Finite Group Databasebeta

← #13168567

Subgroups — #13168567

Order 1728.

1094 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#11723688C211yesmaximal, characteristic, complemented
2#11723530C211yesmaximal, characteristic
3#11723410C211yesmaximal, characteristic, complemented
4#11723391C211yesmaximal, characteristic, complemented
5C3×#63896C211yesmaximal, characteristic, complemented
6C3×#63858C211yesmaximal, characteristic, complemented
7C3×#63848C211yesmaximal, characteristic, complemented
8#11723037C211yesmaximal, characteristic, complemented
9#11723025C211yesmaximal, characteristic, complemented
10#11723019C211yesmaximal, characteristic, complemented
11#11723009C211yesmaximal, characteristic
12#11722942C211yesmaximal, characteristic, complemented
13#11722936C211yesmaximal, characteristic
14#11722922C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10594554—31nomaximal
17#10594472—31nomaximal
18#10594025—31nomaximal
19C2×C3×#634C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C32×(C2×D3)⋊C4C2211yescharacteristic
29C32×C4⋊Dic3C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88807C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88803C2211yescharacteristic
38(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3×C3⋊Dic3C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64096—31no—
55#64096—31no—
56#64094—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#898—31no—
60C3×#896—31no—
61C3×#879—31no—
62C3×#878—31no—
63#63956—31no—
64#63955—31no—
65#63953—31no—
66#63952—31no—
67#63919—31no—
68C4×#627—31no—
69#63915—31no—
70#63915—31no—
71#63915—31no—
72#63915—61no—
73#63913—31no—
74#63902—31no—
75#63896—31no—
76#63896D311yescharacteristic, complemented
77#63888—31no—
78#63887—31no—
79#63879—31no—
80#63878—31no—
81#63877—31no—
82#63877—31no—
83#63862—31no—
84#63862—31no—
85#63858—31no—
86#63858—31no—
87#63858D311yescharacteristic, complemented
88#63855—31no—
89#63848—31no—
90#63848D311yescharacteristic, complemented
91#63844—31no—
92#63843—31no—
93#63843—31no—
94#63843—61no—
95#63840—31no—
96#63840—31no—
97#63838—31no—
98#63838—31no—
99#63838—61no—
100#63837—31no—
101#63836—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
112C3×#634—22no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6294—22no—
119#6293—22no—
120#6293—22no—
121#6290—22no—
122C3×D3×Dic3—22no—
123#5702—91no—
124#5702—91no—
125#5641—91no—
126C2×#638—31no—
127C2×#634—31no—
128C2×#634—31no—
129C2×#634C2×D311yescharacteristic
130C22×C3×Dic3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×Dic6—31no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—61no—
135C2×#627—31no—
136C2×#627—31no—
137C2×#627—31no—
138C2×#627—31no—
139C2×#627—61no—
140C2×#627—61no—
141C2×#625—31no—
142C2×#625—31no—
143C2×#625—61no—
144C2×#624—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3C2×D311yescharacteristic
148C32×C4⋊C4—31no—
149C32×C4⋊C4—31no—
150C32×C22⋊C4—31no—
151#3757—31no—
152#3752—31no—
153#3752C2×D311yescharacteristic
154#3750—31no—
155#3750—31no—
156#3750—31no—
157#3750C2×D311yescharacteristic
158C4×C3⋊Dic3—31no—
159C4×C3⋊Dic3—31no—
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×(C2×D3)⋊C4—21no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—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×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—61no—
183C3×(C2×D3)⋊C4C2×D311yescharacteristic
184C3×(C2×D3)⋊C4C2×D311yescharacteristic
185C3×C4⋊Dic3—21no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—31no—
189C3×C4⋊Dic3C2×D311yescharacteristic
190C3×C4⋊Dic3C2×D311yescharacteristic
