Finite Group Databasebeta

← C3×#83900 #11865736

Subgroups — C3×#83900 #11865736

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#135C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic, complemented
3C3×Dic3×#41C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5185C211yesmaximal, characteristic, complemented
7C3×#5182C211yesmaximal, characteristic, complemented
8C3×#5166C211yesmaximal, characteristic, complemented
9C3×#5165C211yesmaximal, characteristic, complemented
10C3×#5163C211yesmaximal, characteristic, complemented
11C3×#5162C211yesmaximal, characteristic, complemented
12C3×#5153C211yesmaximal, characteristic, complemented
13C3×#5150C211yesmaximal, characteristic, complemented
14C3×#5113C211yesmaximal, characteristic, complemented
15C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
16C3×#3035—31nomaximal
17#83900C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C32×#41C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×#135—24no—
22C2×C32×Q16C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic
24C2×C32×SD16C2211yescharacteristic
25C2×C32×D8C2211yescharacteristic
26C22×C32×C8C2211yescharacteristic
27C3×#950—24no—
28C3×#947C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×Q8×Dic3C2211yescharacteristic
31C3×#944C2211yescharacteristic
32C2×C3×#216C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic
34C3×#940C2211yescharacteristic
35C3×#939—21no—
36C3×#939—21no—
37C3×#936C2211yescharacteristic
38C3×D4×Dic3—21no—
39C3×D4×Dic3—21no—
40C3×D4×Dic3C2211yescharacteristic
41C3×D4×Dic3C2211yescharacteristic
42C2×C3×#214C2211yescharacteristic
43C2×C3×#213C2211yescharacteristic
44C3×C4×#67—21no—
45C3×C4×#67—21no—
46C3×#926—21no—
47C3×#926C2211yescharacteristic
48C2×C3×C4×Dic3—21no—
49C2×C3×C4×Dic3C2211yescharacteristic
50C22×C3×C3⋊C8C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×#835C2211yescharacteristic
53C3×#832C2211yescharacteristic
54C3×#832C2211yescharacteristic
55C3×#821C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×Dic3⋊C8C2211yescharacteristic
60C3×Dic3⋊C8C2211yescharacteristic
61C3×Dic3⋊C8C2211yescharacteristic
62C3×Dic3⋊C8C2211yescharacteristic
63C2×C3×#135—21no—
64C2×C3×#135—31no—
65C2×C3×#135D311yescharacteristic, complemented
66C2×C3×#135C2×C311yescharacteristic, complemented
67C3×#532—31no—
68C3×C4×#41—31no—
69#5832C2×C311yescharacteristic, complemented
70Dic3×#41C2×C311yescharacteristic, complemented
71C2×#950C2×C311yescharacteristic, complemented
72C3×#464—31no—
73C3×#464—31no—
74C3×#463—31no—
75C3×#463—31no—
76C3×#462—31no—
77C3×#461—31no—
78C3×#460—31no—
79C3×#459—31no—
80C2×C3×C4⋊C8—31no—
81C3×#416—31no—
82C3×#416—31no—
83#5233C2×C311yescharacteristic, complemented
84#5185C2×C311yescharacteristic, complemented
85#5182C2×C311yescharacteristic, complemented
86#5166C2×C311yescharacteristic, complemented
87#5165C2×C311yescharacteristic, complemented
88#5163C2×C311yescharacteristic, complemented
89#5162C2×C311yescharacteristic, complemented
90#5153C2×C311yescharacteristic, complemented
91#5150C2×C311yescharacteristic, complemented
92#5113C2×C311yescharacteristic, complemented
93C2×Dic3⋊C8C2×C311yescharacteristic, complemented
94C32×#41—22no—
95C32×#41—22no—
96C32×#41—22no—
97C32×#41D414yescomplemented
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4C2311yescharacteristic
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—
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C22×C3×Dic3D411yescharacteristic
113C22×C3×Dic3D411yescharacteristic
114C3×#235—22no—
115C3×#235—22no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×Dic6C2311yescharacteristic
119C32×Q16—22no—
120C32×SD16—22no—
121C32×SD16—22no—
122C32×D8—22no—
123C2×C32×C8—22no—
