Finite Group Databasebeta

← #11811923

Subgroups — #11811923

Order 1152.

1837 conjugacy classes of subgroups.

The subgroup lattice has 1035 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic
2C2×#64094C211yesmaximal, characteristic, complemented
3C2×#63896C211yesmaximal, characteristic, complemented
4C2×#63840C211yesmaximal, characteristic, complemented
5C3×#4959C211yesmaximal, characteristic, complemented
6C3×#4946C211yesmaximal, characteristic, complemented
7#10591718C211yesmaximal, characteristic, complemented
8#10591709C211yesmaximal, characteristic, complemented
9#10591704C211yesmaximal, characteristic, complemented
10#10591396C211yesmaximal, characteristic, complemented
11#10591375C211yesmaximal, characteristic, complemented
12#10591374C211yesmaximal, characteristic, complemented
13#10591368C211yesmaximal, characteristic, complemented
14#10591312C211yesmaximal, characteristic, complemented
15#10591291C211yesmaximal, characteristic, complemented
16#76904—31nomaximal
17#74411—31nomaximal
18C22×#638C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3804—24no—
26C2×#3804—24no—
27C2×#3804—24no—
28C22×D3×Dic3C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34#64094—24no—
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×#3724C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×#3722C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51#63896—24no—
52#63840—24no—
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58#63579C2211yescharacteristic
59C22×#237—31no—
60C22×#235—31no—
61C2×#896—31no—
62C2×#888—31no—
63C2×#888—31no—
64C2×#885—31no—
65C2×#885—31no—
66C2×#885—61no—
67C2×#878—31no—
68C3×#394—31no—
69C3×#385—31no—
70#5222—31no—
71#5210—31no—
72#4991—31no—
73#4989—31no—
74#4989—31no—
75#4961—31no—
76#4961—31no—
77#4959—31no—
78#4959D311yescharacteristic, complemented
79#4957—31no—
80#4957—31no—
81#4950—31no—
82#4946D311yescharacteristic, complemented
83Dic3×C22⋊C4—31no—
84#4672—31no—
85#4668—31no—
86#4668—31no—
87#4666—31no—
88#4646—31no—
89#4646—31no—
90C24×C32C2311yescharacteristic
91C23×C3⋊D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—22no—
96C2×#638—22no—
97C2×#638D414yes—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×#634—22no—
102C2×#634—22no—
103C2×#634—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C22×C3×Dic3—22no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3—22no—
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×#627—22no—
118C2×#627—22no—
119C2×#627D414yes—
120C2×#626—22no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#624—22no—
124C2×#624—22no—
125C2×#624—22no—
126#3804—232no—
127C2×D3×Dic3—22no—
128C2×D3×Dic3—22no—
129C2×D3×Dic3D414yes—
130C32×C22⋊C4—22no—
131#3757—22no—
132#3752—22no—
133#3752—22no—
134C4×C3⋊Dic3—22no—
135C3×#217—22no—
136C3×#217—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×Dic3⋊C4—22no—
140C3×Dic3⋊C4—22no—
141C3×Dic3⋊C4—22no—
142#3724—22no—
143Dic3⋊Dic3—22no—
144Dic3⋊Dic3—22no—
145Dic3⋊Dic3—22no—
146#3722—22no—
147#3722—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—22no—
150Dic32—22no—
151#2432—91noSylow
152C22×C3×D4—31no—
153C23×C3×C4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—61no—
158C22×#67C2×D311yescharacteristic
159C23×Dic3—31no—
160C23×Dic3C2×D311yescharacteristic
161C2×#237—64no—
162C2×#237—64no—
163C2×#237—64no—
164C2×#235—64no—
165C2×#235—64no—
166C2×#235—64no—
167C22×D12—31no—
168C22×C4×D3—31no—
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×Dic6—31no—
172C22×Dic6—31no—
173C22×Dic6—31no—
174C22×Dic6—31no—
175C22×Dic6—61no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C22⋊C4—21no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4C2×D311yescharacteristic
185C2×C3×C22⋊C4C2×D311yescharacteristic
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—61no—
191C2×#217C2×D311yescharacteristic
192C2×#217C2×D311yescharacteristic
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—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4C2×D311yescharacteristic
