Finite Group Databasebeta

← C3×#83990 #11884825

Subgroups — C3×#83990 #11884825

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic, complemented
2C3×#5834C211yesmaximal, characteristic, complemented
3C3×#5817C211yesmaximal, characteristic, complemented
4C2×C3×#919C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6C3×#5227C211yesmaximal, characteristic, complemented
7C3×#5187C211yesmaximal, characteristic, complemented
8C3×#5185C211yesmaximal, characteristic, complemented
9C3×#5184C211yesmaximal, characteristic, complemented
10C3×#5176C211yesmaximal, characteristic, complemented
11C3×#5172C211yesmaximal, characteristic, complemented
12C3×#5171C211yesmaximal, characteristic, complemented
13C3×#5163C211yesmaximal, characteristic, complemented
14C3×#5135C211yesmaximal, characteristic, complemented
15C3×#5127C211yesmaximal, characteristic, complemented
16C3×#3271—31nomaximal
17#83990C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×#239C2211yescharacteristic
22C32×#137—24no—
23C2×C32×Q16C2211yescharacteristic
24C2×C32×Q16C2211yescharacteristic
25C2×C32×SD16C2211yescharacteristic
26C2×C32×SD16C2211yescharacteristic
27C2×C32×M16C2211yescharacteristic
28C3×#947—21no—
29C3×#947C2211yescharacteristic
30C3×#946—21no—
31C3×#946C2211yescharacteristic
32C3×Q8×Dic3C2211yescharacteristic
33C3×Q8×Dic3C2211yescharacteristic
34C2×C3×#215C2211yescharacteristic
35C2×C3×#215C2211yescharacteristic
36C2×C3×#215C2211yescharacteristic
37C3×#940—21no—
38C3×#940C2211yescharacteristic
39C3×#938—21no—
40C3×#938C2211yescharacteristic
41C2×C3×#213C2211yescharacteristic
42C3×#930—21no—
43C3×#930—21no—
44C3×#930C2211yescharacteristic
45C3×#930C2211yescharacteristic
46C3×C4×#67—21no—
47C3×C4×#67—21no—
48C3×C4×#67C2211yescharacteristic
49C3×#919—24no—
50C2×C3×D24C2211yescharacteristic
51C2×C3×D3×C8C2211yescharacteristic
52C3×#835C2211yescharacteristic
53C3×#835C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#832C2211yescharacteristic
56C3×#830C2211yescharacteristic
57C3×#821C2211yescharacteristic
58C3×#821C2211yescharacteristic
59C3×(C2×D3)⋊C8C2211yescharacteristic
60C3×#817C2211yescharacteristic
61C3×#815C2211yescharacteristic
62C3×Dic3⋊C8C2211yescharacteristic
63C2×C3×#137—21no—
64C2×C3×#137D311yescharacteristic, complemented
65C2×C3×#137C2×C311yescharacteristic, complemented
66C2×C3×#135—31no—
67C3×#550—31no—
68C3×#548—31no—
69#5834C2×C311yescharacteristic, complemented
70#5817C2×C311yescharacteristic, complemented
71C2×#919C2×C311yescharacteristic, complemented
72C3×#496—31no—
73C3×#469—31no—
74C3×#465—31no—
75C3×#464—31no—
76C3×#460—31no—
77C3×#452—31no—
78C3×#449—31no—
79C3×#449—31no—
80C3×#448—31no—
81C3×#441—31no—
82C3×#435—31no—
83#5238C2×C311yescharacteristic, complemented
84#5227C2×C311yescharacteristic, complemented
85#5187C2×C311yescharacteristic, complemented
86#5185C2×C311yescharacteristic, complemented
87#5184C2×C311yescharacteristic, complemented
88#5176C2×C311yescharacteristic, complemented
89#5172C2×C311yescharacteristic, complemented
90#5171C2×C311yescharacteristic, complemented
91#5163C2×C311yescharacteristic, complemented
