Finite Group Databasebeta

← #13168508

Subgroups — #13168508

Order 1728.

1094 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723675C211yesmaximal, characteristic, complemented
2#11723466C211yesmaximal, characteristic, complemented
3#11723460C211yesmaximal, characteristic, complemented
4#11723450C211yesmaximal, characteristic, complemented
5C3×#63893C211yesmaximal, characteristic, complemented
6C3×#63890C211yesmaximal, characteristic
7C3×#63846C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723013C211yesmaximal, characteristic, complemented
10#11722990C211yesmaximal, characteristic
11#11722974C211yesmaximal, characteristic, complemented
12#11722940C211yesmaximal, characteristic, complemented
13Dic3×#626C211yesmaximal, characteristic
14#11722914C211yesmaximal, characteristic, complemented
15D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
16#10594457—31nomaximal
17#10594431—31nomaximal
18#10594135—31nomaximal
19C2×Dic3×C3⋊D3C2211yescharacteristic
20C2×D3×C3⋊Dic3C2211yescharacteristic
21C2×C3×#627C2211yescharacteristic
22C2×C3×#626C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×C4⋊Dic3C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88813C2211yescharacteristic
36#88807C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42#88803C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64101—31no—
55#64099—31no—
56#64086—31no—
57C3×#897—31no—
58C3×#894—31no—
59C3×#890—31no—
60C3×#889—31no—
61C3×#886—31no—
62C3×#878—31no—
63Dic3×#67—31no—
64C2×Dic3⋊Dic3—31no—
65#63962—31no—
66#63955—31no—
67C4×#626—31no—
68#63893—31no—
69#63893D311yescharacteristic, complemented
70Dic3×D12—31no—
71#63890—31no—
72#63890D311yescharacteristic
73D3×C4⋊Dic3—31no—
74#63887—31no—
75#63884—31no—
76#63878—31no—
77#63878—31no—
78#63878—31no—
79#63878—31no—
80#63878—31no—
81#63878—61no—
82#63878—61no—
83D3×Dic3⋊C4—31no—
84#63872—31no—
85#63872—31no—
86#63872—31no—
87#63872—61no—
88#63871—31no—
89#63862—31no—
90#63861—31no—
91#63858—31no—
92#63858—31no—
93#63848—31no—
94#63848—31no—
95#63846—31no—
96#63846D311yescharacteristic, complemented
97#63845—31no—
98#63843—31no—
99Dic3×Dic6—31no—
100#63841—31no—
101#63837—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×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
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117Dic3×C3⋊D3—22no—
118D3×C3⋊Dic3—22no—
119C3×#627—22no—
120C3×#626—22no—
121C3×D3×Dic3—22no—
122C3×D3×Dic3—22no—
123#5694—91no—
124#5650—91no—
125#5642—91no—
126C22×C3⋊Dic3—31no—
127C2×C4×C3⋊D3—31no—
128C2×C3×#67—31no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3—31no—
131C2×C3×D12—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×#627C2×D311yescharacteristic
137C2×#626C2×D311yescharacteristic
138C2×D3×Dic3—31no—
139C2×D3×Dic3—31no—
140C2×D3×Dic3—31no—
141C2×D3×Dic3—31no—
142C2×D3×Dic3—61no—
143C2×D3×Dic3—61no—
144C2×D3×Dic3C2×D311yescharacteristic
145C2×D3×Dic3C2×D311yescharacteristic
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C22⋊C4—31no—
149#3757—31no—
150#3752—31no—
151#3752C2×D311yescharacteristic
152C4⋊(C3⋊Dic3)—31no—
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—31no—
155C4⋊(C3⋊Dic3)C2×D311yescharacteristic
156#3750—31no—
157#3750—31no—
158#3750—31no—
159#3750C2×D311yescharacteristic