124C2×C32×C8C2311yescharacteristic
125C2×C32×C8C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#216—22no—
132C3×#215—22no—
133C3×#214—22no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×C4×Dic3—21no—
144C3×C4×Dic3—21no—
145C3×C4×Dic3—21no—
146C3×C4×Dic3D411yescharacteristic
147C3×C4×Dic3D411yescharacteristic
148C3×C4×Dic3C2311yescharacteristic
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153#3035—31noSylow
154C2×C3×#41—21no—
155C2×C3×#41—21no—
156C2×C3×#41—31no—
157C2×C3×#41C2×D311yescharacteristic
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C22×C311yescharacteristic
160C2×C3×#41C22×C311yescharacteristic
161C2×#235C22×C311yescharacteristic
162C3×#135—28no—
163C3×#135—24no—
164C3×#135—24no—
165C3×#135—64no—
166C2×C3×Q16—21no—
167C2×C3×Q16—31no—
168C2×C3×Q16C2×D311yescharacteristic
169C2×C3×Q16C22×C311yescharacteristic
170C2×C3×SD16—21no—
171C2×C3×SD16—21no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16C2×D311yescharacteristic
175C2×C3×SD16C2×D311yescharacteristic
176C2×C3×SD16C22×C311yescharacteristic
177C2×C3×SD16C22×C311yescharacteristic
178C2×C3×D8—21no—
179C2×C3×D8—31no—
180C2×C3×D8C2×D311yescharacteristic
181C2×C3×D8C22×C311yescharacteristic
182C22×C3×C8—21no—
183C22×C3×C8—31no—
184C22×C3×C8C2×D311yescharacteristic
185C22×C3×C8C22×C311yescharacteristic
186C3×C4⋊Q8—31no—
187C3×#127—31no—
188C3×#124—31no—
189C3×#124—31no—
190C3×#121—61no—
191C3×#121—61no—
192C3×C4×Q8—31no—
193C3×C4×Q8—31no—
194C3×C4×D4—31no—
195C3×C4×D4—31no—
196C3×C4×D4—61no—
197C3×C4×D4—61no—
198C3×C4×D4—61no—
199C3×C4×D4—61no—
200C3×#117—31no—
201C3×#117—61no—
202C2×C3×C42—31no—
203C2×C3×C42—61no—
204#950—24no—
205#947C22×C311yescharacteristic
206Q8×Dic3C22×C311yescharacteristic
207Q8×Dic3C22×C311yescharacteristic
208#944C22×C311yescharacteristic
209C2×#216C22×C311yescharacteristic
210C2×#215C22×C311yescharacteristic
211#940C22×C311yescharacteristic
212#939—21no—
213#939—21no—
214#936C22×C311yescharacteristic
215D4×Dic3—21no—
216D4×Dic3—21no—
217D4×Dic3C22×C311yescharacteristic
218D4×Dic3C22×C311yescharacteristic
219C2×#214C22×C311yescharacteristic
220C2×#213C22×C311yescharacteristic
221C4×#67—21no—
222C4×#67—21no—
223#926—21no—
224#926C22×C311yescharacteristic
225C2×C4×Dic3—21no—
226C2×C4×Dic3C22×C311yescharacteristic
227C22×C3⋊C8C22×C311yescharacteristic
228C3×C4⋊C8—31no—
229C3×C4⋊C8—31no—
230C3×C4⋊C8—31no—
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102—31no—
240#835C22×C311yescharacteristic
241#835C22×C311yescharacteristic
242#832C22×C311yescharacteristic
243#832C22×C311yescharacteristic
244#821C22×C311yescharacteristic
245#821C22×C311yescharacteristic
246#816C22×C311yescharacteristic
247#816C22×C311yescharacteristic
248Dic3⋊C8C22×C311yescharacteristic
249Dic3⋊C8C22×C311yescharacteristic
250Dic3⋊C8C22×C311yescharacteristic
251Dic3⋊C8C22×C311yescharacteristic
252C23×C32—21no—
253C23×C32—21no—
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C32×Q8—21no—
257C32×Q8—21no—
258C32×Q8—21no—
259C32×Q8C2×D412yes—
260C32×D4—21no—
261C32×D4—24no—
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—42no—
265C32×D4C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4—24no—
268C2×C32×C4—21no—
269C2×C32×C4—42no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2×D412yes—
272C2×C32×C4#4112yes—
273C2×C32×C4C2411yescharacteristic
274C3×#67—42no—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—41no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×C4×D3—42no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C32×C8—21no—
294C32×C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8—21no—
297C2×#135—31no—
298C2×#135C3×D311yescharacteristic, complemented
299#532—31no—
