Finite Group Databasebeta

← #11811927

Subgroups — #11811927

Order 1152.

1789 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3798C211yesmaximal, characteristic
2C2×C3×#896C211yesmaximal, characteristic, complemented
3C2×#63907C211yesmaximal, characteristic, complemented
4C2×#63839C211yesmaximal, characteristic, complemented
5#10592688C211yesmaximal, characteristic, complemented
6C3×#4989C211yesmaximal, characteristic, complemented
7#10591390C211yesmaximal, characteristic, complemented
8#10591388C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic, complemented
10#10591292C211yesmaximal, characteristic, complemented
11#10591291C211yesmaximal, characteristic, complemented
12#10591290C211yesmaximal, characteristic, complemented
13#10591277C211yesmaximal, characteristic, complemented
14#10591237C211yesmaximal, characteristic, complemented
15#10591235C211yesmaximal, characteristic, complemented
16#82759—31nomaximal
17#74411—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C2×#3798—24no—
27C2×#3798—24no—
28C2×#3798—24no—
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C3×#896—24no—
41C2×#3724C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51#63907—24no—
52#63839—24no—
53#63658C2211yescharacteristic
54#63658C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57#63579C2211yescharacteristic
58#63579C2211yescharacteristic
59C22×#235—31no—
60C22×#235—31no—
61C2×C3×C22⋊Q8—31no—
62C2×#947—31no—
63C2×#944—31no—
64C2×#896D311yescharacteristic, complemented
65C2×#888—31no—
66C2×#885—31no—
67C3×#385—31no—
68#5210—31no—
69C4×#217—31no—
70#4991—31no—
71#4989—31no—
72#4989—31no—
73#4989—31no—
74#4989—31no—
75#4989—61no—
76#4989D311yescharacteristic, complemented
77#4988—31no—
78#4973—31no—
79#4961—31no—
80#4959—31no—
81#4959—31no—
82#4959—31no—
83#4959—31no—
84#4959—31no—
85#4957—31no—
86#4672—31no—
87#4668—31no—
88#4666—31no—
89#4646—31no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3D414yes—
114C2×C3×Dic6—22no—
115C2×C3×Dic6—22no—
116C2×C3×Dic6—22no—
117C2×#627—22no—
118C2×#627—22no—
119C2×#627D414yes—
120C2×#626—22no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#626—22no—
125C2×#626D414yes—
126C2×#625—22no—
127C2×#625—22no—
128C2×#625—22no—
129#3798—232no—
130C32×C4⋊C4—22no—
131#3752—22no—
132#3752—22no—
133#3750—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×Dic3⋊C4—22no—
139C3×Dic3⋊C4—22no—
140C3×Dic3⋊C4—22no—
141#3724—22no—
142Dic3⋊Dic3—22no—
143#3722—22no—
144#3722—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149Dic32—22no—
150Dic32—22no—
151#2432—91noSylow
152C22×C3×Q8—31no—
153C23×C3×C4—31no—
154C23×C3×C4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C2×#235—64no—
160C2×#235—64no—
161C2×#235—64no—
162C2×#235—64no—
163C2×#235—64no—
164C2×#235—64no—
165C22×D12—31no—
166C22×D12—31no—
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C22×C4×D3—61no—
170C22×C4×D3C2×D311yescharacteristic
171C22×C4×D3C2×D311yescharacteristic
172C22×Dic6—31no—
173C22×Dic6—31no—
174C22×Dic6C2×D311yescharacteristic
175C3×C22⋊Q8—64no—
176C2×C3×C4⋊C4—21no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4C2×D311yescharacteristic
181C2×C3×C4⋊C4C2×D311yescharacteristic
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190#947—64no—
191#944—64no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×C4⋊Dic3—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—61no—
217C2×Dic3⋊C4C2×D311yescharacteristic
218C2×Dic3⋊C4C2×D311yescharacteristic
219C2×Dic3⋊C4C2×D311yescharacteristic
220C2×C4×Dic3—31no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3—31no—
223C2×C4×Dic3—31no—
224#896—24no—
225#888—64no—
226#885—64no—
227C3×#95—31no—
228C3×#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—61no—
238C3⋊#95—61no—