92#5135C2×C311yescharacteristic, complemented
93#5127C2×C311yescharacteristic, complemented
94C32×#41—22no—
95C32×#41—41no—
96C2×C32×Q8—21no—
97C2×C32×Q8—22no—
98C2×C32×Q8—41no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4—21no—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4—21no—
105C22×C32×C4—21no—
106C22×C32×C4C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67D411yescharacteristic
113C3×#239—22no—
114C3×#239—22no—
115C3×#239—41no—
116C3×#239—41no—
117C2×C3×D12—21no—
118C2×C3×D12—21no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3C2311yescharacteristic
124C32×Q16—22no—
125C32×Q16D414yescomplemented
126C32×SD16—22no—
127C32×SD16—22no—
128C32×M16—22no—
129C2×C32×C8C2311yescharacteristic
130C2×C32×C8C2311yescharacteristic
131C3×#217—21no—
132C3×#217D411yescharacteristic
133C3×#215—22no—
134C3×#215—22no—
135C3×#215—41no—
136C3×#213—41no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4D411yescharacteristic
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3—21no—
145C3×C4⋊Dic3C2311yescharacteristic
146C3×C4⋊Dic3C2311yescharacteristic
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4D411yescharacteristic
149C3×C4×Dic3—21no—
150C3×C4×Dic3—21no—
151C3×C4×Dic3C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C3×D24—22no—
155C3×D3×C8—22no—
156#3271—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic
161C2×C3×#41C22×C311yescharacteristic
162C22×C3×Q8—21no—
163C22×C3×Q8C2×D311yescharacteristic
164C22×C3×Q8C22×C311yescharacteristic
165C2×#239C22×C311yescharacteristic
166C2×#239C22×C311yescharacteristic
167C3×#137—28no—
168C3×#137—24no—
169C3×#137—24no—
170C3×#135—64no—
171C2×C3×Q16—21no—
172C2×C3×Q16—21no—
173C2×C3×Q16C2×D311yescharacteristic
174C2×C3×Q16C2×D311yescharacteristic
175C2×C3×Q16C22×C311yescharacteristic
176C2×C3×Q16C22×C311yescharacteristic
177C2×C3×SD16—21no—
178C2×C3×SD16—21no—
179C2×C3×SD16—31no—
180C2×C3×SD16—31no—
181C2×C3×SD16—31no—
182C2×C3×SD16C2×D311yescharacteristic
183C2×C3×SD16C2×D311yescharacteristic
184C2×C3×SD16C22×C311yescharacteristic
185C2×C3×SD16C22×C311yescharacteristic
186C2×C3×D8—31no—
187C2×C3×D8—31no—
188C2×C3×M16—21no—
189C2×C3×M16C2×D311yescharacteristic
190C2×C3×M16C22×C311yescharacteristic
191C22×C3×C8—31no—
192C3×#127—31no—
193C3×#127—61no—
194C3×#124—31no—
195C3×#124—61no—
196C3×C22⋊Q8—31no—
197C3×C22⋊Q8—61no—
198C3×#121—31no—
199C3×#121—31no—
200C3×#121—31no—
201C3×#121—61no—
202C3×#121—61no—
203C3×#121—61no—
204C3×C4×Q8—31no—
205C3×C4×Q8—31no—
206C3×C4×D4—31no—
207C3×C4×D4—61no—
208C3×C4×D4—61no—
209#947—21no—
210#947C22×C311yescharacteristic
211#946—21no—
212#946C22×C311yescharacteristic
213Q8×Dic3C22×C311yescharacteristic
214Q8×Dic3C22×C311yescharacteristic
215C2×#215C22×C311yescharacteristic
216C2×#215C22×C311yescharacteristic
217C2×#215C22×C311yescharacteristic
218#940—21no—
219#940C22×C311yescharacteristic
220#938—21no—
221#938C22×C311yescharacteristic
222C2×#213C22×C311yescharacteristic
223#930—21no—
224#930—21no—
225#930C22×C311yescharacteristic
226#930C22×C311yescharacteristic
227C4×#67—21no—
228C4×#67—21no—
