Finite Group Databasebeta

← C3×#80944 #11868158

Subgroups — C3×#80944 #11868158

Order 1152.

942 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5777C211yesmaximal, characteristic
2C3×D3×#137C211yesmaximal, characteristic, complemented
3C2×C3×#918C211yesmaximal, characteristic, complemented
4C3×#5750C211yesmaximal, characteristic, complemented
5C32×#473C211yesmaximal, characteristic, complemented
6C3×#5204C211yesmaximal, characteristic, complemented
7C3×#5203C211yesmaximal, characteristic, complemented
8C3×#5192C211yesmaximal, characteristic, complemented
9C3×#5141C211yesmaximal, characteristic, complemented
10C3×#4898C211yesmaximal, characteristic, complemented
11C3×#4893C211yesmaximal, characteristic, complemented
12C3×#4755C211yesmaximal, characteristic, complemented
13C3×#4754C211yesmaximal, characteristic, complemented
14C3×#4751C211yesmaximal, characteristic, complemented
15C3×D3×#101C211yesmaximal, characteristic, complemented
16C3×#3069—31nomaximal
17#80944C311yesmaximal, characteristic, direct product factor
18C3×D3×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C32×#137C2211yescharacteristic
22C32×#137C2211yescharacteristic
23C2×C32×Q16C2211yescharacteristic, complemented
24C32×#131C2211yescharacteristic
25C3×#951C2211yescharacteristic
26C3×#949C2211yescharacteristic
27C3×#948C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic, complemented
29C3×#942C2211yescharacteristic
30C3×#942C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic, complemented
32C3×#919—21no—
33C3×#918—21no—
34C3×#918—21no—
35C3×#918—21no—
36C3×#918—21no—
37C3×#918—21no—
38C3×#918—21no—
39C3×D3×Q16—21no—
40C3×#916—21no—
41C3×#915—21no—
42C3×#914—21no—
43C3×D3×SD16—21no—
44C3×#909C2211yescharacteristic
45C3×#908C2211yescharacteristic
46C3×#907—21no—
47C3×#907C2211yescharacteristic
48C3×D3×M16—21no—
49C3×D3×M16C2211yescharacteristic
50C3×D3×M16C2211yescharacteristic
51C3×D3×M16C2211yescharacteristic
52C2×C3×#204C2211yescharacteristic, complemented
53C3×#901—21no—
54C3×#901C2211yescharacteristic
55C2×C3×ΓL(1,𝔽25)—21no—
56C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
57C32×#108C2211yescharacteristic, complemented
58C32×#101C2211yescharacteristic, complemented
59C32×#101C2211yescharacteristic, complemented
60C3×#836C2211yescharacteristic, complemented
61C3×#836C2211yescharacteristic, complemented
62C3×#824C2211yescharacteristic, complemented
63C3×#824C2211yescharacteristic, complemented
64C3×#823C2211yescharacteristic, complemented
65C3×#823C2211yescharacteristic, complemented
66C3×#822C2211yescharacteristic, complemented
67C3×#822C2211yescharacteristic, complemented
68C3×#819C2211yescharacteristic, complemented
69C3×#575—31no—
70C2×C3×#137—31no—
71C2×C3×#137—31no—
72C3×#568—31no—
73#5777C2×C311yescharacteristic
74D3×#137C2×C311yescharacteristic, complemented
75C2×#918C2×C311yescharacteristic, complemented
76#5750C2×C311yescharacteristic, complemented
77C3×#473—21no—
78C3×#473—31no—
79C3×#473—31no—
80C3×#473—31no—
81C3×#473D311yescharacteristic, complemented
82C3×#473C2×C311yescharacteristic, complemented
83C3×#471—31no—
84C3×#471—31no—