216C2×Dic3⋊C4C2×D311yescharacteristic
217C2×Dic3⋊C4C2×D311yescharacteristic
218C2×C4×Dic3—31no—
219C2×C4×Dic3—31no—
220C2×C4×Dic3—31no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3—61no—
223#896—64no—
224#888—64no—
225#888—64no—
226#885—64no—
227#885—64no—
228#885—68no—
229#878—64no—
230C3×#95—31no—
231C3×#95—31no—
232C3×#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95C2×D311yescharacteristic
240C3⋊#95C2×D311yescharacteristic
241C3⋊#95C2×D311yescharacteristic
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32C2×D412yes—
249C23×C32C2411yescharacteristic
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⋊D3C2×D412yes—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3C2×D412yes—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270#638—28no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3C2×D412yes—
278C2×C3⋊Dic3C2×D412yes—
279C2×C3⋊Dic3C2×D412yes—
280#634—44no—
281C3×#67—28no—
282C2×C3×Dic3—28no—
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×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3C2×D412yes—
300C2×C3×Dic3C2×D412yes—
301C2×C3×Dic3C2×D412yes—
302C2×C3×Dic3#4112yescomplemented
303C2×C3×Dic3#4112yescomplemented
304#627—28no—
305#626—28no—
306#624—28no—
307D3×Dic3—28no—
308C22×#41—91no—
309C2×C4⋊Q8—91no—
310C2×#124—91no—
311C2×C22⋊Q8—91no—
312#394—31no—
313#394—91no—
314#394—91no—
315#394—91no—
316#391—91no—
317#390—91no—
318#385—31no—
319#385—91no—
320#385—91no—
321#385—91no—
322C4×C22⋊C4—91no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3C22×D311yescharacteristic
326C24×C3C22×D311yescharacteristic
327C23×D3—31no—
328C23×D3—31no—
329C23×D3—61no—
330C23×D3C22×D311yescharacteristic
331C2×C3×D4—62no—
332C2×C3×D4—62no—
333C2×C3×D4—62no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—22no—
351C2×#67—22no—
352C2×#67—22no—
353C2×#67—34no—
354C2×#67—34no—
355C2×#67—64no—
356C2×#67—62no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—62no—
361C2×#67—62no—
362C2×#67—62no—
363C2×#67—122no—
364C2×#67—122no—
365C22×Dic3—22no—
366C22×Dic3—22no—
367C22×Dic3—22no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—34no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—62no—
379C22×Dic3—62no—
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387#237—632no—
388#235—632no—
389C2×D12—62no—
390C2×D12—62no—
391C2×D12—62no—
392C2×C4×D3—34no—
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—62no—
400C2×C4×D3—62no—
401C2×Dic6—34no—
402C2×Dic6—34no—
403C2×Dic6—62no—
404C2×Dic6—62no—
405C2×Dic6—62no—
406C2×Dic6—62no—
407C2×Dic6—62no—
408C2×Dic6—62no—
409C2×Dic6—62no—
410C2×Dic6—62no—
411C2×Dic6—62no—
412C2×Dic6—62no—
413C2×Dic6—64no—
414C2×Dic6—122no—
415C2×Dic6—122no—
416C3×C4⋊C4—62no—
417C3×C4⋊C4—62no—
418C3×C4⋊C4—62no—
419C3×C22⋊C4—24no—
420C3×C22⋊C4—22no—
421C3×C22⋊C4—22no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—62no—
426#217—22no—
427#217—22no—
428#217—62no—
429#217—64no—
430#217—62no—
431#217—62no—
432#217—62no—
433(C2×D3)⋊C4—22no—
434(C2×D3)⋊C4—22no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—64no—
442(C2×D3)⋊C4—64no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447C4⋊Dic3—62no—
448C4⋊Dic3—62no—
449C4⋊Dic3—62no—
450Dic3⋊C4—22no—
451Dic3⋊C4—22no—
452Dic3⋊C4—22no—
453Dic3⋊C4—62no—
454Dic3⋊C4—62no—
455Dic3⋊C4—62no—
456Dic3⋊C4—62no—
457Dic3⋊C4—62no—
458C4×Dic3—62no—
459C4×Dic3—62no—
460C4×Dic3—62no—
461C4×Dic3—62no—
462C4×Dic3—64no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32C22×D411yescharacteristic
471C22×C32C22×D411yescharacteristic
472C22×C32C22×D411yescharacteristic
473C22×C32C2×#4111yescharacteristic
474C22×C32C2×#4111yescharacteristic
475C22×C322−1+411yescharacteristic
476C22×C322−1+411yescharacteristic
477C2×C3⋊D3—22no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C32×C4—41no—
492C32×C4—41no—
493C3⋊Dic3—41no—
494C3⋊Dic3—41no—
495C3⋊Dic3#12014yes—
496C3×Dic3—22no—