239C3⋊#95C2×D311yescharacteristic
240C3⋊#95C2×D311yescharacteristic
241C23×C32C2411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3C2×D412yes—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3C2×D412yes—
262C22×C3×D3C2×D412yes—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2×D412yes—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3C2×D412yes—
280C2×C3⋊Dic3#4112yescomplemented
281C4×C3⋊D3—28no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3C2×D412yes—
296C2×C3×Dic3C2×D412yes—
297C2×C3×Dic3C2×D412yes—
298C2×C3×Dic3C2×D412yes—
299C2×C3×Dic3#4112yescomplemented
300C3×C4×D3—28no—
301C3×C4×D3—28no—
302C3×Dic6—44no—
303#627—28no—
304#626—28no—
305#626—28no—
306#625—28no—
307C22×#41—91no—
308C2×C4⋊Q8—91no—
309C2×#124—91no—
310C2×C22⋊Q8—31no—
311#394—91no—
312#394—91no—
313#394—91no—
314#394—91no—
315#391—91no—
316#390—91no—
317#385—31no—
318#385—91no—
319#385—91no—
320#385—91no—
321C4×C22⋊C4—91no—
322C24×C3—31no—
323C24×C3—31no—
324C23×D3—31no—
325C23×D3—31no—
326C23×D3—61no—
327C23×D3C22×D311yescharacteristic
328C23×D3C22×D311yescharacteristic
329C2×C3×Q8—62no—
330C2×C3×Q8—62no—
331C2×C3×Q8—62no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—34no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—34no—
354C2×#67—62no—
355C2×#67—62no—
356C2×#67—62no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—62no—
361C2×#67—62no—
362C2×#67—62no—
363C2×#67—62no—
364C2×#67—62no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380#235—632no—
381#235—632no—
382C2×D12—34no—
383C2×D12—62no—
384C2×D12—62no—
385C2×D12—62no—
386C2×D12—62no—
387C2×D12—62no—
388C2×C4×D3—22no—
389C2×C4×D3—22no—
390C2×C4×D3—22no—
391C2×C4×D3—22no—
392C2×C4×D3—22no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—62no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—62no—
399C2×C4×D3—122no—
400C2×C4×D3—122no—
401C2×C4×D3—122no—
402C2×C4×D3#6714yes—
403C2×Dic6—22no—
404C2×Dic6—22no—
405C2×Dic6—22no—
406C2×Dic6—34no—
407C2×Dic6—34no—
408C2×Dic6—62no—
409C2×Dic6—62no—
410C2×Dic6—62no—
411C2×Dic6—62no—
412C3×C4⋊C4—22no—
413C3×C4⋊C4—22no—
414C3×C4⋊C4—42no—
415C3×C4⋊C4—62no—
416C3×C4⋊C4—62no—
417C3×C4⋊C4—62no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4—62no—
422#217—62no—
423#217—62no—
424#217—62no—
425#217—62no—
426(C2×D3)⋊C4—22no—
427(C2×D3)⋊C4—22no—
428(C2×D3)⋊C4—22no—
429(C2×D3)⋊C4—22no—
430(C2×D3)⋊C4—62no—
431(C2×D3)⋊C4—62no—
432(C2×D3)⋊C4—62no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—64no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—122no—
444C4⋊Dic3—62no—
445Dic3⋊C4—22no—
446Dic3⋊C4—22no—
447Dic3⋊C4—22no—
448Dic3⋊C4—62no—
449Dic3⋊C4—62no—
450Dic3⋊C4—62no—
451Dic3⋊C4—62no—
452Dic3⋊C4—62no—
453Dic3⋊C4—122no—
454C4×Dic3—62no—
455C4×Dic3—62no—
456C4×Dic3—62no—
457C4×Dic3—62no—
458C22×C32C22×D411yescharacteristic
459C22×C32C22×D411yescharacteristic
460C22×C32C22×D411yescharacteristic
461C22×C32C2×#4111yescharacteristic
462C22×C32C2×#4111yescharacteristic
463C22×C322−1+411yescharacteristic
464C22×C322−1+411yescharacteristic
465C2×C3⋊D3—22no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—22no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C32×C4—22no—
487C32×C4—41no—
488C32×C4—41no—
489C3⋊Dic3—22no—
490C3⋊Dic3—22no—
491C3⋊Dic3—41no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C3×Dic3—41no—
497C3×Dic3#12014yes—
498C2×#41—184no—
499C2×#41—184no—
500C2×#41—184no—
501C22×Q8—31no—
502C22×Q8—91no—
503C22×D4—91no—
504C22×D4—91no—
505C22×D4—91no—
506C23×C4—31no—
507C23×C4—31no—
508C23×C4—91no—
509C4⋊Q8—184no—
510#124—184no—
511C22⋊Q8—64no—
512C2×C4⋊C4—31no—
513C2×C4⋊C4—31no—
514C2×C4⋊C4—31no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4—91no—
518C2×C4⋊C4D3211yescharacteristic
519C2×C22⋊C4—31no—