85C3×#471—31no—
86C3×#471—31no—
87C3×#430—31no—
88C3×#413—31no—
89C2×C3×#101—31no—
90#5204C2×C311yescharacteristic, complemented
91#5203C2×C311yescharacteristic, complemented
92#5192C2×C311yescharacteristic, complemented
93#5141C2×C311yescharacteristic, complemented
94#4898C2×C311yescharacteristic, complemented
95#4893C2×C311yescharacteristic, complemented
96#4755C2×C311yescharacteristic, complemented
97#4754C2×C311yescharacteristic, complemented
98#4751C2×C311yescharacteristic, complemented
99D3×#101C2×C311yescharacteristic, complemented
100C32×#41C2311yescharacteristic
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2311yescharacteristic
103C3×#239—21no—
104C3×#239—21no—
105C3×#239—21no—
106C3×#239—21no—
107C3×#239D411yescharacteristic
108C3×D3×Q8—21no—
109C3×D3×Q8—21no—
110C3×D3×Q8—21no—
111C3×D3×Q8—21no—
112C3×D3×Q8D411yescharacteristic
113C3×#237—21no—
114C3×#237D411yescharacteristic
115C3×D3×D4—21no—
116C3×D3×D4D411yescharacteristic
117C3×#235—21no—
118C3×#235C2311yescharacteristic
119C2×C3×D12—21no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×Dic6—21no—
126C2×C3×Dic6C2311yescharacteristic
127C32×Q16—21no—
128C32×Q16—21no—
129C32×Q16—21no—
130C32×Q16—21no—
131C32×SD16—21no—
132C32×SD16—21no—
133C32×M16—21no—
134C32×M16C2311yescharacteristic
135C32×M16C2311yescharacteristic
136C32×M16C2311yescharacteristic
137C2×C32×C8—21no—
138C2×C32×C8C2311yescharacteristic
139C3×#216—21no—
140C3×#216—21no—
141C3×#216—21no—
142C3×#216—21no—
143C3×#216—21no—
144C3×#215—21no—
145C3×#215—21no—
146C3×#215—21no—
147C3×#215—21no—
148C3×#215—21no—
149C3×#214—21no—
150C3×#213—21no—
151C3×#208—21no—
152C3×#208C2311yescharacteristic
153C3×#208C2311yescharacteristic
154C3×#208C2311yescharacteristic
155C2×C3×C3⋊C8—21no—
156C2×C3×C3⋊C8C2311yescharacteristic
157C3×Dic12—21no—
158C3×D24—21no—
159C3×#204—21no—
160C3×#204—21no—
161C3×#204—21no—
162C3×#204—21no—
163C3×ΓL(1,𝔽25)—21no—
164C3×ΓL(1,𝔽25)—21no—
165C3×ΓL(1,𝔽25)—21no—
166C3×ΓL(1,𝔽25)—21no—
167C3×ΓL(1,𝔽25)—21no—
168C3×ΓL(1,𝔽25)D411yescharacteristic
169C3×ΓL(1,𝔽25)D411yescharacteristic
170C3×ΓL(1,𝔽25)D411yescharacteristic
171C3×ΓL(1,𝔽25)D411yescharacteristic
172C3×D3×C8—21no—
173C3×D3×C8—21no—
174C3×D3×C8—21no—
175C3×D3×C8—21no—
176C3×D3×C8—21no—
177#3069—31noSylow
178C2×C3×#41—31no—
179C2×C3×#41—31no—
180C22×C3×Q8—31no—
181D3×#41C22×C311yescharacteristic
182C2×#239C22×C311yescharacteristic
183C2×D3×Q8C22×C311yescharacteristic
184C3×#137—21no—
185C3×#137—21no—
186C3×#137—31no—
187C3×#137—31no—
188C3×#137—31no—
189C3×#137—31no—
190C3×#137—61no—
191C3×#137—61no—
192C3×#137—61no—
193C3×#137—61no—
194C3×#137—61no—
195C3×#137—61no—
196C3×#137—61no—
197C3×#137C2×D311yescharacteristic
198C3×#137C2×D311yescharacteristic
199C3×#137C22×C311yescharacteristic
200C3×#137C22×C311yescharacteristic
201C3×AGL(1,ℤ/8)—31no—
202C3×AGL(1,ℤ/8)—31no—
203C3×AGL(1,ℤ/8)—61no—
204C3×#135—61no—
205C3×#135—61no—
206C2×C3×Q16—21no—
207C2×C3×Q16—31no—
208C2×C3×Q16—61no—
209C2×C3×Q16C2×D311yescharacteristic, complemented
210C2×C3×Q16C22×C311yescharacteristic, complemented
211C2×C3×SD16—31no—
212C2×C3×SD16—31no—
213C2×C3×SD16—61no—
