Finite Group Databasebeta

← #11811925

Subgroups — #11811925

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×C3×#235C211yesmaximal, characteristic
2C2×#63959C211yesmaximal, characteristic, complemented
3C2×#63851C211yesmaximal, characteristic, complemented
4C2×#63839C211yesmaximal, characteristic, complemented
5#10592909C211yesmaximal, characteristic, complemented
6C3×#5210C211yesmaximal, characteristic, complemented
7#10591709C211yesmaximal, characteristic, complemented
8#10591708C211yesmaximal, characteristic, complemented
9#10591707C211yesmaximal, characteristic, complemented
10#10591302C211yesmaximal, characteristic, complemented
11#10591300C211yesmaximal, characteristic, complemented
12#10591278C211yesmaximal, characteristic, complemented
13#10591277C211yesmaximal, characteristic, complemented
14#10591261C211yesmaximal, characteristic, complemented
15#10591237C211yesmaximal, characteristic, complemented
16#84093—31nomaximal
17#74411—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C2×C3×#235—24no—
22C2×C3×#235—24no—
23C2×C3×#235—24no—
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic
28C22×#627C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48#63959—24no—
49C2×Dic32C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51#63851—24no—
52#63839—24no—
53#63658C2211yescharacteristic
54#63658C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57#63579C2211yescharacteristic
58#63579C2211yescharacteristic
59C22×C3×#41—31no—
60C22×#235D311yescharacteristic
61C2×#944—31no—
62C2×#936—31no—
63C2×#924—31no—
64C2×#896—31no—
65C2×#888—31no—
66C2×#885—31no—
67C3×#385—31no—
68#5229—31no—
69#5222—31no—
70#5222—31no—
71#5222—31no—
72#5222—31no—
73#5221—31no—
74#5210—31no—
75#5210—31no—
76#5210—31no—
77#5210—31no—
78#5210—61no—
79#5210D311yescharacteristic, complemented
80C4×#217—31no—
81#4991—31no—
82#4989—31no—
83#4961—31no—
84#4959—31no—
85#4957—31no—
86#4672—31no—
87#4668—31no—
88#4666—31no—
89#4646—31no—
90C24×C32C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×C32×C4—22no—
94C22×C32×C4—22no—
95C22×C32×C4—22no—
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67D414yes—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C3×#235—232no—
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—22no—
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3D414yes—
124C2×C3×Dic6—22no—
125C2×C3×Dic6—22no—
126C2×C3×Dic6D414yes—
127C2×#627—22no—
128C2×#627—22no—
129C2×#627—22no—
130#3757—22no—
131#3757—22no—
132#3750—22no—
133#3750—22no—
134C3×#217—22no—
135C3×#217—22no—
136C3×Dic3⋊C4—22no—
137C3×Dic3⋊C4—22no—
138#3724—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—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
152C2×C3×#41—64no—
153C2×C3×#41—64no—
154C2×C3×#41—64no—
155C22×C3×Q8—31no—
156C22×C3×D4—31no—
157C22×C3×D4—31no—
158C22×C3×D4—31no—
159C23×C3×C4—21no—
160C23×C3×C4—31no—
161C23×C3×C4—31no—
162C23×C3×C4C2×D311yescharacteristic
163C23×C3×C4C2×D311yescharacteristic
164C22×#67C2×D311yescharacteristic
165C22×#67C2×D311yescharacteristic
166C2×#235—24no—
167C2×#235—24no—
168C2×#235—24no—
169C22×D12C2×D311yescharacteristic
170C22×C4×D3C2×D311yescharacteristic
171C22×C4×D3C2×D311yescharacteristic
172C22×Dic6—31no—
173C22×Dic6—31no—
174C22×Dic6C2×D311yescharacteristic
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—61no—
192C2×#217—61no—
193C2×#217C2×D311yescharacteristic
194C2×#217C2×D311yescharacteristic
195#944—64no—
196#936—64no—
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—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207#924—64no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—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⋊C4—61no—
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—64no—
