Finite Group Databasebeta

← C3×#83988 #11884515

Subgroups — C3×#83988 #11884515

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic, complemented
2C3×#5824C211yesmaximal, characteristic, complemented
3C3×#5817C211yesmaximal, characteristic, complemented
4C2×C3×#916C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6C3×#5228C211yesmaximal, characteristic, complemented
7C3×#5190C211yesmaximal, characteristic, complemented
8C3×#5188C211yesmaximal, characteristic, complemented
9C3×#5187C211yesmaximal, characteristic, complemented
10C3×#5182C211yesmaximal, characteristic, complemented
11C3×#5173C211yesmaximal, characteristic, complemented
12C3×#5165C211yesmaximal, characteristic, complemented
13C3×#5164C211yesmaximal, characteristic, complemented
14C3×#5134C211yesmaximal, characteristic, complemented
15C3×#5127C211yesmaximal, characteristic, complemented
16C3×#3269—31nomaximal
17#83988C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×#237C2211yescharacteristic
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×#946C2211yescharacteristic
33C3×Q8×Dic3C2211yescharacteristic
34C3×#944C2211yescharacteristic
35C2×C3×#216C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic
37C2×C3×#215C2211yescharacteristic
38C3×#939—21no—
39C3×#935—21no—
40C3×D4×Dic3C2211yescharacteristic
41C2×C3×#213C2211yescharacteristic
42C3×#930—21no—
43C3×#930C2211yescharacteristic
44C3×#929—21no—
45C3×C4×#67—21no—
46C3×C4×#67C2211yescharacteristic
47C3×#924C2211yescharacteristic
48C2×C3×Dic3⋊C4—21no—
49C3×#916—24no—
50C2×C3×#204C2211yescharacteristic
51C2×C3×D3×C8C2211yescharacteristic
52C3×#835C2211yescharacteristic
53C3×#835C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#832C2211yescharacteristic
56C3×#830C2211yescharacteristic
57C3×#821C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×#818C2211yescharacteristic
60C3×#816C2211yescharacteristic
61C3×#815C2211yescharacteristic
62C3×Dic3⋊C8C2211yescharacteristic
63C2×C3×#137—21no—
64C2×C3×#137D311yescharacteristic, complemented
65C2×C3×#137C2×C311yescharacteristic, complemented
66C2×C3×#135—31no—
67C3×#548—31no—
68C3×#547—31no—
69#5824C2×C311yescharacteristic, complemented
70#5817C2×C311yescharacteristic, complemented
71C2×#916C2×C311yescharacteristic, complemented
72C3×#497—31no—
73C3×#468—31no—
74C3×#467—31no—
75C3×#463—31no—
76C3×#462—31no—
77C3×#452—31no—
78C3×#452—31no—
79C3×#451—31no—
80C3×#449—31no—
81C3×#440—31no—
82C3×#435—31no—
83#5238C2×C311yescharacteristic, complemented
84#5228C2×C311yescharacteristic, complemented
85#5190C2×C311yescharacteristic, complemented
86#5188C2×C311yescharacteristic, complemented
87#5187C2×C311yescharacteristic, complemented
88#5182C2×C311yescharacteristic, complemented
89#5173C2×C311yescharacteristic, complemented
90#5165C2×C311yescharacteristic, complemented
91#5164C2×C311yescharacteristic, complemented
92#5134C2×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×#67D411yescharacteristic
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C3×#239—22no—
113C3×#239—41no—
114C3×#237—22no—
115C3×#237—41no—
116C2×C3×D12—21no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×Q16—22no—
122C32×Q16—22no—
123C32×SD16—22no—
124C32×SD16D414yescomplemented
125C32×M16—22no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—22no—
132C3×#216—41no—