497C3×Dic3—22no—
498C3×Dic3—22no—
499C3×Dic3—22no—
500C3×Dic3—22no—
501C3×Dic3—41no—
502C3×Dic3—41no—
503C2×#41—184no—
504C2×#41—184no—
505C2×#41—184no—
506C22×Q8—91no—
507C22×Q8—91no—
508C22×D4—31no—
509C22×D4—91no—
510C22×D4—91no—
511C23×C4—31no—
512C23×C4—91no—
513C23×C4—91no—
514C4⋊Q8—184no—
515#124—184no—
516C22⋊Q8—184no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4D3211yescharacteristic
536C2×C42—91no—
537C2×C42—91no—
538#95—31no—
539#95—31no—
540#95—31no—
541#95—91no—
542#95—91no—
543#95—91no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—22no—
558C23×C3—32no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3D3×D412yes—
572C23×C3D3×D412yes—
573C23×C3C23×D311yescharacteristic
574C23×C3C23×D311yescharacteristic
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—32no—
582C22×D3—32no—
583C22×D3—62no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—121no—
597C22×D3—121no—
598C22×D3—121no—
599C22×D3—121no—
600C22×D3—121no—
601C22×D3—121no—
602C22×D3D3×D412yes—
603C3×D4—68no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—32no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—68no—
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×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644#67—28no—
645#67—68no—
646#67—68no—
647#67—68no—
648#67—128no—
649C2×Dic3—28no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—32no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—68no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—121no—
691C2×Dic3—121no—
692C2×Dic3—121no—
693C2×Dic3—121no—
694C2×Dic3#23512yescomplemented
695C2×Dic3D3×D412yes—
696C2×Dic3D3×D412yes—
697C2×Dic3D3×D412yes—
698C2×Dic3#23712yescomplemented
699D12—68no—
700C4×D3—68no—
701C4×D3—68no—
702C4×D3—68no—
703Dic6—68no—
704Dic6—68no—
705Dic6—124no—
706Dic6—124no—
707Dic6—128no—
708C2×C32—42no—
709C2×C32C2×#12011yescharacteristic
710C2×C32#53211yescharacteristic
711C2×C32#53611yescharacteristic
712C2×C32#54711yescharacteristic
713C2×C32#54711yescharacteristic
714C2×C32#54811yescharacteristic
715C2×C32#54811yescharacteristic
716C3⋊D3—42no—
717C3×D3—42no—
718C24—31no—
719C24—91no—
720C24C2×D3211yescharacteristic
721#41—1832no—
722C2×Q8—94no—
723C2×Q8—182no—
724C2×Q8—182no—
725C2×Q8—182no—
726C2×Q8—182no—
727C2×Q8—182no—
728C2×D4—62no—
729C2×D4—62no—
730C2×D4—62no—
731C2×D4—94no—
732C2×D4—182no—
733C2×D4—182no—
734C2×D4—182no—
735C2×D4—182no—
736C2×D4—182no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—31no—
742C22×C4—31no—
743C22×C4—31no—
744C22×C4—62no—
745C22×C4—62no—
746C22×C4—62no—
747C22×C4—94no—
748C22×C4—91no—
749C22×C4—91no—
750C22×C4—91no—
751C22×C4—182no—
752C22×C4—182no—
753C22×C4—182no—
754C22×C4—182no—
755C22×C4—182no—
756C22×C4C2×D3211yescharacteristic
757C22×C4C2×D3211yescharacteristic
758C4⋊C4—62no—
759C4⋊C4—62no—
760C4⋊C4—62no—
761C4⋊C4—182no—
762C4⋊C4—182no—
763C4⋊C4—182no—
764C4⋊C4—182no—
765C22⋊C4—22no—
766C22⋊C4—62no—
767C22⋊C4—62no—
768C22⋊C4—62no—
769C22⋊C4—62no—
770C22⋊C4—182no—
771C22⋊C4—182no—
772C22⋊C4—182no—
773C22⋊C4—182no—
774C22⋊C4—182no—
775C22⋊C4—182no—
776C22⋊C4—182no—
777C42—182no—
778C42—182no—
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—41no—
800C22×C3—41no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3—81no—
809C22×C3—81no—
810C22×C3—121no—
811C22×C3—121no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3C2×#23511yescharacteristic
815C22×C3C2×D3×D411yescharacteristic
816C22×C3C2×D3×D411yescharacteristic
817C22×C3C2×D3×D411yescharacteristic
818C22×C3C2×D3×D411yescharacteristic
819C22×C3C2×D3×D411yescharacteristic
820C22×C3C2×D3×D411yescharacteristic
821C22×C3C2×#23711yescharacteristic
822C22×C3#100711yescharacteristic
823C22×C3D3×#4111yescharacteristic
824C22×C3D3×#4111yescharacteristic
825C22×C3#101011yescharacteristic
826C22×C3#101011yescharacteristic
827C22×C3#101011yescharacteristic
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—122no—
842C2×D3—122no—
