Finite Group Databasebeta

← #13168468

Subgroups — #13168468

Order 1728.

1106 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2#11723499C211yesmaximal, characteristic
3#11723448C211yesmaximal, characteristic, complemented
4#11723391C211yesmaximal, characteristic, complemented
5C3×#63884C211yesmaximal, characteristic
6C3×#63884C211yesmaximal, characteristic
7C3×#63845C211yesmaximal, characteristic, complemented
8#11723022C211yesmaximal, characteristic, complemented
9#11723019C211yesmaximal, characteristic, complemented
10#11722980C211yesmaximal, characteristic, complemented
11#11722980C211yesmaximal, characteristic, complemented
12#11722916C211yesmaximal, characteristic, complemented
13#11722914C211yesmaximal, characteristic, complemented
14#11722913C211yesmaximal, characteristic, complemented
15D3×#3724C211yesmaximal, characteristic, complemented
16#10595120—31nomaximal
17#10594430—31nomaximal
18#10594429—31nomaximal
19C2×C32×D12C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88813C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54D4×C3⋊Dic3—31no—
55#64098—31no—
56#64096—31no—
57C3×#935—31no—
58C3×#935—31no—
59C3×#894—31no—
60C3×#894—31no—
61C3×#890—31no—
62C3×#889—31no—
63#63982—31no—
64#63982—31no—
65C2×#3724—31no—
66#63957—31no—
67#63956—31no—
68#63956—31no—
69#63955—31no—
70#63955—31no—
71#63899—31no—
72#63899—31no—
73#63898—31no—
74#63898—31no—
75#63898—61no—
76#63896—31no—
77#63896—31no—
78#63884D311yescharacteristic
79#63884D311yescharacteristic
80#63878—31no—
81#63877—31no—
82#63877—31no—
83#63877—31no—
84D3×Dic3⋊C4—31no—
85D3×Dic3⋊C4—31no—
86#63870—31no—
87#63870—31no—
88#63870—61no—
89#63862—31no—
90#63862—31no—
91#63861—31no—
92#63858—31no—
93#63855—31no—
94#63847—31no—
95#63846—31no—
96#63845—31no—
97#63845D311yescharacteristic, complemented
98#63841—31no—
99#63838—31no—
100#63838—31no—
101#63838—61no—
102C22×C32×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×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—22no—
118#6293—22no—
119D3×C3⋊Dic3—22no—
120D3×C3⋊Dic3—22no—
121C3×D3×Dic3—22no—
122C3×D3×Dic3—22no—
123#5693—91no—
124#5650—91no—
125#5650—91no—
126C2×C32×D4—31no—
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—31no—
129C2×#634—31no—
130C22×C3×Dic3—31no—
131C22×C3×Dic3—31no—
132C2×C3×D12—21no—
133C2×C3×D12C2×D311yescharacteristic
134C2×C3×D12C2×D311yescharacteristic
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×#627—31no—
138C2×#627—31no—
139C2×#627—61no—
140C2×D3×Dic3—31no—
141C2×D3×Dic3—31no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—61no—
145C2×D3×Dic3—61no—
146C2×D3×Dic3C2×D311yescharacteristic
147C2×D3×Dic3C2×D311yescharacteristic
148C32×C4⋊C4—31no—
149C32×C4⋊C4—31no—
150#3757—31no—
151#3757—31no—
152C4⋊(C3⋊Dic3)—31no—
153C4⋊(C3⋊Dic3)C2×D311yescharacteristic
154#3750—31no—
155#3750—31no—
156#3750—31no—
157#3750—31no—
158#3750C2×D311yescharacteristic
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×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—31no—
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×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—61no—
186C3×Dic3⋊C4—21no—
187C3×Dic3⋊C4—21no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—61no—
197C3×Dic3⋊C4—61no—
198C3×Dic3⋊C4C2×D311yescharacteristic
199C3×Dic3⋊C4C2×D311yescharacteristic
200C3×Dic3⋊C4C2×D311yescharacteristic
201C3×Dic3⋊C4C2×D311yescharacteristic
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—61no—
214#3724—61no—
215#3724—61no—
216#3724C2×D311yescharacteristic
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—61no—
236(C2×D3)⋊Dic3—61no—
237(C2×D3)⋊Dic3C2×D311yescharacteristic
238(C2×D3)⋊Dic3C2×D311yescharacteristic
239(C2×D3)⋊Dic3C2×D311yescharacteristic
240(C2×D3)⋊Dic3C2×D311yescharacteristic
