Finite Group Databasebeta

← #13168451

Subgroups — #13168451

Order 1728.

1120 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723694C211yesmaximal, characteristic, complemented
2#11723528C211yesmaximal, characteristic, complemented
3#11723431C211yesmaximal, characteristic, complemented
4#11723395C211yesmaximal, characteristic, complemented
5C3×#63895C211yesmaximal, characteristic, complemented
6C3×#63881C211yesmaximal, characteristic, complemented
7C3×#63858C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723010C211yesmaximal, characteristic, complemented
10#11723001C211yesmaximal, characteristic, complemented
11#11722988C211yesmaximal, characteristic, complemented
12#11722971C211yesmaximal, characteristic, complemented
13#11722957C211yesmaximal, characteristic
14Dic3×#627C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10594592—31nomaximal
17#10594451—31nomaximal
18#10594108—31nomaximal
19C2×#6308C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C32×(C2×D3)⋊C4C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33#88815C2211yescharacteristic
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64106—31no—
55#64097—31no—
56#64094—31no—
57C3×#898—31no—
58C3×#897—31no—
59C3×#896—31no—
60C3×#893—31no—
61C3×#67⋊C4—31no—
62C3×#879—31no—
63#63966—31no—
64#63964—31no—
65#63959—31no—
66#63958—31no—
67C4×#627—31no—
68#63913—31no—
69#63913—31no—
70#63913—31no—
71#63913—61no—
72#63908—31no—
73#63907—31no—
74#63906—31no—
75#63905—31no—
76#63905—31no—
77#63895D311yescharacteristic, complemented
78#63893—31no—
79#63891—31no—
80#63881D311yescharacteristic, complemented
81#63863—31no—
82#63862—31no—
83#63858—31no—
84#63858D311yescharacteristic, complemented
85#63857—31no—
86#63857—31no—
87#63857—31no—
88#63857—61no—
89#63855—31no—
90#63853—31no—
91#63852—31no—
92#63852—31no—
93#63850—31no—
94#63848—31no—
95Dic3×Dic6—31no—
96Dic3×Dic6—31no—
97#63841—31no—
98#63840—31no—
99#63840—31no—
100#63840—61no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108#6308—41no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C3×C4×C3⋊D3—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119#6295—41no—
120#6293—41no—
121#6290—41no—
122C3×#627—22no—
123C3×#626—22no—
124C3×#624—22no—
125C3×D3×Dic3—41no—
126#5710—91no—
127#5643—91no—
128#5561—91no—
129C2×#638—31no—
130C2×C4×C3⋊D3C2×D311yescharacteristic
131C2×#634—31no—
132C2×#634—31no—
133C2×#634—31no—
134C2×#634—31no—
135C2×#634—61no—
136C2×#634—61no—
137C2×#634—61no—
138C2×#634—121no—
139C2×C3×#67—31no—
140C22×C3×Dic3—31no—
141C2×C3×D12—31no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—61no—
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×#627—31no—
151C2×#627—31no—
152C2×#627—61no—
153C2×#627C2×D311yescharacteristic
154C2×#626—31no—
155C2×#626—31no—
156C2×#626C2×D311yescharacteristic
157C2×#625—31no—
158C2×#625—31no—
159C2×#625—31no—
160C2×#625—61no—
161C2×#624C2×D311yescharacteristic
162C2×D3×Dic3C2×D311yescharacteristic
163C32×C4⋊C4—31no—
164C32×C4⋊C4—31no—
165C32×C22⋊C4—31no—
166#3757—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752C2×D311yescharacteristic
171C4⋊(C3⋊Dic3)—31no—
172C4⋊(C3⋊Dic3)—31no—
173C4⋊(C3⋊Dic3)—31no—
174#3750—31no—
175#3750C2×D311yescharacteristic
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—31no—
178C3×#217—31no—
179C3×#217—31no—
180C3×(C2×D3)⋊C4—21no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—61no—
190C3×(C2×D3)⋊C4C2×D311yescharacteristic
191C3×(C2×D3)⋊C4C2×D311yescharacteristic
192C3×C4⋊Dic3—21no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3C2×D311yescharacteristic