229C4×#67C22×C311yescharacteristic
230#919—24no—
231C2×D24C22×C311yescharacteristic
232C2×D3×C8C22×C311yescharacteristic
233C3×#106—31no—
234C3×C4⋊C8—31no—
235C3×#103—31no—
236C3×#103—31no—
237C3×#103—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×C22⋊C8—31no—
242C3×C22⋊C8—31no—
243C3×#97—31no—
244#835C22×C311yescharacteristic
245#835C22×C311yescharacteristic
246#835C22×C311yescharacteristic
247#832C22×C311yescharacteristic
248#830C22×C311yescharacteristic
249#821C22×C311yescharacteristic
250#821C22×C311yescharacteristic
251(C2×D3)⋊C8C22×C311yescharacteristic
252#817C22×C311yescharacteristic
253#815C22×C311yescharacteristic
254Dic3⋊C8C22×C311yescharacteristic
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C32×Q8—21no—
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—42no—
265C32×Q8C2×D412yes—
266C32×Q8C2×D412yes—
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—42no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—42no—
276C2×C32×C4—42no—
277C2×C32×C4C2×D411yescharacteristic
278C2×C32×C4C2411yescharacteristic
279C3×#67—41no—
280C3×#67—42no—
281C3×#67—42no—
282C3×#67—81no—
283C3×#67—81no—
284C3×#67—81no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—42no—
295C3×D12—42no—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298C3×C4×D3—42no—
299C3×C4×D3—42no—
300C32×C8—21no—
301C32×C8C2×D412yes—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C2×#137C3×D311yescharacteristic, complemented
305C2×#135—31no—
306#550—31no—
307#548—31no—
308#496—31no—
309#469—31no—
310#465—31no—
311#464—31no—
312#460—31no—
313#452—31no—
314#449—31no—
315#449—31no—
316#448—31no—
317#441—31no—
318#435—31no—
319C3×#41—24no—
320C3×#41—22no—
321C3×#41—22no—
322C3×#41—41no—
323C3×#41—41no—
324C3×#41—42no—
325C3×#41—62no—
326C3×#41—62no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—21no—
331C2×C3×Q8—24no—
332C2×C3×Q8—22no—
333C2×C3×Q8—22no—
334C2×C3×Q8—21no—
335C2×C3×Q8—21no—
336C2×C3×Q8—21no—
337C2×C3×Q8—41no—
338C2×C3×Q8—41no—
339C2×C3×Q8—41no—
340C2×C3×Q8—42no—
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×Q8C23×C311yescharacteristic
345C2×C3×Q8C23×C311yescharacteristic
346C2×C3×Q8C23×C311yescharacteristic
347C2×C3×D4—21no—
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—31no—
351C2×C3×D4—31no—
352C2×C3×D4—31no—
353C2×C3×D4—41no—
354C2×C3×D4—61no—
355C2×C3×D4—61no—
356C2×C3×D4—61no—
357C2×C3×D4—61no—
358C2×C3×D4—61no—
359C2×C3×D4—61no—
360C2×C3×D4—61no—
361C2×C3×D4C22×D311yescharacteristic
362C2×C3×D4C23×C311yescharacteristic
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—31no—
369C22×C3×C4—41no—
370C22×C3×C4—41no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C23×C311yescharacteristic
375C2×#67—21no—
376C2×#67—21no—
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—21no—
380C2×#67C3×D411yescharacteristic
381#239—22no—
382#239—22no—
383#239—41no—
384#239—41no—
385C2×D12—21no—
386C2×D12—21no—
387C2×D12C23×C311yescharacteristic
388C2×D12C23×C311yescharacteristic
389C2×C4×D3—21no—
390C2×C4×D3—21no—
391C2×C4×D3C23×C311yescharacteristic
392C3×Q16—24no—
393C3×Q16—22no—