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×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32C2×D412yes—
248C23×C32C2411yescharacteristic
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—28no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D412yes—
269C2×C32×C4C2×D412yes—
270C2×C3⋊Dic3—21no—
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⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3#4112yescomplemented
282C3×#67—28no—
283C3×#67—28no—
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×Dic3C2×D412yes—
298C2×C3×Dic3C2×D412yes—
299C2×C3×Dic3C2×D412yes—
300C2×C3×Dic3C2×D412yes—
301C2×C3×Dic3#4112yescomplemented
302C3×D12—28no—
303C3×C4×D3—28no—
304C3×C4×D3—28no—
305C3×Dic6—28no—
306#627—44no—
307C22×#41—31no—
308C2×C4⋊Q8—91no—
309C2×#124—91no—
310C2×C22⋊Q8—91no—
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—21no—
323C24×C3—31no—
324C24×C3—31no—
325C24×C3C22×D311yescharacteristic
326C24×C3C22×D311yescharacteristic
327C23×D3C22×D311yescharacteristic
328C23×D3C22×D311yescharacteristic
329C3×#41—632no—
330C2×C3×Q8—34no—
331C2×C3×Q8—62no—
332C2×C3×Q8—62no—
333C2×C3×D4—34no—
334C2×C3×D4—62no—
335C2×C3×D4—62no—
336C2×C3×D4—62no—
337C2×C3×D4—62no—
338C2×C3×D4—62no—
339C2×C3×D4—62no—
340C2×C3×D4—62no—
341C2×C3×D4—62no—
342C22×C3×C4—22no—
343C22×C3×C4—22no—
344C22×C3×C4—22no—
345C22×C3×C4—22no—
346C22×C3×C4—22no—
347C22×C3×C4—22no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—34no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—42no—
358C22×C3×C4—42no—
359C22×C3×C4—42no—
360C22×C3×C4—62no—
361C22×C3×C4—62no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4—62no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—22no—
370C2×#67—22no—
371C2×#67—22no—
372C2×#67—22no—
373C2×#67—22no—
374C2×#67#6714yes—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393#235—232no—
394C2×D12—22no—
395C2×D12—22no—
396C2×D12—22no—
397C2×C4×D3—22no—
398C2×C4×D3—22no—
399C2×C4×D3—22no—
400C2×C4×D3—22no—
401C2×C4×D3—22no—
402C2×C4×D3#6714yes—
403C2×Dic6—22no—
404C2×Dic6—22no—
405C2×Dic6—62no—
406C2×Dic6—62no—
407C2×Dic6—62no—
408C2×Dic6—62no—
409C2×Dic6—62no—
410C2×Dic6—62no—
411C2×Dic6#6714yes—
412C3×C4⋊C4—62no—
413C3×C4⋊C4—62no—
414C3×C22⋊C4—62no—
415C3×C22⋊C4—62no—
416#217—22no—
417#217—22no—
418#217—62no—
419#217—62no—
420#217—62no—
421#217—62no—
422#217—62no—
423#217—62no—
424#217—62no—
425#217—62no—
426#217—64no—
427#217—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431#217—122no—
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—62no—
440C4⋊Dic3—62no—
441C4⋊Dic3—62no—
442Dic3⋊C4—22no—
443Dic3⋊C4—22no—
444Dic3⋊C4—62no—
445Dic3⋊C4—62no—
446Dic3⋊C4—62no—
447Dic3⋊C4—62no—
448Dic3⋊C4—62no—
449Dic3⋊C4—62no—
450Dic3⋊C4—62no—
451Dic3⋊C4—62no—
452Dic3⋊C4—122no—
453Dic3⋊C4—122no—
454C4×Dic3—62no—
455C4×Dic3—62no—
456C4×Dic3—62no—
457C4×Dic3—62no—
458C22×C32—22no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32C22×D411yescharacteristic
466C22×C32C22×D411yescharacteristic
467C22×C32C22×D411yescharacteristic
468C22×C32C2×#4111yescharacteristic
469C22×C32C2×#4111yescharacteristic
470C22×C322−1+411yescharacteristic
471C22×C322−1+411yescharacteristic
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—22no—
488C3⋊Dic3—22no—
489C3⋊Dic3—41no—
490C3⋊Dic3—41no—
491C3⋊Dic3—41no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C3×Dic3—41no—
497C3×Dic3#12014yes—
498C2×#41—64no—
499C2×#41—64no—
500C2×#41—64no—
501C22×Q8—31no—
502C22×Q8—91no—
503C22×D4—31no—
504C22×D4—31no—
505C22×D4—31no—
506C23×C4—31no—
507C23×C4—31no—
508C23×C4D3211yescharacteristic
509C4⋊Q8—184no—
510#124—184no—
511C22⋊Q8—184no—
512C2×C4⋊C4—31no—
513C2×C4⋊C4—31no—