196C3×C4⋊Dic3C2×D311yescharacteristic
197C3×Dic3⋊C4—21no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—61no—
203C3×Dic3⋊C4C2×D311yescharacteristic
204C3×Dic3⋊C4C2×D311yescharacteristic
205C3×C4×Dic3—31no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209#3724—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—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226#3722—31no—
227#3722—31no—
228#3722C2×D311yescharacteristic
229#3722C2×D311yescharacteristic
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
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—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—61no—
243(C2×D3)⋊Dic3—61no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3C2×D311yescharacteristic
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—61no—
253Dic32—61no—
254Dic32C2×D311yescharacteristic
255Dic32C2×D311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3⋊(C3⋊Dic3)—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3#4112yes—
278C3×#126—91no—
279C3×C22⋊Q8—91no—
280C3×C4×D4—91no—
281#947—91no—
282Q8×Dic3—91no—
283#938—91no—
284#936—91no—
285#930—91no—
286#929—91no—
287#929—91no—
288#926—91no—
289#924—91no—
290#924—91no—
291#898—31no—
292#898—91no—
293#898—91no—
294#897—31no—
295#897—91no—
296#897—91no—
297#897—91no—
298#897—181no—
299#896—31no—
300#894—91no—
301#893—31no—
302#892—91no—
303#888—91no—
304#888—91no—
305#888—91no—
306#888—181no—
307#886—91no—
308#885—91no—
309#885—91no—
310#885—91no—
311#885—91no—
312#885—91no—
313#885—91no—
314#885—181no—
315#884—91no—
316#883—91no—
317#883—91no—
318#67⋊C4—31no—
319#879—31no—
320#879—91no—
321#878—91no—
322#875—91no—
323#872—91no—
324C4×Dic6—91no—
325C4×Dic6—91no—
326C23×C32—31no—
327C22×C3⋊D3C22×D311yescharacteristic
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—21no—
330C22×C3×D3—31no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—61no—
335C22×C3×D3—61no—
336C22×C3×D3C22×D311yescharacteristic
337C22×C3×D3C22×D311yescharacteristic
338C2×C32×C4—21no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—41no—
347C2×C32×C4C22×D311yescharacteristic
348C2×C32×C4C22×D311yescharacteristic
349C2×C32×C4C22×D311yescharacteristic
350#638—121no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—61no—
363C2×C3⋊Dic3—121no—
364C2×C3⋊Dic3—121no—
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C4×C3⋊D3—41no—
370#634—121no—
371#634—121no—
372#634—121no—
373#634—121no—
374#634—122no—
375#634—122no—
376#634—122no—
377#634—124no—
378C3×#67—62no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—21no—
381C2×C3×Dic3—21no—
382C2×C3×Dic3—21no—
383C2×C3×Dic3—21no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—121no—
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C3×D12—62no—
408C3×C4×D3—62no—
409C3×C4×D3—62no—
410C3×C4×D3—121no—
411C3×C4×D3—121no—
412C3×C4×D3—121no—
413C3×C4×D3—122no—
414C3×Dic6—62no—
415C3×Dic6—62no—
416#627—22no—
417#627—121no—
418#627—121no—
419#627—122no—
420#626—22no—
421#626—121no—
422#626—121no—
423#625—121no—
424#625—121no—
425#625—121no—
426#625—122no—
427#624—22no—
428D3×Dic3—41no—
429#542—271noSylow
430C2×C33C2×#4111yescharacteristic
431C2×C33H(5,𝔽2)11yescharacteristic
432C2×C332−1+411yescharacteristic
433C3×C3⋊D3—41no—
434C3×C3⋊D3—41no—
435C32×D3—41no—
436C2×C3×Q8—91no—
437C2×C3×D4—91no—
438C22×C3×C4—91no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C2×#67—31no—
442C2×#67—91no—
443C2×#67—91no—
444C2×#67—91no—
445C2×#67—91no—
446C2×#67—91no—
447C2×#67—181no—