520C2×C22⋊C4—31no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—91no—
524C2×C22⋊C4—91no—
525C2×C22⋊C4—91no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C42—91no—
532C2×C42—91no—
533#95—31no—
534#95—31no—
535#95—91no—
536#95—91no—
537#95—91no—
538#95—91no—
539C23×C3—21no—
540C23×C3—32no—
541C23×C3—32no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3C23×D311yescharacteristic
555C23×C3C23×D311yescharacteristic
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—32no—
569C22×D3—32no—
570C22×D3—62no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—121no—
586C22×D3—121no—
587C22×D3—121no—
588C22×D3—121no—
589C22×D3D3×D412yes—
590C22×D3C2×#6712yes—
591C3×Q8—124no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—22no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—22no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—32no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—68no—
623C2×C3×C4—68no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4D3×D412yes—
638C2×C3×C4C2×#6712yes—
639#67—68no—
640#67—68no—
641#67—68no—
642#67—68no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—121no—
677C2×Dic3—121no—
678C2×Dic3—121no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681C2×Dic3—121no—
682C2×Dic3—121no—
683C2×Dic3#23512yescomplemented
684C2×Dic3D3×D412yes—
685C2×Dic3D3×D412yes—
686C2×Dic3D3×D412yes—
687C2×Dic3C2×#6712yes—
688D12—68no—
689D12—68no—
690C4×D3—28no—
691C4×D3—28no—
692C4×D3—68no—
693C4×D3—68no—
694C4×D3—128no—
695Dic6—44no—
696Dic6—68no—
697Dic6—68no—
698C2×C32C2×#12011yescharacteristic
699C2×C32#53211yescharacteristic
700C2×C32#53611yescharacteristic
701C2×C32#54711yescharacteristic
702C2×C32#54711yescharacteristic
703C2×C32#54811yescharacteristic
704C2×C32#54811yescharacteristic
705C3⋊D3—42no—
706C3×D3—42no—
707C3×D3—42no—
708C24—31no—
709C24—31no—
710C24—91no—
711#41—1832no—
712C2×Q8—62no—
713C2×Q8—62no—
714C2×Q8—62no—
715C2×Q8—94no—
716C2×Q8—182no—
717C2×Q8—182no—
718C2×D4—94no—
719C2×D4—182no—
720C2×D4—182no—
721C2×D4—182no—
722C2×D4—182no—
723C2×D4—182no—
724C2×D4—182no—
725C2×D4—182no—
726C2×D4—182no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—34no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—31no—
734C22×C4—62no—
735C22×C4—62no—
736C22×C4—62no—
737C22×C4—62no—
738C22×C4—62no—
739C22×C4—91no—
740C22×C4—91no—
741C22×C4—91no—
742C22×C4—182no—
743C22×C4—182no—
744C22×C4—182no—
745C22×C4C2×D3211yescharacteristic
746C22×C4C2×D3211yescharacteristic
747C22×C4C2×D3211yescharacteristic
748C4⋊C4—22no—
749C4⋊C4—62no—
750C4⋊C4—62no—
751C4⋊C4—62no—
752C4⋊C4—182no—
753C4⋊C4—182no—
754C4⋊C4—182no—
755C22⋊C4—62no—
756C22⋊C4—62no—
757C22⋊C4—62no—
758C22⋊C4—62no—
759C22⋊C4—182no—
760C22⋊C4—182no—
761C22⋊C4—182no—
762C22⋊C4—182no—
763C22⋊C4—182no—
764C22⋊C4—182no—
765C22⋊C4—182no—
766C22⋊C4—182no—
767C42—182no—
768C42—182no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—121no—
783C22×C3—121no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3C2×#23511yescharacteristic
791C22×C3C2×D3×D411yescharacteristic
792C22×C3C2×D3×D411yescharacteristic
793C22×C3C2×D3×D411yescharacteristic
794C22×C3C2×D3×D411yescharacteristic
795C22×C3C2×D3×D411yescharacteristic
796C22×C3#100711yescharacteristic
797C22×C3#100711yescharacteristic
798C22×C3#100711yescharacteristic
799C22×C3D3×#4111yescharacteristic
800C22×C3D3×#4111yescharacteristic
801C22×C3D3×#4111yescharacteristic
802C22×C3#101011yescharacteristic
803C22×C3C22×#6711yescharacteristic
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—64no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—122no—
826C2×D3—122no—
827C2×D3—122no—
828C2×D3—122no—
829C2×D3—122no—
830C2×D3—122no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—121no—