241(C2×D3)⋊Dic3C2×D311yescharacteristic
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×C32×D3—21no—
255C2×C32×D3—21no—
256C2×C32×D3—21no—
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3#4112yes—
260C33×C4—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3⋊(C3⋊Dic3)#4112yes—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C3×#125—91no—
274C3×#123—91no—
275C3×#123—91no—
276#935—31no—
277#935—31no—
278D4×Dic3—91no—
279D4×Dic3—91no—
280D4×Dic3—181no—
281#926—91no—
282#926—91no—
283C2×Dic3⋊C4—91no—
284C2×Dic3⋊C4—91no—
285#898—91no—
286#898—91no—
287#896—91no—
288#896—91no—
289#894—31no—
290#894—31no—
291#893—91no—
292#892—91no—
293D3×C4⋊C4—91no—
294#890—31no—
295#890—91no—
296#889—31no—
297#889—91no—
298#889—91no—
299#889—91no—
300#889—91no—
301#889—91no—
302#889—181no—
303#887—91no—
304#887—91no—
305#887—91no—
306#887—181no—
307#879—91no—
308#879—91no—
309#879—91no—
310#879—91no—
311#878—91no—
312#878—91no—
313#878—91no—
314#878—91no—
315#877—91no—
316#877—91no—
317#877—91no—
318#877—91no—
319#872—91no—
320#872—91no—
321C23×C32—31no—
322C23×C32—31no—
323C22×C3×D3—21no—
324C22×C3×D3—21no—
325C22×C3×D3C22×D311yescharacteristic
326C22×C3×D3C22×D311yescharacteristic
327C22×C3×D3C22×D311yescharacteristic
328C22×C3×D3C22×D311yescharacteristic
329C32×D4—62no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—21no—
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—62no—
355C2×C3⋊Dic3—121no—
356C2×C3⋊Dic3—121no—
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363#634—62no—
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—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—62no—
387C2×C3×Dic3—62no—
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
395C2×C3×Dic3C22×D311yescharacteristic
396C3×D12—24no—
397C3×D12—22no—
398C3×D12—22no—
399C3×C4×D3—62no—
400C3×C4×D3—62no—
401#627—62no—
402#627—62no—
403#627—64no—
404D3×Dic3—22no—
405D3×Dic3—22no—
406D3×Dic3—62no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—122no—
411D3×Dic3—122no—
412#552—271noSylow
413C2×C33C2×#4111yescharacteristic
414C2×C33C2×#4111yescharacteristic
415C2×C332−1+411yescharacteristic
416C32×D3—22no—
417C32×D3—41no—
418C2×C3×D4—31no—
419C2×C3×D4—31no—
420C2×C3×D4—61no—
421C22×C3×C4—91no—
422C22×C3×C4—91no—
423C22×Dic3—31no—
424C22×Dic3—31no—
425C22×Dic3—91no—
426C22×Dic3—91no—
427C22×Dic3—91no—
428C22×Dic3—91no—
429C22×Dic3—181no—
430C22×Dic3—181no—
431C2×D12D3211yescharacteristic
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—181no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—61no—
445C3×C4⋊C4—61no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C42—91no—
459#217—31no—
460#217—31no—
461#217—31no—
462#217—31no—
463#217—31no—
464#217—31no—
465#217—91no—
466#217—91no—
467#217—91no—
468#217—91no—
469#217—181no—
470#217—181no—
471(C2×D3)⋊C4—31no—
472(C2×D3)⋊C4—31no—
473(C2×D3)⋊C4—31no—
474(C2×D3)⋊C4—31no—
475(C2×D3)⋊C4—31no—
476(C2×D3)⋊C4—31no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479C4⋊Dic3—31no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—61no—
484C4⋊Dic3—91no—
485C4⋊Dic3—91no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—181no—
491Dic3⋊C4—31no—
492Dic3⋊C4—31no—
493Dic3⋊C4—31no—
494Dic3⋊C4—31no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—61no—
500Dic3⋊C4—61no—
501Dic3⋊C4—91no—
502Dic3⋊C4—91no—
503Dic3⋊C4—91no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
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⋊C4—181no—
523Dic3⋊C4D3211yescharacteristic
524Dic3⋊C4D3211yescharacteristic
525C4×Dic3—31no—
526C4×Dic3—31no—
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—91no—
538C4×Dic3—91no—
539C4×Dic3—181no—
540C4×Dic3—181no—
541C4×Dic3—181no—
542C4×Dic3—181no—
543C4×Dic3—181no—