300C4×#41—31no—
301#464—31no—
302#464—31no—
303#463—31no—
304#463—31no—
305#462—31no—
306#461—31no—
307#460—31no—
308#459—31no—
309C2×C4⋊C8—31no—
310#416—31no—
311#416—31no—
312C3×#41—22no—
313C3×#41—22no—
314C3×#41—24no—
315C3×#41—22no—
316C3×#41—22no—
317C3×#41—22no—
318C3×#41—22no—
319C3×#41—24no—
320C3×#41—42no—
321C3×#41—42no—
322C3×#41—62no—
323C3×#41—62no—
324C3×#41#6714yescomplemented
325C3×#41C3×D414yescomplemented
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8—31no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C23×C311yescharacteristic
332C2×C3×Q8C23×C311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—31no—
340C2×C3×D4—41no—
341C2×C3×D4—41no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C2×C3×D4C23×C311yescharacteristic
348C2×C3×D4C23×C311yescharacteristic
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—41no—
357C22×C3×C4—41no—
358C22×C3×C4—61no—
359C22×C3×C4—61no—
360C22×C3×C4—61no—
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C23×C311yescharacteristic
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3C3×D411yescharacteristic
369C22×Dic3C3×D411yescharacteristic
370#235—22no—
371#235—22no—
372C2×D12C23×C311yescharacteristic
373C2×C4×D3—21no—
374C2×Dic6C23×C311yescharacteristic
375C3×Q16—24no—
376C3×Q16—22no—
377C3×Q16—22no—
378C3×Q16—62no—
379C3×SD16—24no—
380C3×SD16—24no—
381C3×SD16—22no—
382C3×SD16—22no—
383C3×SD16—22no—
384C3×SD16—22no—
385C3×SD16—62no—
386C3×SD16—62no—
387C3×D8—24no—
388C3×D8—22no—
389C3×D8—22no—
390C3×D8—62no—
391C2×C3×C8—24no—
392C2×C3×C8—22no—
393C2×C3×C8—22no—
394C2×C3×C8—21no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—62no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C23×C311yescharacteristic
402C2×C3×C8C23×C311yescharacteristic
403C3×C4⋊C4—31no—
404C3×C4⋊C4—31no—
405C3×C4⋊C4—61no—
406C3×C4⋊C4—61no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C42—31no—
417C3×C42—31no—
418C3×C42—31no—
419C3×C42—31no—
420C3×C42—61no—
421C3×C42—61no—
422C3×C42—61no—
423#217—21no—
424#217—21no—
425#217—21no—
426#217—21no—
427#217—21no—
428#216—22no—
429#215—22no—
430#214—22no—
431#213—22no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434C4⋊Dic3—21no—
435C4⋊Dic3—21no—
436C4⋊Dic3C23×C311yescharacteristic
437C4⋊Dic3C23×C311yescharacteristic
438Dic3⋊C4—21no—
439Dic3⋊C4—21no—
440C4×Dic3—21no—
441C4×Dic3—21no—
442C4×Dic3—21no—
443C4×Dic3C3×D411yescharacteristic
444C4×Dic3C3×D411yescharacteristic
445C4×Dic3C23×C311yescharacteristic
446C4×Dic3C23×C311yescharacteristic
447C2×C3⋊C8—22no—
448C2×C3⋊C8C23×C311yescharacteristic
449C2×C3⋊C8C23×C311yescharacteristic
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—22no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32#12112yes—
459C22×C32C22×D411yescharacteristic
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C32×C4—22no—
464C32×C4—41no—
465C32×C4#12112yes—
466C32×C4C22×D411yescharacteristic
467C32×C4C2×#4111yescharacteristic
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3—41no—
474C3×Dic3#13512yescomplemented
475C2×#41—31no—
476C2×#41C2×C3×D311yescharacteristic
477C2×#41C2×C3×D311yescharacteristic
478#135—24no—
479#135—64no—
480C2×Q16—31no—
481C2×Q16C2×C3×D311yescharacteristic
482C2×SD16—31no—
483C2×SD16—31no—
484C2×SD16C2×C3×D311yescharacteristic
485C2×SD16C2×C3×D311yescharacteristic
486C2×D8—31no—
487C2×D8C2×C3×D311yescharacteristic
488C22×C8—31no—
489C22×C8C2×C3×D311yescharacteristic
490C4⋊Q8—31no—
491#127—31no—
492#124—31no—
493#124—31no—
494#121—61no—
495#121—61no—
496C4×Q8—31no—
497C4×Q8—31no—
498C4×D4—31no—
499C4×D4—31no—
500C4×D4—61no—
501C4×D4—61no—
502C4×D4—61no—
503C4×D4—61no—
504#117—31no—
505#117—61no—
506C2×C42—31no—
507C2×C42—61no—
508C4⋊C8—31no—