191C3×Dic3⋊C4—21no—
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—31no—
199C3×Dic3⋊C4—61no—
200C3×Dic3⋊C4C2×D311yescharacteristic
201C3×Dic3⋊C4C2×D311yescharacteristic
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—61no—
211#3724C2×D311yescharacteristic
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3C2×D311yescharacteristic
223Dic3⋊Dic3C2×D311yescharacteristic
224Dic3⋊Dic3C2×D311yescharacteristic
225#3722—31no—
226#3722C2×D311yescharacteristic
227#3722C2×D311yescharacteristic
228(C2×D3)⋊Dic3—31no—
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—61no—
235(C2×D3)⋊Dic3—61no—
236(C2×D3)⋊Dic3C2×D311yescharacteristic
237(C2×D3)⋊Dic3C2×D311yescharacteristic
238(C2×D3)⋊Dic3C2×D311yescharacteristic
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—61no—
248Dic32—61no—
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×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3—21no—
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#4112yes—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C3×#126—91no—
274C3×#126—91no—
275C3×C22⋊Q8—91no—
276#946—91no—
277Q8×Dic3—91no—
278C4×#67—91no—
279#926—91no—
280#898—31no—
281#898—31no—
282#898—31no—
283#898—91no—
284#898—91no—
285#898—91no—
286#896—31no—
287#896—91no—
288#892—91no—
289#888—91no—
290#888—91no—
291#888—91no—
292#887—91no—
293#887—91no—
294#887—91no—
295#887—91no—
296#887—91no—
297#887—91no—
298#887—181no—
299#887—181no—
300#885—91no—
301#885—91no—
302#885—91no—
303#885—91no—
304#885—91no—
305#885—91no—
306#885—181no—
307#67⋊C4—91no—
308#67⋊C4—91no—
309#879—31no—
310#879—91no—
311#879—91no—
312#879—91no—
313#878—31no—
314#878—91no—
315#877—91no—
316#877—91no—
317#872—91no—
318#872—91no—
319C4×Dic6—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
341#638—62no—
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
360C2×C3⋊Dic3C22×D311yescharacteristic
361#634—22no—
362#634—62no—
363#634—62no—
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—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
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×C4×D3—62no—
396C3×Dic6—62no—
397C3×Dic6—62no—
398C3×Dic6—64no—
399#627—62no—
400#627—62no—
401#627—62no—
402#627—62no—
403#627—64no—
404#627—122no—
405#625—62no—
406#625—62no—
407#625—122no—
408#624—62no—
409D3×Dic3—22no—
410D3×Dic3—62no—
411D3×Dic3—62no—
412#556—271noSylow
413C2×C33C2×#4111yescharacteristic
414C2×C33C2×#4111yescharacteristic
415C2×C332−1+411yescharacteristic
416C3×C3⋊D3—41no—
417C32×D3—41no—
418C2×C3×Q8—91no—
419C22×C3×C4—91no—
420C2×#67—91no—
421C2×#67—91no—
422C2×#67—91no—
423C2×#67—181no—
424C22×Dic3—31no—
425C22×Dic3—91no—
426C2×C4×D3—31no—
427C2×C4×D3—91no—
428C2×C4×D3—91no—
429C2×Dic6—31no—
430C2×Dic6—31no—
431C2×Dic6—61no—
432C2×Dic6—91no—
433C2×Dic6—91no—
434C2×Dic6—91no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—181no—
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×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⋊C4—91no—
460C3×C42—91no—
461C3×C42—91no—
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(C2×D3)⋊C4—31no—
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—31no—
478(C2×D3)⋊C4—31no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—181no—
486(C2×D3)⋊C4D3211yescharacteristic
487C4⋊Dic3—31no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3D3211yescharacteristic
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—61no—
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—181no—
515Dic3⋊C4—181no—
516Dic3⋊C4—181no—
517Dic3⋊C4D3211yescharacteristic
518C4×Dic3—31no—