448C22×Dic3—31no—
449C2×D12—31no—
450C2×D12—91no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—61no—
457C2×Dic6—31no—
458C2×Dic6—31no—
459C2×Dic6—91no—
460C2×Dic6—91no—
461C2×Dic6—91no—
462C2×Dic6—91no—
463C2×Dic6—91no—
464C2×Dic6—91no—
465C2×Dic6—181no—
466C2×Dic6—181no—
467C2×Dic6—181no—
468C2×Dic6—181no—
469C2×Dic6—361no—
470C3×C4⋊C4—31no—
471C3×C4⋊C4—31no—
472C3×C4⋊C4—31no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—61no—
475C3×C4⋊C4—61no—
476C3×C4⋊C4—91no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C22⋊C4—31no—
480C3×C22⋊C4—31no—
481C3×C22⋊C4—61no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C22⋊C4—91no—
485C3×C22⋊C4—91no—
486C3×C22⋊C4—91no—
487C3×C42—91no—
488C3×C42—91no—
489#217—31no—
490#217—31no—
491#217—91no—
492#217—91no—
493#217—91no—
494#217—91no—
495#217—91no—
496#217—91no—
497#217—91no—
498#217—181no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—31no—
505(C2×D3)⋊C4—31no—
506(C2×D3)⋊C4—31no—
507(C2×D3)⋊C4—61no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—91no—
513(C2×D3)⋊C4—91no—
514(C2×D3)⋊C4—91no—
515(C2×D3)⋊C4—91no—
516(C2×D3)⋊C4—91no—
517(C2×D3)⋊C4—91no—
518(C2×D3)⋊C4—91no—
519(C2×D3)⋊C4—181no—
520(C2×D3)⋊C4—181no—
521(C2×D3)⋊C4—181no—
522(C2×D3)⋊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—181no—
534C4⋊Dic3—181no—
535C4⋊Dic3—181no—
536C4⋊Dic3D3211yescharacteristic
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—31no—
541Dic3⋊C4—61no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—181no—
550Dic3⋊C4D3211yescharacteristic
551C4×Dic3—31no—
552C4×Dic3—31no—
553C4×Dic3—31no—
554C4×Dic3—31no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—181no—
562C4×Dic3—181no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—41no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32C23×D311yescharacteristic
571C22×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C2×C3⋊D3—21no—
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3⋊D3—21no—
577C2×C3⋊D3—21no—
578C2×C3⋊D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—21no—
584C2×C3×D3—21no—
585C2×C3×D3—41no—
586C2×C3×D3—41no—
587C2×C3×D3—41no—
588C2×C3×D3—62no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—61no—
594C2×C3×D3—61no—
595C2×C3×D3—61no—
596C2×C3×D3—61no—
597C2×C3×D3—61no—
598C2×C3×D3—61no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—121no—
602C2×C3×D3—121no—
603C2×C3×D3—121no—
604C2×C3×D3—121no—
605C2×C3×D3—121no—
606C32×C4—21no—
607C32×C4—22no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—32no—
611C32×C4—41no—
612C32×C4—41no—
613C32×C4—42no—
614C32×C4—61no—
615C32×C4—61no—
616C32×C4—61no—
617C32×C4—61no—
618C3⋊Dic3—21no—
619C3⋊Dic3—21no—
620C3⋊Dic3—21no—
621C3⋊Dic3—21no—
622C3⋊Dic3—61no—
623C3⋊Dic3—61no—
624C3⋊Dic3—62no—
625C3⋊Dic3—62no—
626C3⋊Dic3—61no—
627C3⋊Dic3—61no—
628C3⋊Dic3—61no—
629C3⋊Dic3—61no—
630C3⋊Dic3—121no—
631C3⋊Dic3—121no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—122no—
635C3⋊Dic3—122no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—22no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—62no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—121no—
659C3×Dic3—121no—
660C3×Dic3—121no—
661C3×Dic3#23512yes—
662C3×Dic3#23712yes—
663C4⋊Q8—271no—
664#126—91no—
665#126—271no—
666#124—271no—
667#124—271no—
668#124—271no—
669#123—271no—
670#123—271no—
671C22⋊Q8—91no—
672C22⋊Q8—271no—
673C22⋊Q8—271no—
674#121—271no—
675C4×Q8—271no—
676C4×D4—91no—
677#117—271no—
678C33#54211yescharacteristic, complemented, Sylow
679C23×C3—31no—
680C23×C3—31no—
681C23×C3—61no—
