirect
85. #63867D3semidirect
99. #63837D3semidirect
651. C33#552semidirect
902. C32#5581semidirect
903. C32#5650semidirect
904. C32#5694semidirect
979. C3#10593947semidirect
980. C3#10594420semidirect
981. C3#10594431semidirect

Maximal subgroups

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

subgroupindex
#117236862
Dic3×C4⋊(C3⋊D3)2
#117234092
#117234002
C3×#638972
C3×#638672
C3×#638372
#117230242
#117230232
#117229742
#117229222
#117229212
#117229152
#117229112
#105944313
#105944203
#105939473