394C3×Q16—22no—
395C3×Q16—24no—
396C3×Q16#6714yescomplemented
397C3×Q16C3×D414yescomplemented
398C3×SD16—24no—
399C3×SD16—24no—
400C3×SD16—22no—
401C3×SD16—22no—
402C3×SD16—22no—
403C3×SD16—22no—
404C3×SD16—62no—
405C3×SD16—62no—
406C3×SD16—121no—
407C3×D8—62no—
408C3×D8—121no—
409C3×M16—24no—
410C3×M16—22no—
411C3×M16—22no—
412C2×C3×C8—21no—
413C2×C3×C8—21no—
414C2×C3×C8—31no—
415C2×C3×C8—31no—
416C2×C3×C8—62no—
417C2×C3×C8C22×D311yescharacteristic
418C2×C3×C8C22×D311yescharacteristic
419C2×C3×C8C23×C311yescharacteristic
420C2×C3×C8C23×C311yescharacteristic
421C3×C4⋊C4—31no—
422C3×C4⋊C4—31no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—61no—
425C3×C4⋊C4—61no—
426C3×C4⋊C4—61no—
427C3×C22⋊C4—31no—
428C3×C22⋊C4—31no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C22⋊C4—61no—
433C3×C22⋊C4—61no—
434C3×C22⋊C4—61no—
435C3×C42—31no—
436C3×C42—61no—
437C3×C42—61no—
438#217—21no—
439#217C3×D411yescharacteristic
440#215—22no—
441#215—22no—
442#215—41no—
443#213—41no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4—21no—
448(C2×D3)⋊C4—21no—
449(C2×D3)⋊C4C3×D411yescharacteristic
450C4⋊Dic3—21no—
451C4⋊Dic3—21no—
452C4⋊Dic3C23×C311yescharacteristic
453C4⋊Dic3C23×C311yescharacteristic
454Dic3⋊C4—21no—
455Dic3⋊C4C3×D411yescharacteristic
456C4×Dic3—21no—
457C4×Dic3—21no—
458C4×Dic3C23×C311yescharacteristic
459C2×C3⋊C8C23×C311yescharacteristic
460C2×C3⋊C8C23×C311yescharacteristic
461D24—22no—
462D3×C8—22no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C32×C4—21no—
480C32×C4—22no—
481C32×C4—22no—
482C32×C4—41no—
483C32×C4C22×D411yescharacteristic
484C32×C4H(5,𝔽2)11yescharacteristic
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—31no—
492C2×#41C2×C3×D311yescharacteristic
493C22×Q8C2×C3×D311yescharacteristic
494#137—24no—
495#135—64no—
496C2×Q16C2×C3×D311yescharacteristic
497C2×Q16C2×C3×D311yescharacteristic
498C2×SD16—31no—
499C2×SD16—31no—
500C2×SD16—31no—
501C2×SD16C2×C3×D311yescharacteristic
502C2×SD16C2×C3×D311yescharacteristic
503C2×D8—31no—
504C2×D8—31no—
505C2×M16C2×C3×D311yescharacteristic
506C22×C8—31no—
507#127—31no—
508#127—61no—
509#124—31no—
510#124—61no—
511C22⋊Q8—31no—
512C22⋊Q8—61no—
513#121—31no—
514#121—31no—
515#121—31no—
516#121—61no—
517#121—61no—
518#121—61no—
519C4×Q8—31no—
520C4×Q8—31no—
521C4×D4—31no—
522C4×D4—61no—
523C4×D4—61no—
524#106—31no—
525C4⋊C8—31no—
526#103—31no—
527#103—31no—
528#103—31no—
529#102—31no—
530#102—31no—
531#102—31no—
532C22⋊C8—31no—
533C22⋊C8—31no—
534#97—31no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—31no—
539C23×C3—41no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3D3×D411yescharacteristic
543C23×C3C2×C3×D411yescharacteristic
544C22×D3—21no—
545C22×D3—21no—
546C22×D3C2×C3×D411yescharacteristic
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—22no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—22no—
557C3×Q8—22no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×Q8—41no—
561C3×Q8—42no—
562C3×Q8—42no—
563C3×Q8—44no—
564C3×Q8C2×#6712yes—
565C3×Q8C2×#6712yes—
566C3×Q8C2×C3×D412yes—
567C3×Q8C2×C3×D412yes—