214C3×#131—21no—
215C3×#131—31no—
216C3×#131—31no—
217C3×#131—31no—
218C3×#131—61no—
219C3×#131—61no—
220C3×#131C2×D311yescharacteristic
221C3×#131C22×C311yescharacteristic
222C2×C3×M16—31no—
223C2×C3×M16—31no—
224C2×C3×M16—31no—
225C2×C3×M16—31no—
226C2×C3×M16—61no—
227C2×C3×M16—61no—
228#951C22×C311yescharacteristic
229#949C22×C311yescharacteristic
230#948C22×C311yescharacteristic
231C2×#216C22×C311yescharacteristic, complemented
232#942C22×C311yescharacteristic
233#942C22×C311yescharacteristic
234C2×#215C22×C311yescharacteristic, complemented
235#919—21no—
236#918—21no—
237#918—21no—
238#918—21no—
239#918—21no—
240#918—21no—
241#918—21no—
242D3×Q16—21no—
243#916—21no—
244#915—21no—
245#914—21no—
246D3×SD16—21no—
247#909C22×C311yescharacteristic
248#908C22×C311yescharacteristic
249#907—21no—
250#907C22×C311yescharacteristic
251D3×M16—21no—
252D3×M16C22×C311yescharacteristic
253D3×M16C22×C311yescharacteristic
254D3×M16C22×C311yescharacteristic
255C2×#204C22×C311yescharacteristic, complemented
256#901—21no—
257#901C22×C311yescharacteristic
258C2×ΓL(1,𝔽25)—21no—
259C2×ΓL(1,𝔽25)C22×C311yescharacteristic
260C3×#108—21no—
261C3×#108—31no—
262C3×#108—31no—
263C3×#108—31no—
264C3×#108C2×D311yescharacteristic, complemented
265C3×#108C22×C311yescharacteristic, complemented
266C3×#101—21no—
267C3×#101—21no—
268C3×#101—31no—
269C3×#101—31no—
270C3×#101—31no—
271C3×#101—31no—
272C3×#101C2×D311yescharacteristic, complemented
273C3×#101C2×D311yescharacteristic, complemented
274C3×#101C22×C311yescharacteristic, complemented
275C3×#101C22×C311yescharacteristic, complemented
276C3×#100—31no—
277C3×#100—31no—
278#836C22×C311yescharacteristic, complemented
279#836C22×C311yescharacteristic, complemented
280#824C22×C311yescharacteristic, complemented
281#824C22×C311yescharacteristic, complemented
282#823C22×C311yescharacteristic, complemented
283#823C22×C311yescharacteristic, complemented
284#822C22×C311yescharacteristic, complemented
285#822C22×C311yescharacteristic, complemented
286#819C22×C311yescharacteristic, complemented
287C22×C3×D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3#4111yescharacteristic
290C32×Q8—21no—
291C32×Q8—21no—
292C32×Q8—21no—
293C32×Q8—21no—
294C32×Q8C2×D411yescharacteristic
295C32×D4—21no—
296C32×D4C2×D411yescharacteristic
297C2×C32×C4—21no—
298C2×C32×C4—21no—
299C2×C32×C4—21no—
300C2×C32×C4C2411yescharacteristic
301C3×#67—21no—
302C3×#67—21no—
303C3×#67—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3#4111yescharacteristic
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—41no—
311C3×D12—41no—
312C3×D12C2×D411yescharacteristic
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3—41no—
317C3×C4×D3—41no—
318C3×C4×D3—41no—
319C3×C4×D3—41no—
320C3×C4×D3C2×D411yescharacteristic
321C3×C4×D3C2×D411yescharacteristic
322C3×C4×D3C2×D411yescharacteristic
323C3×C4×D3C2×D411yescharacteristic
324C3×Dic6—21no—
325C3×Dic6—21no—
326C3×Dic6—21no—
327C3×Dic6—41no—
328C3×Dic6—41no—
329C3×Dic6C2×D411yescharacteristic
330C32×C8—21no—
331C32×C8—21no—
332C32×C8—21no—
333C32×C8C2×D411yescharacteristic
334C32×C8C2×D411yescharacteristic