133C3×#215—41no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4—21no—
149C3×Dic3⋊C4D411yescharacteristic
150C3×C4×Dic3—21no—
151C3×C4×Dic3C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C3×#204—22no—
155C3×D3×C8—22no—
156#3269—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×#237C22×C311yescharacteristic
167C3×#137—28no—
168C3×#137—24no—
169C3×#137—24no—
170C3×#135—64no—
171C2×C3×Q16—21no—
172C2×C3×Q16—21no—
173C2×C3×Q16—31no—
174C2×C3×Q16—31no—
175C2×C3×Q16C2×D311yescharacteristic
176C2×C3×Q16C2×D311yescharacteristic
177C2×C3×Q16C22×C311yescharacteristic
178C2×C3×Q16C22×C311yescharacteristic
179C2×C3×SD16—21no—
180C2×C3×SD16—21no—
181C2×C3×SD16—31no—
182C2×C3×SD16—31no—
183C2×C3×SD16C2×D311yescharacteristic
184C2×C3×SD16C2×D311yescharacteristic
185C2×C3×SD16C22×C311yescharacteristic
186C2×C3×SD16C22×C311yescharacteristic
187C2×C3×D8—31no—
188C2×C3×M16—21no—
189C2×C3×M16C2×D311yescharacteristic
190C2×C3×M16C22×C311yescharacteristic
191C22×C3×C8—31no—
192C3×C4⋊Q8—31no—
193C3×#124—31no—
194C3×#124—61no—
195C3×#123—61no—
196C3×#123—61no—
197C3×C22⋊Q8—31no—
198C3×C22⋊Q8—31no—
199C3×C22⋊Q8—31no—
200C3×C22⋊Q8—61no—
201C3×#121—31no—
202C3×#121—61no—
203C3×#121—61no—
204C3×C4×Q8—31no—
205C3×C4×D4—31no—
206C3×C4×D4—31no—
207C3×C4×D4—61no—
208C2×C3×C4⋊C4—61no—
209#947—21no—
210#947C22×C311yescharacteristic
211#946—21no—
212#946C22×C311yescharacteristic
213#946C22×C311yescharacteristic
214Q8×Dic3C22×C311yescharacteristic
215#944C22×C311yescharacteristic
216C2×#216C22×C311yescharacteristic
217C2×#216C22×C311yescharacteristic
218C2×#215C22×C311yescharacteristic
219#939—21no—
220#935—21no—
221D4×Dic3C22×C311yescharacteristic
222C2×#213C22×C311yescharacteristic
223#930—21no—
224#930C22×C311yescharacteristic
225#929—21no—
226C4×#67—21no—
227C4×#67C22×C311yescharacteristic
228#924C22×C311yescharacteristic
229C2×Dic3⋊C4—21no—
230#916—24no—
231C2×#204C22×C311yescharacteristic
232C2×D3×C8C22×C311yescharacteristic
233C3×#107—31no—
234C3×C4⋊C8—31no—
235C3×#103—31no—
236C3×#103—31no—
237C3×#103—31no—
238C3×#103—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(C2×D3)⋊C8C22×C311yescharacteristic
251#818C22×C311yescharacteristic
252#816C22×C311yescharacteristic
253#815C22×C311yescharacteristic
254Dic3⋊C8C22×C311yescharacteristic
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C32×Q8—21no—
260C32×Q8—21no—
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—42no—
265C32×Q8C2×D412yes—
266C32×D4—21no—
267C32×D4—42no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4—42no—
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278C3×#67—41no—
279C3×#67—42no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—42no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C32×C8—21no—
298C32×C8C2×D412yes—
299C3×C3⋊C8—21no—
300C3×C3⋊C8—21no—
301C2×#137C3×D311yescharacteristic, complemented
302C2×#135—31no—
303#548—31no—
304#547—31no—
305#497—31no—
306#468—31no—
307#467—31no—
308#463—31no—
309#462—31no—
310#452—31no—
311#452—31no—
312#451—31no—
313#449—31no—
314#440—31no—
315#435—31no—
316C3×#41—24no—
317C3×#41—22no—
318C3×#41—22no—
319C3×#41—41no—
320C3×#41—41no—
321C3×#41—42no—
322C3×#41—62no—
323C3×#41—62no—
324C3×#41—121no—
325C3×#41—121no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8—24no—
329C2×C3×Q8—22no—
330C2×C3×Q8—22no—
331C2×C3×Q8—21no—
332C2×C3×Q8—21no—
333C2×C3×Q8—21no—