568C3×D4—22no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—41no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—44no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—122no—
582C3×D4—122no—
583C3×D4—121no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—241no—
587C3×D4—241no—
588C3×D4—241no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
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—31no—
604C2×C3×C4—31no—
605C2×C3×C4—31no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—42no—
612C2×C3×C4—42no—
613C2×C3×C4—44no—
614C2×C3×C4—44no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—122no—
620C2×C3×C4—122no—
621C2×C3×C4D3×D411yescharacteristic
622C2×C3×C4C2×C3×D411yescharacteristic
623C2×C3×C4C23×D311yescharacteristic
624C2×C3×C4C24×C311yescharacteristic
625#67—41no—
626#67—42no—
627#67—42no—
628#67—81no—
629#67—81no—
630#67—81no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3C2×C3×D411yescharacteristic
634C2×Dic3C2×C3×D411yescharacteristic
635C2×Dic3C2×C3×D411yescharacteristic
636D12—21no—
637D12—21no—
638D12—21no—
639D12—21no—
640D12—42no—
641D12—42no—
642C4×D3—21no—
643C4×D3—21no—
644C4×D3—42no—
645C4×D3—42no—
646C3×C8—22no—
647C3×C8—21no—
648C3×C8—21no—
649C3×C8—22no—
650C3×C8—61no—
651C3×C8—61no—
652C3×C8C2×#6712yes—
653C3×C8C2×C3×D412yes—
654C3⋊C8—21no—
655C3⋊C8—21no—
656C2×C32—41no—
657C2×C32—81no—
658C2×C32D4211yescharacteristic
659C2×C32#57511yescharacteristic
660C2×C32#57711yescharacteristic
661C3×D3—41no—
662C3×D3—81no—
663C3×D3—81no—
664#41—22no—
665#41—41no—
666#41—62no—
667#41—62no—
668#41—121no—
669#41—121no—
670C2×Q8—21no—
671C2×Q8—22no—
672C2×Q8—41no—
673C2×Q8C22×C3×D311yescharacteristic
674C2×Q8C22×C3×D311yescharacteristic
675C2×Q8C22×C3×D311yescharacteristic
676C2×D4—21no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4C22×C3×D311yescharacteristic
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—31no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4C22×C3×D311yescharacteristic
694Q16—22no—
695Q16C3×#6714yescomplemented
696SD16—22no—
697SD16—22no—
698SD16—62no—
699SD16—62no—
700SD16—121no—
701D8—62no—
702D8—121no—
703M16—22no—
704C2×C8—31no—
705C2×C8—31no—
706C2×C8—62no—
707C2×C8C22×C3×D311yescharacteristic
708C2×C8C22×C3×D311yescharacteristic
709C4⋊C4—31no—
710C4⋊C4—31no—
711C4⋊C4—31no—
712C4⋊C4—61no—
713C4⋊C4—61no—
714C4⋊C4—61no—
715C22⋊C4—31no—
716C22⋊C4—31no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C42—31no—
724C42—61no—
725C42—61no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—42no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3C2×D3×D411yescharacteristic
755C22×C3C22×C3×D411yescharacteristic
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C3×C4—22no—
766C3×C4—21no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—42no—
775C3×C4—42no—
776C3×C4—42no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—61no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—121no—
783C3×C4—121no—
784C3×C4#100411yescharacteristic
785C3×C4C22×#6711yescharacteristic
786C3×C4C22×C3×D411yescharacteristic
787C3×C4C3×H(5,𝔽2)11yescharacteristic