682C23×C3—91no—
683C23×C3—91no—
684C22×D3—31no—
685C22×D3—31no—
686C22×D3—31no—
687C22×D3—31no—
688C22×D3—61no—
689C22×D3—61no—
690C22×D3C2×D3211yescharacteristic
691C3×Q8—182no—
692C3×D4—182no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—31no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—41no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—91no—
713C2×C3×C4—91no—
714C2×C3×C4—91no—
715C2×C3×C4—91no—
716C2×C3×C4—182no—
717C2×C3×C4—361no—
718C2×C3×C4—361no—
719C2×C3×C4C2×D3211yescharacteristic
720C2×C3×C4C2×D3211yescharacteristic
721C2×C3×C4C2×D3211yescharacteristic
722#67—62no—
723#67—361no—
724#67—361no—
725#67—361no—
726#67—361no—
727#67—361no—
728#67—362no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—31no—
736C2×Dic3—31no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—91no—
742C2×Dic3—91no—
743C2×Dic3—91no—
744C2×Dic3—91no—
745C2×Dic3—91no—
746C2×Dic3—91no—
747C2×Dic3—121no—
748C2×Dic3—181no—
749C2×Dic3—181no—
750C2×Dic3—181no—
751C2×Dic3—181no—
752C2×Dic3—181no—
753C2×Dic3—181no—
754C2×Dic3—361no—
755C2×Dic3—361no—
756C2×Dic3C2×D3211yescharacteristic
757C2×Dic3C2×D3211yescharacteristic
758C2×Dic3C2×D3211yescharacteristic
759C2×Dic3C2×D3211yescharacteristic
760C2×Dic3C2×D3211yescharacteristic
761D12—62no—
762D12—361no—
763C4×D3—62no—
764C4×D3—62no—
765C4×D3—121no—
766C4×D3—121no—
767C4×D3—121no—
768C4×D3—122no—
769Dic6—62no—
770Dic6—62no—
771Dic6—361no—
772Dic6—361no—
773Dic6—361no—
774Dic6—362no—
775Dic6—361no—
776Dic6—361no—
777Dic6—361no—
778Dic6—362no—
779Dic6—362no—
780Dic6—362no—
781Dic6—364no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—41no—
792C2×C32—41no—
793C2×C32—41no—
794C2×C32—121no—
795C2×C32C2×#23511yescharacteristic
796C2×C32C2×#23711yescharacteristic
797C2×C32#100411yescharacteristic
798C2×C32#100711yescharacteristic
799C2×C32D3×#4111yescharacteristic
800C2×C32#100911yescharacteristic
801C2×C32#100911yescharacteristic
802C2×C32#101011yescharacteristic
803C2×C32#101011yescharacteristic
804C3⋊D3—41no—
805C3⋊D3—41no—
806C3×D3—41no—
807C3×D3—41no—
808C3×D3—81no—
809C3×D3—122no—
810C3×D3—121no—
811C3×D3—121no—
812C3×D3—121no—
813C3×D3—121no—
814C3×D3—241no—
815C2×Q8—91no—
816C2×Q8—271no—
817C2×Q8—271no—
818C2×D4—91no—
819C2×D4—271no—
820C2×D4—271no—
821C22×C4—91no—
822C22×C4—91no—
823C22×C4—91no—
824C4⋊C4—31no—
825C4⋊C4—31no—
826C4⋊C4—91no—
827C4⋊C4—91no—
828C4⋊C4—91no—
829C4⋊C4—271no—
830C4⋊C4—271no—
831C4⋊C4—271no—
832C4⋊C4—271no—
833C4⋊C4—271no—
834C22⋊C4—31no—
835C22⋊C4—91no—
836C22⋊C4—91no—
837C22⋊C4—91no—
838C22⋊C4—91no—
839C22⋊C4—91no—
840C22⋊C4—271no—
841C22⋊C4—271no—
842C22⋊C4—271no—
843C22⋊C4—271no—
844C22⋊C4—271no—
845C22⋊C4—271no—
846C42—91no—
847C42—91no—
848C42—271no—
849C42—271no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—41no—
854C22×C3—61no—
855C22×C3—61no—
856C22×C3—61no—
857C22×C3—61no—
858C22×C3—61no—
859C22×C3—61no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—181no—
864C22×C3—181no—
865C22×C3—181no—
866C22×C3—181no—
867C22×C3—181no—
868C22×C3—181no—
869C22×C3C22×D3211yescharacteristic
870C22×C3C22×D3211yescharacteristic
871C22×C3C22×D3211yescharacteristic
872C2×D3—21no—
873C2×D3—21no—
874C2×D3—21no—
875C2×D3—62no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—61no—
884C2×D3—61no—
885C2×D3—61no—
886C2×D3—61no—
887C2×D3—61no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C3×C4—22no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—32no—
898C3×C4—32no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—42no—
902C3×C4—62no—
903C3×C4—61no—