160C4×C3⋊Dic3—31no—
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—31no—
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—61no—
166C4×C3⋊Dic3—61no—
167C4×C3⋊Dic3—61no—
168C4×C3⋊Dic3—121no—
169C3×#217—31no—
170C3×(C2×D3)⋊C4—21no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—61no—
177C3×(C2×D3)⋊C4C2×D311yescharacteristic
178C3×(C2×D3)⋊C4C2×D311yescharacteristic
179C3×C4⋊Dic3—21no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—61no—
188C3×C4⋊Dic3C2×D311yescharacteristic
189C3×C4⋊Dic3C2×D311yescharacteristic
190C3×Dic3⋊C4—21no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—61no—
199C3×Dic3⋊C4C2×D311yescharacteristic
200C3×Dic3⋊C4C2×D311yescharacteristic
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203#3724—31no—
204Dic3⋊Dic3—31no—
205Dic3⋊Dic3—31no—
206Dic3⋊Dic3—31no—
207Dic3⋊Dic3—31no—
208Dic3⋊Dic3—31no—
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—61no—
219Dic3⋊Dic3—61no—
220Dic3⋊Dic3—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226Dic3⋊Dic3C2×D311yescharacteristic
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229#3722—31no—
230#3722—31no—
231#3722C2×D311yescharacteristic
232(C2×D3)⋊Dic3—31no—
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—61no—
241(C2×D3)⋊Dic3—61no—
242(C2×D3)⋊Dic3C2×D311yescharacteristic
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3×C3⋊D3—21no—
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×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—
267C3×C3⋊Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3#4112yes—
273C3×#125—91no—
274C3×#123—91no—
275C3×C22⋊Q8—91no—
276#946—91no—
277Q8×Dic3—91no—
278#935—91no—
279D4×Dic3—91no—
280C4×#67—91no—
281#926—91no—
282C2×C4⋊Dic3—91no—
283C2×Dic3⋊C4—91no—
284#898—91no—
285#898—91no—
286#898—91no—
287#898—91no—
288#897—31no—
289#897—91no—
290#894—31no—
291#894—91no—
292#892—91no—
293#892—91no—
294#892—91no—
295#892—91no—
296#892—181no—
297D3×C4⋊C4—91no—
298#890—31no—
299#890—91no—
300#890—91no—
301#890—91no—
302#890—91no—
303#890—91no—
304#890—181no—
305#889—31no—
306#889—91no—
307#887—91no—
308#886—31no—
309#886—91no—
310#879—91no—
311#879—91no—
312#878—31no—
313#878—91no—
314#877—91no—
315#877—91no—
316#877—91no—
317#877—91no—
318#877—181no—
319C4×D12—91no—
320C4×Dic6—91no—
321C23×C32—31no—
322C22×C3⋊D3C22×D311yescharacteristic
323C22×C3×D3—21no—
324C22×C3×D3—31no—
325C22×C3×D3—31no—
326C22×C3×D3—61no—
327C22×C3×D3C22×D311yescharacteristic
328C22×C3×D3C22×D311yescharacteristic
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—41no—
338C2×C32×C4C22×D311yescharacteristic
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—31no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—62no—
354C2×C3⋊Dic3—121no—
355C2×C3⋊Dic3—121no—
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C4×C3⋊D3—62no—
362C3×#67—62no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—31no—
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—31no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—62no—
384C2×C3×Dic3—62no—
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
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C3×D12—62no—
396C3×C4×D3—62no—
397C3×C4×D3—62no—
398C3×Dic6—62no—
399C3×Dic6—62no—
400#627—22no—
401#626—22no—
402D3×Dic3—22no—