509C4⋊C8—31no—
510C4⋊C8—31no—
511C4⋊C8—31no—
512#103—31no—
513#103—31no—
514#103—31no—
515#103—31no—
516#102—31no—
517#102—31no—
518#102—31no—
519#102—31no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—61no—
528C23×C3D3×D411yescharacteristic
529C23×C3C2×C3×D411yescharacteristic
530C22×D3—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—22no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—22no—
539C3×Q8—41no—
540C3×Q8—41no—
541C3×Q8—61no—
542C3×Q8—61no—
543C3×Q8C2×#6712yes—
544C3×Q8C2×C3×D412yes—
545C3×D4—24no—
546C3×D4—24no—
547C3×D4—22no—
548C3×D4—21no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—22no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—44no—
558C3×D4—44no—
559C3×D4—42no—
560C3×D4—42no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—122no—
564C3×D4—122no—
565C3×D4—122no—
566C3×D4C2×#6712yes—
567C3×D4C2×C3×D412yes—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—24no—
571C2×C3×C4—24no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—44no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—44no—
586C2×C3×C4—42no—
587C2×C3×C4—42no—
588C2×C3×C4—62no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—122no—
593C2×C3×C4—121no—
594C2×C3×C4—122no—
595C2×C3×C4—122no—
596C2×C3×C4D3×D411yescharacteristic
597C2×C3×C4#23712yes—
598C2×C3×C4C2×#6712yes—
599C2×C3×C4C2×C3×D411yescharacteristic
600C2×C3×C4C2×C3×D412yes—
601C2×C3×C4C3×#4112yes—
602C2×C3×C4C23×D311yescharacteristic
603C2×C3×C4C24×C311yescharacteristic
604#67—42no—
605#67—42no—
606#67—42no—
607C2×Dic3—22no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—41no—
612C2×Dic3—42no—
613C2×Dic3—42no—
614C2×Dic3C2×C3×D411yescharacteristic
615C2×Dic3C2×C3×D411yescharacteristic
616C2×Dic3C2×C3×D411yescharacteristic
617C2×Dic3C2×C3×D411yescharacteristic
618D12—21no—
619D12—21no—
620C4×D3—42no—
621Dic6—21no—
622Dic6—21no—
623C3×C8—22no—
624C3×C8—22no—
625C3×C8—21no—
626C3×C8—21no—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—61no—
630C3×C8—61no—
631C3⋊C8—21no—
632C3⋊C8—21no—
633C2×C32—22no—
634C2×C32—42no—
635C2×C32—81no—
636C2×C32C2×#12111yescharacteristic
637C2×C32C2×#13511yescharacteristic
638C2×C32#57511yescharacteristic
639C3×D3—81no—
640#41—22no—
641#41—22no—
642#41—22no—
643#41—62no—
644#41—62no—
645#41C3×#6714yescomplemented
646C2×Q8—31no—
647C2×Q8C22×C3×D311yescharacteristic
648C2×Q8C22×C3×D311yescharacteristic
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—31no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4C22×C3×D311yescharacteristic
656C2×D4C22×C3×D311yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4C22×C3×D311yescharacteristic
665Q16—22no—
666Q16—62no—
667SD16—22no—
668SD16—22no—
669SD16—62no—
670SD16—62no—
671D8—22no—
672D8—62no—
673C2×C8—22no—
674C2×C8—31no—
675C2×C8—31no—
676C2×C8—62no—
677C2×C8C22×C3×D311yescharacteristic
678C2×C8C22×C3×D311yescharacteristic
679C4⋊C4—31no—
680C4⋊C4—31no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—61no—
688C22⋊C4—61no—
689C22⋊C4—61no—
690C22⋊C4—61no—
691C22⋊C4—61no—
692C42—31no—
693C42—31no—
694C42—31no—
695C42—31no—
696C42—61no—
697C42—61no—
698C42—61no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—21no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—81no—
722C22×C3—81no—
723C22×C3—81no—
724C22×C3—81no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3#93912yes—
729C22×C3C3×#12112yes—
730C22×C3C2×D3×D411yescharacteristic
731C22×C3C22×C3×D411yescharacteristic
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—22no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—32no—
741C3×C4—42no—
742C3×C4—42no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—61no—
746C3×C4—61no—