334C2×C3×Q8—31no—
335C2×C3×Q8—41no—
336C2×C3×Q8—41no—
337C2×C3×Q8—41no—
338C2×C3×Q8—42no—
339C2×C3×Q8C22×D311yescharacteristic
340C2×C3×Q8C22×D311yescharacteristic
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×Q8C23×C311yescharacteristic
343C2×C3×Q8C23×C311yescharacteristic
344C2×C3×Q8C23×C311yescharacteristic
345C2×C3×D4—21no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—41no—
351C2×C3×D4—61no—
352C2×C3×D4—61no—
353C2×C3×D4—61no—
354C2×C3×D4C22×D311yescharacteristic
355C2×C3×D4C23×C311yescharacteristic
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—31no—
362C22×C3×C4—41no—
363C22×C3×C4—41no—
364C22×C3×C4—61no—
365C22×C3×C4—61no—
366C22×C3×C4—61no—
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C23×C311yescharacteristic
369C2×#67—21no—
370C2×#67—21no—
371C2×#67C3×D411yescharacteristic
372C22×Dic3—21no—
373C22×Dic3—21no—
374#239—22no—
375#239—41no—
376#237—22no—
377#237—41no—
378C2×D12—21no—
379C2×D12C23×C311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3C23×C311yescharacteristic
382C2×Dic6C23×C311yescharacteristic
383C3×Q16—24no—
384C3×Q16—24no—
385C3×Q16—22no—
386C3×Q16—22no—
387C3×Q16—22no—
388C3×Q16—22no—
389C3×Q16—62no—
390C3×Q16—121no—
391C3×SD16—24no—
392C3×SD16—22no—
393C3×SD16—22no—
394C3×SD16—24no—
395C3×SD16—62no—
396C3×SD16—121no—
397C3×SD16#6714yescomplemented
398C3×SD16C3×D414yescomplemented
399C3×D8—62no—
400C3×M16—24no—
401C3×M16—22no—
402C3×M16—22no—
403C2×C3×C8—21no—
404C2×C3×C8—21no—
405C2×C3×C8—31no—
406C2×C3×C8—31no—
407C2×C3×C8—62no—
408C2×C3×C8C22×D311yescharacteristic
409C2×C3×C8C22×D311yescharacteristic
410C2×C3×C8C23×C311yescharacteristic
411C2×C3×C8C23×C311yescharacteristic
412C3×C4⋊C4—31no—
413C3×C4⋊C4—31no—
414C3×C4⋊C4—31no—
415C3×C4⋊C4—61no—
416C3×C4⋊C4—61no—
417C3×C4⋊C4—61no—
418C3×C4⋊C4—61no—
419C3×C4⋊C4—61no—
420C3×C4⋊C4—61no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C42—31no—
431C3×C42—61no—
432#217—21no—
433#217—21no—
434#217C3×D411yescharacteristic
435#216—22no—
436#216—41no—
437#215—41no—
438#213—22no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4C3×D411yescharacteristic
445C4⋊Dic3—21no—
446C4⋊Dic3C23×C311yescharacteristic
447C4⋊Dic3C23×C311yescharacteristic
448Dic3⋊C4—21no—
449Dic3⋊C4—21no—
450Dic3⋊C4—21no—
451Dic3⋊C4—21no—
452Dic3⋊C4—21no—
453Dic3⋊C4C3×D411yescharacteristic
454C4×Dic3—21no—
455C4×Dic3C23×C311yescharacteristic
456C2×C3⋊C8C23×C311yescharacteristic
457C2×C3⋊C8C23×C311yescharacteristic
458#204—22no—
459D3×C8—22no—
460C22×C32—21no—
461C22×C32—22no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C32×C4—21no—
474C32×C4—22no—
475C32×C4—41no—
476C32×C4—41no—
477C32×C4C22×D411yescharacteristic
478C32×C4H(5,𝔽2)11yescharacteristic
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—31no—
487C2×#41C2×C3×D311yescharacteristic
488C22×Q8C2×C3×D311yescharacteristic
489#137—24no—
490#135—64no—
491C2×Q16—31no—
492C2×Q16—31no—
493C2×Q16C2×C3×D311yescharacteristic
494C2×Q16C2×C3×D311yescharacteristic
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16C2×C3×D311yescharacteristic
498C2×SD16C2×C3×D311yescharacteristic
499C2×D8—31no—
500C2×M16C2×C3×D311yescharacteristic
501C22×C8—31no—
502C4⋊Q8—31no—
503#124—31no—
504#124—61no—
505#123—61no—
506#123—61no—
507C22⋊Q8—31no—
508C22⋊Q8—31no—
509C22⋊Q8—31no—
510C22⋊Q8—61no—
511#121—31no—
512#121—61no—
513#121—61no—