514C2×C4⋊C4—91no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4—91no—
518C2×C4⋊C4—91no—
519C2×C22⋊C4—31no—
520C2×C22⋊C4—31no—
521C2×C22⋊C4—91no—
522C2×C22⋊C4—91no—
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—22no—
540C23×C3—22no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
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—22no—
555C23×C3—32no—
556C23×C3—32no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3D3×D412yes—
574C23×C3C2×#6712yes—
575C23×C3C23×D311yescharacteristic
576C23×C3C23×D311yescharacteristic
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3C2×#6712yes—
590C22×D3C2×#6712yes—
591C3×Q8—68no—
592C3×D4—68no—
593C3×D4—68no—
594C3×D4—68no—
595C2×C3×C4—28no—
596C2×C3×C4—28no—
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—22no—
606C2×C3×C4—22no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—48no—
617C2×C3×C4—68no—
618C2×C3×C4—68no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
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×C4D3×D412yes—
633C2×C3×C4D3×D412yes—
634C2×C3×C4C2×#6712yes—
635C2×C3×C4C2×#6712yes—
636#67—28no—
637#67—28no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
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—32no—
652C2×Dic3—32no—
653C2×Dic3—62no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—62no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
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—61no—
677C2×Dic3—121no—
678C2×Dic3—121no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681C2×Dic3—121no—
682C2×Dic3—121no—
683C2×Dic3—121no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686C2×Dic3—121no—
687C2×Dic3#23512yescomplemented
688C2×Dic3C2×#6712yes—
689C2×Dic3C2×#6712yes—
690C2×Dic3C2×#6712yes—
691C2×Dic3C2×#6712yes—
692D12—28no—
693C4×D3—28no—
694C4×D3—28no—
695Dic6—28no—
696Dic6—124no—
697Dic6—124no—
698C2×C32—42no—
699C2×C32C2×#12011yescharacteristic
700C2×C32#53211yescharacteristic
701C2×C32#53611yescharacteristic
702C2×C32#54711yescharacteristic
703C2×C32#54711yescharacteristic
704C2×C32#54811yescharacteristic
705C2×C32#54811yescharacteristic
706C3×D3—42no—
707C3×D3—42no—
708C24—31no—
709C24—31no—
710C24C2×D3211yescharacteristic
711#41—632no—
712C2×Q8—34no—
713C2×Q8—62no—
714C2×Q8—62no—
715C2×Q8—182no—
716C2×Q8—182no—
717C2×Q8—182no—
718C2×D4—34no—
719C2×D4—62no—
720C2×D4—62no—
721C2×D4—62no—
722C2×D4—62no—
723C2×D4—62no—
724C2×D4—62no—
725C2×D4—62no—
726C2×D4—62no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—31no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—34no—
734C22×C4—31no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—62no—
738C22×C4—62no—
739C22×C4—62no—
740C22×C4—62no—
741C22×C4—62no—
742C22×C4—91no—
743C22×C4—91no—
744C22×C4—91no—
745C22×C4—91no—
746C22×C4C2×D3211yescharacteristic
747C22×C4C2×D3211yescharacteristic
748C4⋊C4—62no—
749C4⋊C4—62no—
750C4⋊C4—182no—
751C4⋊C4—182no—
752C4⋊C4—182no—
753C4⋊C4—182no—
754C4⋊C4—182no—
755C22⋊C4—62no—
756C22⋊C4—62no—
757C22⋊C4—182no—
758C22⋊C4—182no—
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—24no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3C2×#23511yescharacteristic
812C22×C3C2×D3×D411yescharacteristic
813C22×C3C2×D3×D411yescharacteristic
814C22×C3C2×D3×D411yescharacteristic
815C22×C3#100711yescharacteristic
816C22×C3D3×#4111yescharacteristic
817C22×C3D3×#4111yescharacteristic
818C22×C3D3×#4111yescharacteristic
819C22×C3#101011yescharacteristic
820C22×C3#101011yescharacteristic
821C22×C3#101011yescharacteristic
822C22×C3C22×#6711yescharacteristic
823C22×C3C22×#6711yescharacteristic
824C22×C3C22×#6711yescharacteristic
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C3×C4—22no—
840C3×C4—22no—
841C3×C4—22no—
842C3×C4—22no—
843C3×C4—34no—