843C2×D3—122no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—241no—
853C2×D3—241no—
854C2×D3—241no—
855C2×D3—241no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—41no—
859C3×C4—41no—
860C3×C4—41no—
861C3×C4—41no—
862C3×C4—62no—
863C3×C4—62no—
864C3×C4—62no—
865C3×C4—62no—
866C3×C4—62no—
867C3×C4—121no—
868C3×C4—121no—
869Dic3—22no—
870Dic3—22no—
871Dic3—22no—
872Dic3—22no—
873Dic3—22no—
874Dic3—34no—
875Dic3—34no—
876Dic3—41no—
877Dic3—41no—
878Dic3—64no—
879Dic3—122no—
880Dic3—122no—
881Dic3—121no—
882Dic3—121no—
883Dic3—121no—
884Dic3—121no—
885C32#243211yescharacteristic, complemented, Sylow
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—32no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—92no—
900C23—181no—
901C23—181no—
902C23—181no—
903C23—181no—
904C23—181no—
905C23—181no—
906C23#381112yes—
907C23C22×D3211yescharacteristic
908Q8—188no—
909Q8—364no—
910D4—68no—
911D4—188no—
912D4—188no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—32no—
920C2×C4—32no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—68no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—92no—
942C2×C4—92no—
943C2×C4—92no—
944C2×C4—188no—
945C2×C4—188no—
946C2×C4—181no—
947C2×C4—181no—
948C2×C4—181no—
949C2×C4—181no—
950C2×C4—181no—
951C2×C4—181no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—21no—
959C2×C3—42no—
960C2×C3—42no—
961C2×C3—82no—
962C2×C3—122no—
963C2×C3#550711yescharacteristic
964C2×C3#554811yescharacteristic
965C2×C3#555211yescharacteristic
966C2×C3D3×#12011yescharacteristic
967C2×C3D3×#12011yescharacteristic
968C2×C3#559611yescharacteristic
969C2×C3#559811yescharacteristic
970C2×C3#561111yescharacteristic
971C2×C3#562811yescharacteristic
972C2×C3#563311yescharacteristic
973C2×C3#564811yescharacteristic
974C2×C3#565511yescharacteristic
975C2×C3#565511yescharacteristic
976C2×C3#567711yescharacteristic
977D3—42no—
978D3—122no—
979D3—122no—
980D3—242no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—41no—
985C22—41no—
986C22—41no—
987C22—41no—
988C22—62no—
989C22—62no—
990C22—62no—
991C22—121no—
992C22—121no—
993C22—121no—
994C22—121no—
995C22—182no—
996C22—182no—
997C22—182no—
998C22—361no—
999C22—361no—
1000C22—361no—
1001C22—361no—
1002C22#6429711yescharacteristic
1003C22D3×#23511yescharacteristic
1004C22#6430911yescharacteristic
1005C22D32×D411yescharacteristic
1006C22D32×D411yescharacteristic
1007C22D3×#23711yescharacteristic
1008C22C2×#381111yescharacteristic
1009C4—41no—
1010C4—41no—
1011C4—62no—
1012C4—62no—
1013C4—62no—
1014C4—62no—
1015C4—62no—
1016C4—94no—
1017C4—121no—
1018C4—121no—
1019C4—361no—
1020C4—361no—
1021C3—21no—
1022C3#7441111yescharacteristic, complemented
1023C3#7690411yescharacteristic, complemented
1024C2—42no—
1025C2—122no—
1026C2—362no—
1027C2#1059405611yescharacteristic
1028C2#1059405811yescharacteristic
1029C2#1059407311yescharacteristic
1030C2#1059407411yescharacteristic
1031C2#1059491711yescharacteristic
1032C2#1059516211yescharacteristic
1033C2#1059527811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×#3804C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#64094C2semidirect
3. C2×#63896C2semidirect
4. C2×#63840C2semidirect
5. C3×#4959C2semidirect
6. C3×#4946C2semidirect
7. #10591718C2semidirect
8. #10591709C2semidirect
9. #10591704C2semidirect
10. #10591396C2semidirect
11. #10591375C2semidirect
12. #10591374C2semidirect
13. #10591368C2semidirect
14. #10591312C2semidirect
15. #10591291C2semidirect
78. #4959D3semidirect
82. #4946D3semidirect
302. C2×C3×Dic3#41semidirect
303. C2×C3×Dic3#41semidirect
694. C2×Dic3#235semidirect
698. C2×Dic3#237semidirect
885. C32#2432semidirect
1022. C3#74411semidirect
1023. C3#76904semidirect

Maximal subgroups

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

subgroupindex
C22×#38042
C2×#640942
C2×#638962
C2×#638402
C3×#49592
C3×#49462
#105917182
#105917092
#105917042
#105913962
#105913752
#105913742
#105913682
#105913122
#105912912
#769043
#744113