514C4×Q8—31no—
515C4×D4—31no—
516C4×D4—31no—
517C4×D4—61no—
518C2×C4⋊C4—61no—
519#107—31no—
520C4⋊C8—31no—
521#103—31no—
522#103—31no—
523#103—31no—
524#103—31no—
525#102—31no—
526#102—31no—
527C22⋊C8—31no—
528C22⋊C8—31no—
529#97—31no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—31no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3D3×D411yescharacteristic
537C23×C3C2×C3×D411yescharacteristic
538C22×D3—21no—
539C22×D3C2×C3×D411yescharacteristic
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—22no—
543C3×Q8—22no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—22no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×Q8—42no—
557C3×Q8—42no—
558C3×Q8—44no—
559C3×Q8—61no—
560C3×Q8—61no—
561C3×Q8C2×#6712yes—
562C3×Q8C2×C3×D412yes—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—22no—
566C3×D4—41no—
567C3×D4—42no—
568C3×D4—42no—
569C3×D4—44no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—122no—
573C3×D4—121no—
574C3×D4—122no—
575C3×D4—122no—
576C3×D4C2×#6712yes—
577C3×D4C2×C3×D412yes—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—42no—
599C2×C3×C4—42no—
600C2×C3×C4—42no—
601C2×C3×C4—42no—
602C2×C3×C4—44no—
603C2×C3×C4—44no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—122no—
610C2×C3×C4—122no—
611C2×C3×C4—122no—
612C2×C3×C4D3×D411yescharacteristic
613C2×C3×C4C2×C3×D411yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C24×C311yescharacteristic
616#67—41no—
617#67—42no—
618#67—42no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—42no—
623C2×Dic3—42no—
624C2×Dic3C2×C3×D411yescharacteristic
625C2×Dic3C2×C3×D411yescharacteristic
626C2×Dic3C2×C3×D411yescharacteristic
627D12—21no—
628D12—21no—
629D12—42no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—42no—
633Dic6—21no—
634Dic6—21no—
635C3×C8—22no—
636C3×C8—21no—
637C3×C8—21no—
638C3×C8—22no—
639C3×C8—61no—
640C3×C8—61no—
641C3×C8C2×#6712yes—
642C3×C8C2×C3×D412yes—
643C3⋊C8—21no—
644C3⋊C8—21no—
645C2×C32—41no—
646C2×C32—42no—
647C2×C32D4211yescharacteristic
648C2×C32#57511yescharacteristic
649C2×C32#57811yescharacteristic
650C3×D3—41no—
651C3×D3—81no—
652#41—22no—
653#41—41no—
654#41—62no—
655#41—62no—
656#41—121no—
657#41—121no—
658C2×Q8—21no—
659C2×Q8—22no—
660C2×Q8—31no—
661C2×Q8—41no—
662C2×Q8C22×C3×D311yescharacteristic
663C2×Q8C22×C3×D311yescharacteristic
664C2×Q8C22×C3×D311yescharacteristic
665C2×D4—21no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4C22×C3×D311yescharacteristic
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—31no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4C22×C3×D311yescharacteristic
679Q16—22no—
680Q16—22no—
681Q16—62no—
682Q16—121no—
683SD16—22no—
684SD16—62no—
685SD16—121no—
686SD16C3×#6714yescomplemented
687D8—62no—
688M16—22no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—62no—
692C2×C8C22×C3×D311yescharacteristic
693C2×C8C22×C3×D311yescharacteristic
694C4⋊C4—31no—
695C4⋊C4—31no—
696C4⋊C4—31no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4—61no—
701C4⋊C4—61no—
702C4⋊C4—61no—
703C22⋊C4—31no—
704C22⋊C4—31no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C42—31no—
713C42—61no—
714C22×C3—22no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—42no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3C2×D3×D411yescharacteristic
740C22×C3C22×C3×D411yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C3×C4—22no—