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340#575—31no—
341C2×#137—31no—
342C2×#137—31no—
343#568—31no—
344#473—31no—
345#473—31no—
346#473—31no—
347#473C3×D311yescharacteristic, complemented
348#471—31no—
349#471—31no—
350#471—31no—
351#471—31no—
352#430—31no—
353#413—31no—
354C2×#101—31no—
355C3×#41—21no—
356C3×#41—31no—
357C3×#41—31no—
358C3×#41—31no—
359C3×#41—61no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41C22×D311yescharacteristic
366C3×#41C23×C311yescharacteristic
367C2×C3×Q8—21no—
368C2×C3×Q8—21no—
369C2×C3×Q8—31no—
370C2×C3×Q8—31no—
371C2×C3×Q8—61no—
372C2×C3×Q8—61no—
373C2×C3×Q8—61no—
374C2×C3×Q8—61no—
375C2×C3×Q8—61no—
376C2×C3×Q8C22×D311yescharacteristic
377C2×C3×Q8C22×D311yescharacteristic
378C2×C3×Q8C23×C311yescharacteristic
379C2×C3×Q8C23×C311yescharacteristic
380C2×C3×D4—31no—
381C2×C3×D4—31no—
382C2×C3×D4—61no—
383C2×C3×D4—61no—
384C22×C3×C4—31no—
385C22×C3×C4—61no—
386C22×C3×C4—61no—
387C22×C3×C4—61no—
388#239—21no—
389#239—21no—
390#239—21no—
391#239—21no—
392#239C3×D411yescharacteristic
393D3×Q8—21no—
394D3×Q8—21no—
395D3×Q8—21no—
396D3×Q8—21no—
397D3×Q8C3×D411yescharacteristic
398#237—21no—
399#237C3×D411yescharacteristic
400D3×D4—21no—
401D3×D4C3×D411yescharacteristic
402#235—21no—
403#235C23×C311yescharacteristic
404C2×D12—21no—
405C2×D12C23×C311yescharacteristic
406C2×C4×D3—21no—
407C2×C4×D3—21no—
408C2×C4×D3—21no—
409C2×C4×D3C23×C311yescharacteristic
410C2×Dic6—21no—
411C2×Dic6C23×C311yescharacteristic
412C3×Q16—21no—
413C3×Q16—21no—
414C3×Q16—21no—
415C3×Q16—21no—
416C3×Q16—21no—
417C3×Q16—21no—
418C3×Q16—21no—
419C3×Q16—21no—
420C3×Q16—41no—
421C3×Q16—41no—
422C3×Q16—41no—
423C3×Q16—41no—
424C3×Q16—61no—
425C3×Q16—61no—
426C3×Q16—61no—
427C3×Q16—61no—
428C3×Q16—61no—
429C3×Q16—61no—
430C3×SD16—21no—
431C3×SD16—21no—
432C3×SD16—21no—
433C3×SD16—21no—
434C3×SD16—41no—
435C3×SD16—41no—
436C3×SD16—61no—
437C3×SD16—61no—
438C3×SD16—61no—
439C3×SD16—61no—
440C3×SD16—61no—
441C3×SD16—61no—
442C3×SD16—61no—
443C3×SD16—61no—
444C3×SD16—61no—
445C3×SD16—61no—
446C3×D8—61no—
447C3×D8—61no—
448C3×M16—21no—
449C3×M16—21no—
450C3×M16—21no—
451C3×M16—21no—
452C3×M16—21no—
453C3×M16—31no—
454C3×M16—31no—
455C3×M16—31no—
456C3×M16—31no—
457C3×M16—31no—
458C3×M16—31no—
459C3×M16—31no—
460C3×M16—41no—
461C3×M16—61no—
462C3×M16—61no—
463C3×M16—61no—
464C3×M16—61no—
465C3×M16—61no—
466C3×M16—61no—
467C3×M16C22×D311yescharacteristic
468C3×M16C22×D311yescharacteristic
469C3×M16C22×D311yescharacteristic
470C3×M16C23×C311yescharacteristic
471C3×M16C23×C311yescharacteristic
472C3×M16C23×C311yescharacteristic
473C2×C3×C8—21no—
474C2×C3×C8—21no—
475C2×C3×C8—21no—
476C2×C3×C8—31no—
477C2×C3×C8—41no—
478C2×C3×C8—61no—
479C2×C3×C8—61no—
480C2×C3×C8—61no—
481C2×C3×C8—61no—
482C2×C3×C8—61no—
483C2×C3×C8—61no—
484C2×C3×C8C22×D311yescharacteristic
485C2×C3×C8C23×C311yescharacteristic
486#216—21no—
487#216—21no—
488#216—21no—
489#216—21no—
490#216—21no—
491#215—21no—
492#215—21no—
493#215—21no—
494#215—21no—
495#215—21no—
496#214—21no—
497#213—21no—
498#208—21no—
499#208C23×C311yescharacteristic
500#208C23×C311yescharacteristic