403D3×Dic3—22no—
404D3×Dic3—64no—
405D3×Dic3—64no—
406D3×Dic3—62no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410#552—271noSylow
411C2×C33C2×#4111yescharacteristic
412C2×C33C2×#4111yescharacteristic
413C2×C332−1+411yescharacteristic
414C3×C3⋊D3—41no—
415C32×D3—22no—
416C2×C3×Q8—91no—
417C2×C3×D4—91no—
418C22×C3×C4—91no—
419C22×C3×C4—91no—
420C2×#67—31no—
421C22×Dic3—31no—
422C22×Dic3—31no—
423C22×Dic3—91no—
424C22×Dic3—91no—
425C22×Dic3—91no—
426C22×Dic3—181no—
427C2×D12—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—181no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—31no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—61no—
441C3×C4⋊C4—61no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C22⋊C4—31no—
450C3×C22⋊C4—31no—
451C3×C22⋊C4—61no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C42—91no—
456#217—31no—
457#217—91no—
458#217—91no—
459#217—91no—
460#217—91no—
461#217—91no—
462#217—181no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—61no—
469(C2×D3)⋊C4—91no—
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—181no—
477(C2×D3)⋊C4D3211yescharacteristic
478C4⋊Dic3—31no—
479C4⋊Dic3—31no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—61no—
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—91no—
496C4⋊Dic3—181no—
497C4⋊Dic3—181no—
498C4⋊Dic3—181no—
499C4⋊Dic3D3211yescharacteristic
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—61no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—181no—
520Dic3⋊C4—181no—
521Dic3⋊C4—181no—
522Dic3⋊C4D3211yescharacteristic
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—91no—
526C4×Dic3—91no—
527C4×Dic3—91no—
528C4×Dic3—91no—
529C4×Dic3—91no—
530C4×Dic3—91no—
531C4×Dic3—91no—
532C4×Dic3—91no—
533C4×Dic3—91no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—181no—
538C4×Dic3—181no—
539C4×Dic3—181no—
540C4×Dic3—181no—
541C4×Dic3—181no—
542C4×Dic3—361no—
543C22×C32—21no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—32no—
547C22×C32—41no—
548C22×C32—61no—
549C22×C32—61no—
550C22×C32C23×D311yescharacteristic
551C22×C32C23×D311yescharacteristic
552C22×C32C23×D311yescharacteristic
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3⋊D3—21no—
556C2×C3×D3—21no—
557C2×C3×D3—21no—
558C2×C3×D3—21no—
559C2×C3×D3—21no—
560C2×C3×D3—22no—
561C2×C3×D3—41no—
562C2×C3×D3—41no—
563C2×C3×D3—62no—
564C2×C3×D3—61no—
565C2×C3×D3—61no—
566C2×C3×D3—61no—
567C2×C3×D3—61no—
568C2×C3×D3—61no—
569C2×C3×D3—61no—
570C2×C3×D3—121no—
571C2×C3×D3—121no—
572C2×C3×D3#23712yes—
573C2×C3×D3#23912yes—
574C32×C4—21no—
575C32×C4—22no—
576C32×C4—21no—
577C32×C4—21no—
578C32×C4—32no—
579C32×C4—41no—
580C32×C4—41no—
581C32×C4—42no—
582C32×C4—61no—
583C32×C4—61no—
584C32×C4—61no—
585C32×C4—61no—
586C3⋊Dic3—21no—
587C3⋊Dic3—21no—
588C3⋊Dic3—21no—
589C3⋊Dic3—21no—
590C3⋊Dic3—21no—
591C3⋊Dic3—61no—
592C3⋊Dic3—61no—
593C3⋊Dic3—62no—
594C3⋊Dic3—62no—
595C3⋊Dic3—61no—
596C3⋊Dic3—61no—
597C3⋊Dic3—61no—
598C3⋊Dic3—61no—
599C3⋊Dic3—121no—
600C3⋊Dic3—121no—
601C3⋊Dic3—121no—
602C3⋊Dic3—121no—
603C3⋊Dic3—122no—
604C3⋊Dic3—122no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—22no—
614C3×Dic3—41no—
615C3×Dic3—41no—
616C3×Dic3—41no—
617C3×Dic3—41no—
618C3×Dic3—62no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—121no—