844C3×C4—42no—
845C3×C4—42no—
846C3×C4—62no—
847C3×C4—62no—
848C3×C4—121no—
849C3×C4—121no—
850C3×C4—121no—
851Dic3—22no—
852Dic3—22no—
853Dic3—41no—
854Dic3—41no—
855Dic3—41no—
856Dic3—62no—
857Dic3—62no—
858Dic3—122no—
859Dic3—122no—
860Dic3—121no—
861Dic3—121no—
862Dic3—121no—
863Dic3—121no—
864Dic3—121no—
865Dic3—121no—
866Dic3—241no—
867Dic3—241no—
868Dic3#95314yes—
869C32#243211yescharacteristic, complemented, Sylow
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—32no—
877C23—32no—
878C23—61no—
879C23—61no—
880C23—61no—
881C23—61no—
882C23—61no—
883C23—61no—
884C23—61no—
885C23—61no—
886C23—61no—
887C23—61no—
888C23—61no—
889C23—61no—
890C23D3×#6712yes—
891C23C22×D3211yescharacteristic
892Q8—68no—
893Q8—364no—
894D4—68no—
895D4—68no—
896D4—68no—
897C2×C4—28no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—32no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—68no—
908C2×C4—68no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
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—92no—
923C2×C4—181no—
924C2×C4—181no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—181no—
928C2×C4—181no—
929C2×C4—181no—
930C2×C4—181no—
931C2×C4—181no—
932C2×C4—181no—
933C2×C4—181no—
934C2×C4D3×#6712yes—
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—44no—
944C2×C3—42no—
945C2×C3—42no—
946C2×C3—122no—
947C2×C3—122no—
948C2×C3#550711yescharacteristic
949C2×C3#554811yescharacteristic
950C2×C3#555211yescharacteristic
951C2×C3D3×#12011yescharacteristic
952C2×C3#562811yescharacteristic
953C2×C3#563311yescharacteristic
954C2×C3#565511yescharacteristic
955C2×C3#582411yescharacteristic
956C2×C3#582411yescharacteristic
957C2×C3#582511yescharacteristic
958C2×C3#583111yescharacteristic
959C2×C3#583111yescharacteristic
960C2×C3#583211yescharacteristic
961C2×C3C2×#95311yescharacteristic
962D3—42no—
963D3—42no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—62no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—62no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—121no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22#6429711yescharacteristic
986C22#6429811yescharacteristic
987C22D3×#23511yescharacteristic
988C22#6430611yescharacteristic
989C22C2×D3×#6711yescharacteristic
990C22C2×D3×#6711yescharacteristic
991C22C2×D3×#6711yescharacteristic
992C4—22no—
993C4—22no—
994C4—34no—
995C4—62no—
996C4—62no—
997C4—121no—
998C4—121no—
999C4—121no—
1000C4—182no—
1001C4—361no—
1002C4—361no—
1003C4—361no—
1004C3—21no—
1005C3#7441111yescharacteristic, complemented
1006C3#8409311yescharacteristic, complemented
1007C2—42no—
1008C2—122no—
1009C2—122no—
1010C2#1059483011yescharacteristic
1011C2#1059488411yescharacteristic
1012C2#1059488511yescharacteristic
1013C2#1059488811yescharacteristic
1014C2#1059489911yescharacteristic
1015C2#1059500311yescharacteristic
1016C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC22×C3×#235C2
hypercenterC23×C4D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63959C2semidirect
3. C2×#63851C2semidirect
4. C2×#63839C2semidirect
5. #10592909C2semidirect
6. C3×#5210C2semidirect
7. #10591709C2semidirect
8. #10591708C2semidirect
9. #10591707C2semidirect
10. #10591302C2semidirect
11. #10591300C2semidirect
12. #10591278C2semidirect
13. #10591277C2semidirect
14. #10591261C2semidirect
15. #10591237C2semidirect
79. #5210D3semidirect
281. C2×C3⋊Dic3#41semidirect
301. C2×C3×Dic3#41semidirect
687. C2×Dic3#235semidirect
869. C32#2432semidirect
1005. C3#74411semidirect
1006. C3#84093semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#639592
C2×#638512
C2×#638392
#105929092
C3×#52102
#105917092
#105917082
#105917072
#105913022
#105913002
#105912782
#105912772
#105912612
#105912372
#840933
#744113