519C4×Dic3—31no—
520C4×Dic3—31no—
521C4×Dic3—31no—
522C4×Dic3—91no—
523C4×Dic3—91no—
524C4×Dic3—91no—
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—181no—
543C4×Dic3—181no—
544C4×Dic3—361no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—41no—
549C22×C32—61no—
550C22×C32—61no—
551C22×C32—61no—
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C22×C32C23×D311yescharacteristic
555C2×C3⋊D3—21no—
556C2×C3⋊D3—21no—
557C2×C3⋊D3—21no—
558C2×C3×D3—21no—
559C2×C3×D3—21no—
560C2×C3×D3—21no—
561C2×C3×D3—21no—
562C2×C3×D3—21no—
563C2×C3×D3—21no—
564C2×C3×D3—41no—
565C2×C3×D3—41no—
566C2×C3×D3—41no—
567C2×C3×D3—61no—
568C2×C3×D3—61no—
569C2×C3×D3—61no—
570C2×C3×D3—61no—
571C2×C3×D3—61no—
572C2×C3×D3—61no—
573C2×C3×D3—121no—
574C2×C3×D3—121no—
575C2×C3×D3—121no—
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—
587C32×C4—61no—
588C3⋊Dic3—21no—
589C3⋊Dic3—21no—
590C3⋊Dic3—21no—
591C3⋊Dic3—21no—
592C3⋊Dic3—32no—
593C3⋊Dic3—32no—
594C3⋊Dic3—32no—
595C3⋊Dic3—62no—
596C3⋊Dic3—62no—
597C3⋊Dic3—62no—
598C3⋊Dic3—61no—
599C3⋊Dic3—62no—
600C3⋊Dic3—61no—
601C3⋊Dic3—61no—
602C3⋊Dic3—122no—
603C3⋊Dic3—121no—
604C3⋊Dic3—121no—
605C3⋊Dic3—122no—
606C3⋊Dic3#23712yes—
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—21no—
617C3×Dic3—21no—
618C3×Dic3—32no—
619C3×Dic3—32no—
620C3×Dic3—41no—
621C3×Dic3—41no—
622C3×Dic3—41no—
623C3×Dic3—41no—
624C3×Dic3—62no—
625C3×Dic3—62no—
626C3×Dic3—62no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—121no—
636C3×Dic3—121no—
637C4⋊Q8—271no—
638#126—91no—
639#126—91no—
640#126—271no—
641#126—271no—
642#124—271no—
643#124—271no—
644C22⋊Q8—91no—
645C22⋊Q8—271no—
646C4×Q8—271no—
647C4×Q8—271no—
648C4×Q8—271no—
649C4×D4—271no—
650#117—271no—
651#117—271no—
652C33#55611yescharacteristic, complemented, Sylow
653C23×C3—31no—
654C23×C3—31no—
655C23×C3—61no—
656C23×C3—91no—
657C22×D3—31no—
658C22×D3—31no—
659C22×D3—61no—
660C22×D3C2×D3211yescharacteristic
661C3×Q8—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—41no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
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×C4C2×D3211yescharacteristic
688C2×C3×C4C2×D3211yescharacteristic
689C2×C3×C4C2×D3211yescharacteristic
690#67—182no—
691#67—182no—
692#67—182no—
693#67—362no—
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—31no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—62no—
710C2×Dic3—91no—
711C2×Dic3—91no—
712C2×Dic3—91no—
713C2×Dic3—91no—
714C2×Dic3—91no—
715C2×Dic3—91no—
716C2×Dic3—181no—
717C2×Dic3—181no—
718C2×Dic3—181no—
719C2×Dic3—181no—
720C2×Dic3—181no—
721C2×Dic3—181no—
722C2×Dic3—182no—
723C2×Dic3—361no—
724C2×Dic3—361no—
725C2×Dic3C2×D3211yescharacteristic
726C2×Dic3C2×D3211yescharacteristic
727C2×Dic3C2×D3211yescharacteristic
728C2×Dic3C2×D3211yescharacteristic
729C2×Dic3C2×D3211yescharacteristic
730C4×D3—62no—
731C4×D3—182no—
732C4×D3—182no—
733Dic6—62no—
734Dic6—62no—
735Dic6—64no—
736Dic6—182no—
737Dic6—182no—
738Dic6—182no—
739Dic6—182no—
740Dic6—182no—
741Dic6—182no—
742Dic6—184no—
743Dic6—362no—
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—121no—
757C2×C32C2×#23711yescharacteristic
758C2×C32#100711yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C2×C32D3×#4111yescharacteristic
761C2×C32D3×#4111yescharacteristic
762C2×C32D3×#4111yescharacteristic
763C2×C32D3×#4111yescharacteristic
764C2×C32#101011yescharacteristic
765C2×C32#101011yescharacteristic
766C3⋊D3—41no—
767C3×D3—41no—
768C3×D3—41no—
769C3×D3—81no—
770C3×D3—121no—
771C3×D3—121no—
772C3×D3—241no—
773C2×Q8—91no—
774C2×Q8—271no—