630C3×Dic3—121no—
631C3×Dic3—121no—
632C3×Dic3—121no—
633C3×Dic3#23712yes—
634C3×Dic3#23912yes—
635#126—271no—
636#126—271no—
637#125—91no—
638#125—271no—
639#125—271no—
640#123—91no—
641#123—271no—
642C22⋊Q8—91no—
643C22⋊Q8—271no—
644C4×Q8—271no—
645C4×D4—271no—
646#117—271no—
647#117—271no—
648#117—271no—
649C2×C4⋊C4—271no—
650C33#55211yescharacteristic, complemented, Sylow
651C23×C3—31no—
652C23×C3—31no—
653C23×C3—61no—
654C23×C3—91no—
655C22×D3—31no—
656C22×D3—31no—
657C22×D3—61no—
658C22×D3C2×D3211yescharacteristic
659C3×Q8—182no—
660C3×D4—182no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—31no—
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—41no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—91no—
681C2×C3×C4—91no—
682C2×C3×C4—91no—
683C2×C3×C4—91no—
684C2×C3×C4—91no—
685C2×C3×C4—182no—
686C2×C3×C4—182no—
687C2×C3×C4C2×D3211yescharacteristic
688C2×C3×C4C2×D3211yescharacteristic
689C2×C3×C4C2×D3211yescharacteristic
690#67—62no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—62no—
707C2×Dic3—62no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—91no—
711C2×Dic3—91no—
712C2×Dic3—91no—
713C2×Dic3—91no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—181no—
717C2×Dic3—181no—
718C2×Dic3—181no—
719C2×Dic3—181no—
720C2×Dic3—182no—
721C2×Dic3—182no—
722C2×Dic3—184no—
723C2×Dic3—182no—
724C2×Dic3—361no—
725C2×Dic3—361no—
726C2×Dic3C2×D3211yescharacteristic
727C2×Dic3C2×D3211yescharacteristic
728C2×Dic3C2×D3211yescharacteristic
729C2×Dic3C2×D3211yescharacteristic
730C2×Dic3C2×D3211yescharacteristic
731D12—62no—
732C4×D3—62no—
733C4×D3—62no—
734C4×D3—182no—
735C4×D3—182no—
736C4×D3—184no—
737C4×D3—182no—
738Dic6—62no—
739Dic6—62no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—41no—
750C2×C32—41no—
751C2×C32—41no—
752C2×C32—62no—
753C2×C32C2×#23711yescharacteristic
754C2×C32C2×#23711yescharacteristic
755C2×C32C2×#23911yescharacteristic
756C2×C32C2×#23911yescharacteristic
757C2×C32D3×#4111yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32#101011yescharacteristic
760C2×C32#101011yescharacteristic
761C2×C32#101011yescharacteristic
762C3⋊D3—41no—
763C3×D3—22no—
764C3×D3—22no—
765C3×D3—42no—
766C3×D3—122no—
767C3×D3—121no—
768C3×D3—121no—
769C2×Q8—91no—
770C2×D4—91no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—271no—
774C22×C4—271no—
775C4⋊C4—31no—
776C4⋊C4—31no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C4⋊C4—271no—
787C4⋊C4—271no—
788C4⋊C4—271no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C22⋊C4—31no—
792C22⋊C4—91no—
793C22⋊C4—91no—
794C22⋊C4—91no—
795C22⋊C4—271no—
796C22⋊C4—271no—
797C22⋊C4—271no—
798C22⋊C4—271no—
799C42—91no—
800C42—271no—
801C42—271no—
802C42—271no—
803C42—271no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—32no—
808C22×C3—32no—
809C22×C3—41no—
810C22×C3—62no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—121no—
816C22×C3—121no—
817C22×C3—181no—
818C22×C3—181no—
819C22×C3—181no—
820C22×C3C22×D3211yescharacteristic
821C22×C3C22×D3211yescharacteristic
822C22×C3C22×D3211yescharacteristic
823C2×D3—21no—
824C2×D3—21no—
825C2×D3—62no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3#379612yes—
835C3×C4—22no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—32no—
840C3×C4—32no—