544C4×Dic3—361no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—32no—
549C22×C32—41no—
550C22×C32—61no—
551C22×C32—61no—
552C22×C32—61no—
553C22×C32—61no—
554C22×C32—61no—
555C22×C32C23×D311yescharacteristic
556C22×C32C23×D311yescharacteristic
557C22×C32C23×D311yescharacteristic
558C2×C3×D3—21no—
559C2×C3×D3—21no—
560C2×C3×D3—21no—
561C2×C3×D3—21no—
562C2×C3×D3—22no—
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—22no—
570C2×C3×D3—41no—
571C2×C3×D3—41no—
572C2×C3×D3—41no—
573C2×C3×D3—41no—
574C2×C3×D3#23712yes—
575C2×C3×D3#23712yes—
576C32×C4—21no—
577C32×C4—22no—
578C32×C4—21no—
579C32×C4—21no—
580C32×C4—41no—
581C32×C4—41no—
582C32×C4—42no—
583C32×C4—61no—
584C32×C4—61no—
585C32×C4—61no—
586C32×C4—61no—
587C3⋊Dic3—21no—
588C3⋊Dic3—21no—
589C3⋊Dic3—21no—
590C3⋊Dic3—21no—
591C3⋊Dic3—21no—
592C3⋊Dic3—21no—
593C3⋊Dic3—32no—
594C3⋊Dic3—32no—
595C3⋊Dic3—32no—
596C3⋊Dic3—62no—
597C3⋊Dic3—62no—
598C3⋊Dic3—62no—
599C3⋊Dic3—61no—
600C3⋊Dic3—62no—
601C3⋊Dic3—61no—
602C3⋊Dic3—61no—
603C3⋊Dic3—122no—
604C3⋊Dic3—121no—
605C3⋊Dic3—121no—
606C3⋊Dic3—122no—
607C3×Dic3—22no—
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—41no—
617C3×Dic3—41no—
618C3×Dic3—41no—
619C3×Dic3—62no—
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—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—121no—
633C3×Dic3—121no—
634C3×Dic3—121no—
635C3×Dic3—121no—
636C3×Dic3—121no—
637#126—271no—
638#126—271no—
639#125—91no—
640#125—271no—
641#125—271no—
642#123—91no—
643#123—91no—
644C22⋊Q8—271no—
645C22⋊Q8—271no—
646C4×Q8—271no—
647C4×D4—271no—
648#117—271no—
649#117—271no—
650#117—271no—
651C2×C4⋊C4—271no—
652C33#55211yescharacteristic, complemented, Sylow
653C23×C3—31no—
654C23×C3—31no—
655C23×C3—31no—
656C23×C3—31no—
657C23×C3—61no—
658C23×C3—61no—
659C22×D3C2×D3211yescharacteristic
660C22×D3C2×D3211yescharacteristic
661C3×D4—62no—
662C3×D4—62no—
663C3×D4—64no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
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—41no—
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—91no—
686C2×C3×C4—182no—
687C2×C3×C4—182no—
688C2×C3×C4C2×D3211yescharacteristic
689C2×C3×C4C2×D3211yescharacteristic
690C2×C3×C4C2×D3211yescharacteristic
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—31no—
702C2×Dic3—31no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—62no—
710C2×Dic3—62no—
711C2×Dic3—91no—
712C2×Dic3—91no—
713C2×Dic3—91no—
714C2×Dic3—91no—
715C2×Dic3—91no—
716C2×Dic3—91no—
717C2×Dic3—181no—
718C2×Dic3—181no—
719C2×Dic3—181no—
720C2×Dic3—181no—
721C2×Dic3—181no—
722C2×Dic3—181no—
723C2×Dic3—182no—
724C2×Dic3—182no—
725C2×Dic3—182no—
726C2×Dic3—182no—
727C2×Dic3—361no—
728C2×Dic3—361no—
729C2×Dic3—362no—
730C2×Dic3—362no—
731C2×Dic3C2×D3211yescharacteristic
732C2×Dic3C2×D3211yescharacteristic
733C2×Dic3C2×D3211yescharacteristic
734C2×Dic3C2×D3211yescharacteristic
735D12—22no—
736C4×D3—62no—
737C4×D3—62no—
738C4×D3—182no—
739C4×D3—182no—
740Dic6—182no—
741Dic6—182no—
742Dic6—182no—
743Dic6—184no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—41no—
754C2×C32—41no—
755C2×C32—41no—
756C2×C32—62no—
757C2×C32—121no—
758C2×C32C2×#23711yescharacteristic
759C2×C32C2×#23711yescharacteristic
760C2×C32#100711yescharacteristic
761C2×C32D3×#4111yescharacteristic
762C2×C32D3×#4111yescharacteristic
763C2×C32D3×#4111yescharacteristic
764C2×C32D3×#4111yescharacteristic
765C2×C32#101011yescharacteristic
766C2×C32#101011yescharacteristic
767C3×D3—22no—
768C3×D3—22no—
769C3×D3—42no—
770C3×D3—42no—
771C3×D3—41no—
772C3×D3—41no—
773C2×Q8—271no—
774C2×D4—31no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—271no—
778C22×C4—271no—
779C4⋊C4—31no—
780C4⋊C4—31no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4—91no—
786C4⋊C4—91no—
787C4⋊C4—271no—