839C3×C4—22no—
840C3×C4—22no—
841C3×C4—34no—
842C3×C4—42no—
843C3×C4—42no—
844C3×C4—41no—
845C3×C4—41no—
846C3×C4—41no—
847C3×C4—41no—
848C3×C4—62no—
849C3×C4—62no—
850C3×C4—81no—
851C3×C4—121no—
852C3×C4—121no—
853C3×C4—121no—
854Dic3—22no—
855Dic3—22no—
856Dic3—41no—
857Dic3—41no—
858Dic3—41no—
859Dic3—62no—
860Dic3—62no—
861Dic3—62no—
862Dic3—62no—
863Dic3—122no—
864Dic3—122no—
865Dic3—121no—
866Dic3—121no—
867Dic3—241no—
868Dic3#93714yes—
869C32#243211yescharacteristic, complemented, Sylow
870C23—32no—
871C23—32no—
872C23—61no—
873C23—61no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23—61no—
880C23—61no—
881C23—61no—
882C23—61no—
883C23—61no—
884C23—92no—
885C23—181no—
886C23—181no—
887C23—181no—
888C23—181no—
889C23—181no—
890C23—181no—
891C23C22×D3211yescharacteristic
892Q8—124no—
893Q8—188no—
894D4—188no—
895D4—188no—
896D4—188no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—68no—
911C2×C4—68no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—92no—
926C2×C4—92no—
927C2×C4—188no—
928C2×C4—181no—
929C2×C4—181no—
930C2×C4—181no—
931C2×C4—181no—
932C2×C4—181no—
933C2×C4—181no—
934C2×C4—181no—
935C2×C4D3×#6712yes—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—122no—
944C2×C3—122no—
945C2×C3#550711yescharacteristic
946C2×C3#554811yescharacteristic
947C2×C3#555211yescharacteristic
948C2×C3D3×#12011yescharacteristic
949C2×C3#562811yescharacteristic
950C2×C3#563111yescharacteristic
951C2×C3#563111yescharacteristic
952C2×C3#563311yescharacteristic
953C2×C3#563311yescharacteristic
954C2×C3#563311yescharacteristic
955C2×C3#565511yescharacteristic
956C2×C3C2×#93711yescharacteristic
957C2×C3#581611yescharacteristic
958C2×C3#583211yescharacteristic
959D3—42no—
960D3—42no—
961D3—124no—
962D3—122no—
963D3—122no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—62no—
970C22—121no—
971C22—121no—
972C22—121no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—182no—
979C22—182no—
980C22—182no—
981C22—361no—
982C22—361no—
983C22—361no—
984C22—361no—
985C22D3×#23511yescharacteristic
986C22#6430611yescharacteristic
987C22D32×D411yescharacteristic
988C22D32×D411yescharacteristic
989C22#6431511yescharacteristic
990C22#6431611yescharacteristic
991C22C2×D3×#6711yescharacteristic
992C4—22no—
993C4—34no—
994C4—41no—
995C4—41no—
996C4—62no—
997C4—62no—
998C4—121no—
999C4—121no—
1000C4—121no—
1001C4—182no—
1002C4—182no—
1003C4—361no—
1004C3—21no—
1005C3#7441111yescharacteristic, complemented
1006C3#8275911yescharacteristic, complemented
1007C2—122no—
1008C2—122no—
1009C2—362no—
1010C2#1059437111yescharacteristic
1011C2#1059437511yescharacteristic
1012C2#1059451611yescharacteristic
1013C2#1059452111yescharacteristic
1014C2#1059500311yescharacteristic
1015C2D3×#93711yescharacteristic
1016C2#1059539711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#3798C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#896C2semidirect
3. C2×#63907C2semidirect
4. C2×#63839C2semidirect
5. #10592688C2semidirect
6. C3×#4989C2semidirect
7. #10591390C2semidirect
8. #10591388C2semidirect
9. #10591384C2semidirect
10. #10591292C2semidirect
11. #10591291C2semidirect
12. #10591290C2semidirect
13. #10591277C2semidirect
14. #10591237C2semidirect
15. #10591235C2semidirect
64. C2×#896D3semidirect
76. #4989D3semidirect
280. C2×C3⋊Dic3#41semidirect
299. C2×C3×Dic3#41semidirect
683. C2×Dic3#235semidirect
869. C32#2432semidirect
1005. C3#74411semidirect
1006. C3#82759semidirect

Maximal subgroups

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

subgroupindex
C22×#37982
C2×C3×#8962
C2×#639072
C2×#638392
#105926882
C3×#49892
#105913902
#105913882
#105913842
#105912922
#105912912
#105912902
#105912772
#105912372
#105912352
#827593
#744113