841C3×C4—41no—
842C3×C4—41no—
843C3×C4—42no—
844C3×C4—62no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—121no—
854C3×C4—121no—
855C3×C4—121no—
856C3×C4—121no—
857C3×C4—181no—
858C3×C4—181no—
859C3×C4—181no—
860C3×C4—181no—
861C3×C4—181no—
862Dic3—21no—
863Dic3—21no—
864Dic3—21no—
865Dic3—21no—
866Dic3—62no—
867Dic3—61no—
868Dic3—61no—
869Dic3—61no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—121no—
878Dic3—121no—
879Dic3—121no—
880Dic3—121no—
881Dic3—182no—
882Dic3—182no—
883Dic3—181no—
884Dic3—181no—
885Dic3—181no—
886Dic3—181no—
887Dic3—181no—
888Dic3—181no—
889Dic3—361no—
890Dic3—361no—
891Dic3—361no—
892Dic3—361no—
893Dic3—362no—
894Dic3—362no—
895Dic3#379612yes—
896C32—21no—
897C32—21no—
898C32—21no—
899C32—41no—
900C32#564211yescharacteristic, complemented
901C32#565011yescharacteristic, complemented
902C32#569411yescharacteristic, complemented
903C23—31no—
904C23—91no—
905Q8—182no—
906D4—182no—
907C2×C4—31no—
908C2×C4—31no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—91no—
913C2×C4—91no—
914C2×C4—91no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—182no—
918C2×C4—182no—
919C2×C4—271no—
920C2×C4—271no—
921C2×C4—542no—
922C2×C4—542no—
923C2×C4D3311yescharacteristic
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—41no—
934C2×C3—41no—
935C2×C3—41no—
936C2×C3—62no—
937C2×C3—62no—
938C2×C3—122no—
939C2×C3—361no—
940C2×C3C2×#379611yescharacteristic
941C2×C3C2×#379611yescharacteristic
942C2×C3#6429811yescharacteristic
943C2×C3#6430911yescharacteristic
944C2×C3#6430911yescharacteristic
945C2×C3D3×#23711yescharacteristic
946C2×C3D3×#23711yescharacteristic
947C2×C3D3×#23911yescharacteristic
948C2×C3D3×#23911yescharacteristic
949D3—22no—
950D3—122no—
951D3—121no—
952D3—121no—
953C22—32no—
954C22—61no—
955C22—61no—
956C22—181no—
957C22—181no—
958C22—181no—
959C22C2×D3311yescharacteristic
960C4—21no—
961C4—32no—
962C4—61no—
963C4—61no—
964C4—61no—
965C4—61no—
966C4—181no—
967C4—181no—
968C4—181no—
969C4—181no—
970C4—181no—
971C4—541no—
972C4—541no—
973C3—21no—
974C3—21no—
975C3—21no—
976C3—41no—
977C3#1059413511yescharacteristic, complemented
978C3#1059443111yescharacteristic, complemented
979C3#1059445711yescharacteristic, complemented
980C2—62no—
981C2—361no—
982C2D3×#379611yescharacteristic
983C2D3×#379611yescharacteristic
984C2#1172442711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#626C22
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
1. #11723675C2semidirect
2. #11723466C2semidirect
3. #11723460C2semidirect
4. #11723450C2semidirect
5. C3×#63893C2semidirect
7. C3×#63846C2semidirect
8. #11723025C2semidirect
9. #11723013C2semidirect
11. #11722974C2semidirect
12. #11722940C2semidirect
14. #11722914C2semidirect
15. D3×Dic3⋊Dic3C2semidirect
69. #63893D3semidirect
96. #63846D3semidirect
650. C33#552semidirect
900. C32#5642semidirect
901. C32#5650semidirect
902. C32#5694semidirect
977. C3#10594135semidirect
978. C3#10594431semidirect
979. C3#10594457semidirect

Maximal subgroups

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

subgroupindex
#117236752
#117234662
#117234602
#117234502
C3×#638932
C3×#638902
C3×#638462
#117230252
#117230132
#117229902
#117229742
#117229402
Dic3×#6262
#117229142
D3×Dic3⋊Dic32
#105944573
#105944313
#105941353