748C3×C4—21no—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—42no—
755C3×C4—42no—
756C3×C4—42no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4—121no—
767C3×C4#100411yescharacteristic
768C3×C4C22×#6711yescharacteristic
769C3×C4C22×C3×D411yescharacteristic
770C3×C4C3×H(5,𝔽2)11yescharacteristic
771Dic3—21no—
772Dic3—21no—
773Dic3—21no—
774Dic3—41no—
775Dic3—41no—
776Dic3—41no—
777C32#326911yescharacteristic, complemented, Sylow
778C23—21no—
779C23—31no—
780C23—61no—
781C23C3×D3×D411yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—21no—
785Q8—21no—
786Q8—21no—
787Q8—42no—
788Q8—61no—
789Q8—61no—
790Q8C2×C3×#6712yes—
791D4—21no—
792D4—42no—
793D4—61no—
794D4—61no—
795D4—122no—
796D4—121no—
797D4—122no—
798D4—122no—
799D4C2×C3×#6712yes—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—122no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4C3×D3×D411yescharacteristic
819C2×C4C23×C3×D311yescharacteristic
820C8—21no—
821C8—61no—
822C8—61no—
823C8C2×C3×#6712yes—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—42no—
828C2×C3—41no—
829C2×C3—42no—
830C2×C3—41no—
831C2×C3—42no—
832C2×C3—82no—
833C2×C3—121no—
834C2×C3—241no—
835C2×C3#577711yescharacteristic
836C2×C3#577911yescharacteristic
837C2×C3D4×#6711yescharacteristic
838C2×C3C3×D4211yescharacteristic
839C2×C3C3×#57511yescharacteristic
840C2×C3C3×#57811yescharacteristic
841D3—41no—
842D3—81no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—61no—
850C22—61no—
851C22—61no—
852C22—121no—
853C22—121no—
854C22—121no—
855C22C2×C3×D3×D411yescharacteristic
856C4—21no—
857C4—22no—
858C4—41no—
859C4—41no—
860C4—61no—
861C4—61no—
862C4—61no—
863C4—121no—
864C4—121no—
865C4—121no—
866C4C3×#100411yescharacteristic
867C4C22×C3×#6711yescharacteristic
868C3—21no—
869C3#8398811yescharacteristic, direct product factor
870C3C3×#326911yescharacteristic, complemented
871C2—41no—
872C2—42no—
873C2—121no—
874C2—241no—
875C2C3×#577711yescharacteristic
876C2C3×#577911yescharacteristic
877C2C3×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×#3269
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×#5824C2semidirect
3. C3×#5817C2semidirect
4. C2×C3×#916C2semidirect
5. C3×#5238C2semidirect
6. C3×#5228C2semidirect
7. C3×#5190C2semidirect
8. C3×#5188C2semidirect
9. C3×#5187C2semidirect
10. C3×#5182C2semidirect
11. C3×#5173C2semidirect
12. C3×#5165C2semidirect
13. C3×#5164C2semidirect
14. C3×#5134C2semidirect
15. C3×#5127C2semidirect
17. #83988C3direct (N × H)
64. C2×C3×#137D3semidirect
65. C2×C3×#137C2×C3semidirect
69. #5824C2×C3semidirect
70. #5817C2×C3semidirect
71. C2×#916C2×C3semidirect
83. #5238C2×C3semidirect
84. #5228C2×C3semidirect
85. #5190C2×C3semidirect
86. #5188C2×C3semidirect
87. #5187C2×C3semidirect
88. #5182C2×C3semidirect
89. #5173C2×C3semidirect
90. #5165C2×C3semidirect
91. #5164C2×C3semidirect
92. #5134C2×C3semidirect
93. #5127C2×C3semidirect
124. C32×SD16D4semidirect
301. C2×#137C3×D3semidirect
397. C3×SD16#67semidirect
398. C3×SD16C3×D4semidirect
686. SD16C3×#67semidirect
777. C32#3269semidirect
869. C3#83988direct (N × H)
870. C3C3×#3269semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C3×#58242
C3×#58172
C2×C3×#9162
C3×#52382
C3×#52282
C3×#51902
C3×#51882
C3×#51872
C3×#51822
C3×#51732
C3×#51652
C3×#51642
C3×#51342
C3×#51272
C3×#32693
#839883