904C3×C4—61no—
905C3×C4—61no—
906C3×C4—61no—
907C3×C4—61no—
908C3×C4—61no—
909C3×C4—61no—
910C3×C4—61no—
911C3×C4—121no—
912C3×C4—121no—
913C3×C4—121no—
914C3×C4—121no—
915C3×C4—181no—
916C3×C4—181no—
917C3×C4—181no—
918C3×C4—181no—
919Dic3—21no—
920Dic3—21no—
921Dic3—21no—
922Dic3—21no—
923Dic3—62no—
924Dic3—61no—
925Dic3—61no—
926Dic3—61no—
927Dic3—61no—
928Dic3—61no—
929Dic3—61no—
930Dic3—61no—
931Dic3—61no—
932Dic3—121no—
933Dic3—121no—
934Dic3—121no—
935Dic3—182no—
936Dic3—182no—
937Dic3—181no—
938Dic3—181no—
939Dic3—181no—
940Dic3—181no—
941Dic3—181no—
942Dic3—181no—
943Dic3—361no—
944Dic3—361no—
945Dic3—361no—
946Dic3—361no—
947Dic3—362no—
948Dic3—362no—
949Dic3#379512yes—
950C32—21no—
951C32—21no—
952C32—21no—
953C32—41no—
954C32#556111yescharacteristic, complemented
955C32#564311yescharacteristic, complemented
956C32#571011yescharacteristic, complemented
957C23—31no—
958C23—91no—
959C23—91no—
960Q8—182no—
961Q8—1081no—
962Q8—1081no—
963D4—182no—
964D4—1081no—
965D4—1081no—
966C2×C4—31no—
967C2×C4—31no—
968C2×C4—31no—
969C2×C4—31no—
970C2×C4—31no—
971C2×C4—91no—
972C2×C4—91no—
973C2×C4—91no—
974C2×C4—91no—
975C2×C4—182no—
976C2×C4—271no—
977C2×C4—271no—
978C2×C4—361no—
979C2×C4—361no—
980C2×C4D3311yescharacteristic
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—41no—
991C2×C3—41no—
992C2×C3—41no—
993C2×C3—121no—
994C2×C3—121no—
995C2×C3—241no—
996C2×C3—361no—
997C2×C3—361no—
998C2×C3C2×#379511yescharacteristic
999C2×C3D3×#23511yescharacteristic
1000C2×C3#6430811yescharacteristic
1001C2×C3#6430911yescharacteristic
1002C2×C3D3×#23711yescharacteristic
1003C2×C3#6431411yescharacteristic
1004C2×C3#6431411yescharacteristic
1005C2×C3#6431511yescharacteristic
1006C2×C3#6431511yescharacteristic
1007D3—41no—
1008D3—122no—
1009D3—121no—
1010D3—121no—
1011D3—121no—
1012D3—121no—
1013D3—241no—
1014C22—61no—
1015C22—61no—
1016C22—61no—
1017C22—181no—
1018C22—181no—
1019C22—181no—
1020C22—181no—
1021C22—181no—
1022C22—181no—
1023C22C2×D3311yescharacteristic
1024C4—21no—
1025C4—32no—
1026C4—61no—
1027C4—61no—
1028C4—61no—
1029C4—61no—
1030C4—181no—
1031C4—181no—
1032C4—181no—
1033C4—181no—
1034C4—541no—
1035C4—541no—
1036C3—21no—
1037C3—21no—
1038C3—21no—
1039C3—41no—
1040C3#1059410811yescharacteristic, complemented
1041C3#1059445111yescharacteristic, complemented
1042C3#1059459211yescharacteristic, complemented
1043C2—121no—
1044C2—361no—
1045C2—361no—
1046C2D3×#379511yescharacteristic
1047C2#1172439411yescharacteristic
1048C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722957C2
hypercenterC2×C4D33
hypocenterC33#542
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723694C2semidirect
2. #11723528C2semidirect
3. #11723431C2semidirect
4. #11723395C2semidirect
5. C3×#63895C2semidirect
6. C3×#63881C2semidirect
7. C3×#63858C2semidirect
8. #11723025C2semidirect
9. #11723010C2semidirect
10. #11723001C2semidirect
11. #11722988C2semidirect
12. #11722971C2semidirect
14. Dic3×#627C2semidirect
15. #11722915C2semidirect
77. #63895D3semidirect
80. #63881D3semidirect
84. #63858D3semidirect
678. C33#542semidirect
954. C32#5561semidirect
955. C32#5643semidirect
956. C32#5710semidirect
1040. C3#10594108semidirect
1041. C3#10594451semidirect
1042. C3#10594592semidirect

Maximal subgroups

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

subgroupindex
#117236942
#117235282
#117234312
#117233952
C3×#638952
C3×#638812
C3×#638582
#117230252
#117230102
#117230012
#117229882
#117229712
#117229572
Dic3×#6272
#117229152
#105945923
#105944513
#105941083