788Dic3—21no—
789Dic3—21no—
790Dic3—21no—
791Dic3—41no—
792Dic3—41no—
793C32#327111yescharacteristic, complemented, Sylow
794C23—21no—
795C23—31no—
796C23—61no—
797C23—61no—
798C23C3×D3×D411yescharacteristic
799Q8—21no—
800Q8—21no—
801Q8—21no—
802Q8—21no—
803Q8—42no—
804Q8C2×C3×#6712yes—
805Q8C2×C3×#6712yes—
806D4—21no—
807D4—21no—
808D4—42no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—122no—
814D4—122no—
815D4—121no—
816D4—122no—
817D4—122no—
818D4—241no—
819D4—241no—
820D4—241no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—31no—
827C2×C4—31no—
828C2×C4—31no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4C3×D3×D411yescharacteristic
838C2×C4C23×C3×D311yescharacteristic
839C8—21no—
840C8—61no—
841C8—61no—
842C8C2×C3×#6712yes—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—42no—
847C2×C3—41no—
848C2×C3—41no—
849C2×C3—82no—
850C2×C3—81no—
851C2×C3—81no—
852C2×C3—121no—
853C2×C3—241no—
854C2×C3—241no—
855C2×C3#577711yescharacteristic
856C2×C3#577811yescharacteristic
857C2×C3D4×#6711yescharacteristic
858C2×C3C3×D4211yescharacteristic
859C2×C3C3×#57511yescharacteristic
860C2×C3C3×#57711yescharacteristic
861D3—41no—
862D3—81no—
863D3—81no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22C2×C3×D3×D411yescharacteristic
880C4—21no—
881C4—22no—
882C4—22no—
883C4—41no—
884C4—61no—
885C4—61no—
886C4—61no—
887C4—121no—
888C4—121no—
889C4C3×#100411yescharacteristic
890C4C22×C3×#6711yescharacteristic
891C3—21no—
892C3#8399011yescharacteristic, direct product factor
893C3C3×#327111yescharacteristic, complemented
894C2—41no—
895C2—81no—
896C2—121no—
897C2—241no—
898C2—241no—
899C2C3×#577711yescharacteristic
900C2C3×#577811yescharacteristic
901C2C3×D4×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
hypercenterC2×C3×#137D3
hypocenterC3C3×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
1. C2×C32×#137C2semidirect
2. C3×#5834C2semidirect
3. C3×#5817C2semidirect
4. C2×C3×#919C2semidirect
5. C3×#5238C2semidirect
6. C3×#5227C2semidirect
7. C3×#5187C2semidirect
8. C3×#5185C2semidirect
9. C3×#5184C2semidirect
10. C3×#5176C2semidirect
11. C3×#5172C2semidirect
12. C3×#5171C2semidirect
13. C3×#5163C2semidirect
14. C3×#5135C2semidirect
15. C3×#5127C2semidirect
17. #83990C3direct (N × H)
64. C2×C3×#137D3semidirect
65. C2×C3×#137C2×C3semidirect
69. #5834C2×C3semidirect
70. #5817C2×C3semidirect
71. C2×#919C2×C3semidirect
83. #5238C2×C3semidirect
84. #5227C2×C3semidirect
85. #5187C2×C3semidirect
86. #5185C2×C3semidirect
87. #5184C2×C3semidirect
88. #5176C2×C3semidirect
89. #5172C2×C3semidirect
90. #5171C2×C3semidirect
91. #5163C2×C3semidirect
92. #5135C2×C3semidirect
93. #5127C2×C3semidirect
125. C32×Q16D4semidirect
304. C2×#137C3×D3semidirect
396. C3×Q16#67semidirect
397. C3×Q16C3×D4semidirect
695. Q16C3×#67semidirect
793. C32#3271semidirect
892. C3#83990direct (N × H)
893. C3C3×#3271semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C3×#58342
C3×#58172
C2×C3×#9192
C3×#52382
C3×#52272
C3×#51872
C3×#51852
C3×#51842
C3×#51762
C3×#51722
C3×#51712
C3×#51632
C3×#51352
C3×#51272
C3×#32713
#839903