747C3×C4—61no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4—121no—
751C3×C4#93912yes—
752C3×C4C3×#12112yes—
753C3×C4C2×#23711yescharacteristic
754C3×C4C22×#6711yescharacteristic
755C3×C4C22×C3×D411yescharacteristic
756C3×C4C2×C3×#4111yescharacteristic
757Dic3—21no—
758Dic3—21no—
759Dic3—21no—
760Dic3—41no—
761Dic3—41no—
762Dic3—41no—
763Dic3C3×#13512yescomplemented
764C32#303511yescharacteristic, complemented, Sylow
765C23—21no—
766C23—21no—
767C23—61no—
768C23C3×D3×D411yescharacteristic
769Q8—21no—
770Q8—21no—
771Q8—21no—
772Q8—61no—
773Q8—61no—
774Q8C2×C3×#6712yes—
775D4—24no—
776D4—21no—
777D4—21no—
778D4—21no—
779D4—42no—
780D4—61no—
781D4—61no—
782D4—122no—
783D4—122no—
784D4—122no—
785D4C2×C3×#6712yes—
786C2×C4—21no—
787C2×C4—24no—
788C2×C4—21no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—31no—
793C2×C4—42no—
794C2×C4—62no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—122no—
799C2×C4—121no—
800C2×C4—122no—
801C2×C4—122no—
802C2×C4C3×D3×D411yescharacteristic
803C2×C4C3×#23712yes—
804C2×C4C2×C3×#6712yes—
805C2×C4C23×C3×D311yescharacteristic
806C8—21no—
807C8—21no—
808C8—61no—
809C8—61no—
810C2×C3—22no—
811C2×C3—22no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—42no—
816C2×C3—42no—
817C2×C3—42no—
818C2×C3—82no—
819C2×C3—82no—
820C2×C3—81no—
821C2×C3—81no—
822C2×C3—241no—
823C2×C3D3×#13511yescharacteristic
824C2×C3#576811yescharacteristic
825C2×C3C2×#93911yescharacteristic
826C2×C3C2×C3×#12111yescharacteristic
827C2×C3C2×C3×#13511yescharacteristic
828C2×C3C3×#57511yescharacteristic
829D3—81no—
830C22—21no—
831C22—21no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22C3×#93912yes—
842C22C2×C3×D3×D411yescharacteristic
843C4—22no—
844C4—32no—
845C4—41no—
846C4—61no—
847C4—61no—
848C4—61no—
849C4—121no—
850C4—121no—
851C4—121no—
852C4C3×#93912yes—
853C4C2×C3×#23711yescharacteristic
854C4C22×C3×#6711yescharacteristic
855C3—21no—
856C3#8390011yescharacteristic, direct product factor
857C3C3×#303511yescharacteristic, complemented
858C2—22no—
859C2—42no—
860C2—81no—
861C2—241no—
862C2C3×D3×#13511yescharacteristic
863C2C3×#576811yescharacteristic
864C2C2×C3×#93911yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#135C2
socleC22×C32C22×D4
hypercenterC2×C3×#135D3
hypocenterC3C3×#3035
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#135

Complements

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

NH ≅ G/Ntype
1. C2×C32×#135C2semidirect
2. C3×#5832C2semidirect
3. C3×Dic3×#41C2semidirect
4. C2×C3×#950C2semidirect
5. C3×#5233C2semidirect
6. C3×#5185C2semidirect
7. C3×#5182C2semidirect
8. C3×#5166C2semidirect
9. C3×#5165C2semidirect
10. C3×#5163C2semidirect
11. C3×#5162C2semidirect
12. C3×#5153C2semidirect
13. C3×#5150C2semidirect
14. C3×#5113C2semidirect
15. C2×C3×Dic3⋊C8C2semidirect
17. #83900C3direct (N × H)
65. C2×C3×#135D3semidirect
66. C2×C3×#135C2×C3semidirect
69. #5832C2×C3semidirect
70. Dic3×#41C2×C3semidirect
71. C2×#950C2×C3semidirect
83. #5233C2×C3semidirect
84. #5185C2×C3semidirect
85. #5182C2×C3semidirect
86. #5166C2×C3semidirect
87. #5165C2×C3semidirect
88. #5163C2×C3semidirect
89. #5162C2×C3semidirect
90. #5153C2×C3semidirect
91. #5150C2×C3semidirect
92. #5113C2×C3semidirect
93. C2×Dic3⋊C8C2×C3semidirect
97. C32×#41D4semidirect
298. C2×#135C3×D3semidirect
324. C3×#41#67semidirect
325. C3×#41C3×D4semidirect
474. C3×Dic3#135semidirect
645. #41C3×#67semidirect
763. Dic3C3×#135semidirect
764. C32#3035semidirect
856. C3#83900direct (N × H)
857. C3C3×#3035semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1352
C3×#58322
C3×Dic3×#412
C2×C3×#9502
C3×#52332
C3×#51852
C3×#51822
C3×#51662
C3×#51652
C3×#51632
C3×#51622
C3×#51532
C3×#51502
C3×#51132
C2×C3×Dic3⋊C82
C3×#30353
#839003