775C2×Q8—271no—
776C2×D4—271no—
777C22×C4—91no—
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—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—91no—
796C22⋊C4—91no—
797C22⋊C4—91no—
798C22⋊C4—271no—
799C22⋊C4—271no—
800C22⋊C4—271no—
801C42—91no—
802C42—91no—
803C42—271no—
804C42—271no—
805C42—271no—
806C42—271no—
807C42—271no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—41no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—181no—
822C22×C3—181no—
823C22×C3—181no—
824C22×C3C22×D3211yescharacteristic
825C22×C3C22×D3211yescharacteristic
826C22×C3C22×D3211yescharacteristic
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—21no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—121no—
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—61no—
856C3×C4—61no—
857C3×C4—92no—
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—32no—
872Dic3—32no—
873Dic3—62no—
874Dic3—62no—
875Dic3—62no—
876Dic3—61no—
877Dic3—61no—
878Dic3—61no—
879Dic3—61no—
880Dic3—61no—
881Dic3—61no—
882Dic3—61no—
883Dic3—61no—
884Dic3—92no—
885Dic3—92no—
886Dic3—92no—
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#564111yescharacteristic, complemented
905C32#570211yescharacteristic, complemented
906C32#570211yescharacteristic, complemented
907C23—31no—
908C23—91no—
909Q8—182no—
910Q8—542no—
911Q8—542no—
912D4—542no—
913C2×C4—31no—
914C2×C4—31no—
915C2×C4—31no—
916C2×C4—31no—
917C2×C4—31no—
918C2×C4—91no—
919C2×C4—91no—
920C2×C4—91no—
921C2×C4—91no—
922C2×C4—91no—
923C2×C4—182no—
924C2×C4—271no—
925C2×C4—271no—
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—121no—
941C2×C3—121no—
942C2×C3—241no—
943C2×C3—361no—
944C2×C3#6429711yescharacteristic
945C2×C3#6430611yescharacteristic
946C2×C3#6430611yescharacteristic
947C2×C3#6430911yescharacteristic
948C2×C3D3×#23711yescharacteristic
949C2×C3D3×#23711yescharacteristic
950C2×C3#6431211yescharacteristic
951C2×C3#6431511yescharacteristic
952C2×C3#6431911yescharacteristic
953D3—41no—
954D3—121no—
955D3—121no—
956D3—241no—
957C22—61no—
958C22—61no—
959C22—61no—
960C22—181no—
961C22—181no—
962C22—181no—
963C22C2×D3311yescharacteristic
964C4—21no—
965C4—61no—
966C4—61no—
967C4—61no—
968C4—61no—
969C4—61no—
970C4—92no—
971C4—181no—
972C4—181no—
973C4—181no—
974C4—181no—
975C4—272no—
976C4—541no—
977C3—21no—
978C3—21no—
979C3—21no—
980C3—41no—
981C3#1059402511yescharacteristic, complemented
982C3#1059447211yescharacteristic, complemented
983C3#1059455411yescharacteristic, complemented
984C2—121no—
985C2—361no—
986C2#1172437611yescharacteristic
987C2#1172439311yescharacteristic
988C2#1172440711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6290C22
hypercenterC2×C4D33
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723688C2semidirect
3. #11723410C2semidirect
4. #11723391C2semidirect
5. C3×#63896C2semidirect
6. C3×#63858C2semidirect
7. C3×#63848C2semidirect
8. #11723037C2semidirect
9. #11723025C2semidirect
10. #11723019C2semidirect
12. #11722942C2semidirect
14. #11722922C2semidirect
15. #11722913C2semidirect
76. #63896D3semidirect
87. #63858D3semidirect
90. #63848D3semidirect
652. C33#556semidirect
904. C32#5641semidirect
905. C32#5702semidirect
906. C32#5702semidirect
981. C3#10594025semidirect
982. C3#10594472semidirect
983. C3#10594554semidirect

Maximal subgroups

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

subgroupindex
#117236882
#117235302
#117234102
#117233912
C3×#638962
C3×#638582
C3×#638482
#117230372
#117230252
#117230192
#117230092
#117229422
#117229362
#117229222
#117229132
#105945543
#105944723
#105940253