788C4⋊C4—271no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C4⋊C4—271no—
792C4⋊C4—271no—
793C4⋊C4—271no—
794C4⋊C4—271no—
795C22⋊C4—91no—
796C22⋊C4—91no—
797C22⋊C4—91no—
798C22⋊C4—91no—
799C22⋊C4—91no—
800C22⋊C4—91no—
801C22⋊C4—271no—
802C22⋊C4—271no—
803C42—91no—
804C42—271no—
805C42—271no—
806C42—271no—
807C42—271no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—32no—
812C22×C3—32no—
813C22×C3—41no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3C22×D3211yescharacteristic
831C22×C3C22×D3211yescharacteristic
832C22×C3C22×D3211yescharacteristic
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3#380512yes—
839C3×C4—22no—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—41no—
844C3×C4—41no—
845C3×C4—42no—
846C3×C4—62no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—61no—
855C3×C4—121no—
856C3×C4—121no—
857C3×C4—121no—
858C3×C4—181no—
859C3×C4—181no—
860C3×C4—181no—
861C3×C4—181no—
862C3×C4—181no—
863C3×C4—181no—
864Dic3—21no—
865Dic3—21no—
866Dic3—21no—
867Dic3—21no—
868Dic3—62no—
869Dic3—61no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—61no—
878Dic3—61no—
879Dic3—61no—
880Dic3—61no—
881Dic3—92no—
882Dic3—92no—
883Dic3—92no—
884Dic3—121no—
885Dic3—121no—
886Dic3—121no—
887Dic3—121no—
888Dic3—121no—
889Dic3—182no—
890Dic3—182no—
891Dic3—182no—
892Dic3—182no—
893Dic3—181no—
894Dic3—181no—
895Dic3—181no—
896Dic3—362no—
897Dic3—361no—
898Dic3—361no—
899Dic3—362no—
900C32—21no—
901C32—21no—
902C32—21no—
903C32—41no—
904C32#565011yescharacteristic, complemented
905C32#565011yescharacteristic, complemented
906C32#569311yescharacteristic, complemented
907C23—31no—
908C23—31no—
909Q8—542no—
910D4—62no—
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—91no—
920C2×C4—91no—
921C2×C4—182no—
922C2×C4—182no—
923C2×C4—271no—
924C2×C4—271no—
925C2×C4—542no—
926C2×C4—542no—
927C2×C4D3311yescharacteristic
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—41no—
938C2×C3—41no—
939C2×C3—41no—
940C2×C3—62no—
941C2×C3—62no—
942C2×C3—122no—
943C2×C3—122no—
944C2×C3—121no—
945C2×C3—121no—
946C2×C3#6429711yescharacteristic
947C2×C3#6430611yescharacteristic
948C2×C3#6430911yescharacteristic
949C2×C3D3×#23711yescharacteristic
950C2×C3D3×#23711yescharacteristic
951C2×C3#6431211yescharacteristic
952C2×C3#6431511yescharacteristic
953C2×C3#6431911yescharacteristic
954C2×C3C2×#380511yescharacteristic
955D3—22no—
956D3—41no—
957C22—32no—
958C22—61no—
959C22—61no—
960C22—61no—
961C22—61no—
962C22—61no—
963C22C2×D3311yescharacteristic
964C4—21no—
965C4—61no—
966C4—61no—
967C4—61no—
968C4—61no—
969C4—181no—
970C4—181no—
971C4—181no—
972C4—181no—
973C4—181no—
974C4—181no—
975C4—272no—
976C4—541no—
977C3—21no—
978C3—21no—
979C3—21no—
980C3—41no—
981C3#1059442911yescharacteristic, complemented
982C3#1059443011yescharacteristic, complemented
983C3#1059512011yescharacteristic, complemented
984C2—62no—
985C2—121no—
986C2#1172437611yescharacteristic
987C2#1172439311yescharacteristic
988C2D3×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C32×D12C22
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. #11723669C2semidirect
3. #11723448C2semidirect
4. #11723391C2semidirect
7. C3×#63845C2semidirect
8. #11723022C2semidirect
9. #11723019C2semidirect
10. #11722980C2semidirect
11. #11722980C2semidirect
12. #11722916C2semidirect
13. #11722914C2semidirect
14. #11722913C2semidirect
15. D3×#3724C2semidirect
97. #63845D3semidirect
652. C33#552semidirect
904. C32#5650semidirect
905. C32#5650semidirect
906. C32#5693semidirect
981. C3#10594429semidirect
982. C3#10594430semidirect
983. C3#10595120semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117234992
#117234482
#117233912
C3×#638842
C3×#638452
#117230222
#117230192
#117229802
#117229162
#117229142
#117229132
D3×#37242
#105951203
#105944303
#105944293