501#208C23×C311yescharacteristic
502C2×C3⋊C8—21no—
503C2×C3⋊C8C23×C311yescharacteristic
504Dic12—21no—
505D24—21no—
506#204—21no—
507#204—21no—
508#204—21no—
509#204—21no—
510ΓL(1,𝔽25)—21no—
511ΓL(1,𝔽25)—21no—
512ΓL(1,𝔽25)—21no—
513ΓL(1,𝔽25)—21no—
514ΓL(1,𝔽25)—21no—
515ΓL(1,𝔽25)C3×D411yescharacteristic
516ΓL(1,𝔽25)C3×D411yescharacteristic
517ΓL(1,𝔽25)C3×D411yescharacteristic
518ΓL(1,𝔽25)C3×D411yescharacteristic
519D3×C8—21no—
520D3×C8—21no—
521D3×C8—21no—
522D3×C8—21no—
523D3×C8—21no—
524C22×C32—21no—
525C22×C32C2×#4111yescharacteristic
526C2×C3×D3—21no—
527C2×C3×D3—41no—
528C2×C3×D3—41no—
529C2×C3×D3—81no—
530C2×C3×D3—81no—
531C2×C3×D3#12111yescharacteristic
532C2×C3×D3#12111yescharacteristic
533C32×C4—21no—
534C32×C4—41no—
535C32×C4—41no—
536C32×C4C22×D411yescharacteristic
537C32×C4C22×D411yescharacteristic
538C3×Dic3—21no—
539C3×Dic3—41no—
540C3×Dic3#12111yescharacteristic
541C3×Dic3#12111yescharacteristic
542C2×#41—31no—
543C2×#41—31no—
544C22×Q8—31no—
545#137—31no—
546#137—31no—
547#137—31no—
548#137—31no—
549#137—61no—
550#137—61no—
551#137—61no—
552#137—61no—
553#137—61no—
554#137—61no—
555#137—61no—
556#137C2×C3×D311yescharacteristic
557#137C2×C3×D311yescharacteristic
558AGL(1,ℤ/8)—31no—
559AGL(1,ℤ/8)—31no—
560AGL(1,ℤ/8)—61no—
561#135—61no—
562#135—61no—
563C2×Q16—31no—
564C2×Q16—61no—
565C2×Q16C2×C3×D311yescharacteristic, complemented
566C2×SD16—31no—
567C2×SD16—31no—
568C2×SD16—61no—
569#131—31no—
570#131—31no—
571#131—31no—
572#131—61no—
573#131—61no—
574#131C2×C3×D311yescharacteristic
575C2×M16—31no—
576C2×M16—31no—
577C2×M16—31no—
578C2×M16—31no—
579C2×M16—61no—
580C2×M16—61no—
581#108—31no—
582#108—31no—
583#108—31no—
584#108C2×C3×D311yescharacteristic, complemented
585#101—31no—
586#101—31no—
587#101—31no—
588#101—31no—
589#101C2×C3×D311yescharacteristic, complemented
590#101C2×C3×D311yescharacteristic, complemented
591#100—31no—
592#100—31no—
593C23×C3—31no—
594C23×C3—61no—
595C23×C3—61no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3C3×#4111yescharacteristic
599C3×Q8—21no—
600C3×Q8—21no—
601C3×Q8—21no—
602C3×Q8—21no—
603C3×Q8—21no—
604C3×Q8—21no—
605C3×Q8—21no—
606C3×Q8—21no—
607C3×Q8—21no—
608C3×Q8—31no—
609C3×Q8—41no—
610C3×Q8—41no—
611C3×Q8—41no—
612C3×Q8—41no—
613C3×Q8—61no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8—121no—
617C3×Q8—121no—
618C3×Q8D3×D411yescharacteristic
619C3×Q8C2×C3×D411yescharacteristic
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—31no—
624C3×D4—41no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—61no—
629C3×D4—61no—
630C3×D4—61no—
631C3×D4—121no—
632C3×D4—121no—
633C3×D4D3×D411yescharacteristic
634C3×D4C2×C3×D411yescharacteristic
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—31no—
643C2×C3×C4—31no—
644C2×C3×C4—31no—
645C2×C3×C4—31no—
646C2×C3×C4—31no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—121no—
656C2×C3×C4—121no—
657C2×C3×C4—121no—
658C2×C3×C4—121no—
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C24×C311yescharacteristic
661#67—21no—
662#67—21no—
663#67—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3C3×#4111yescharacteristic
667D12—21no—
668D12—21no—
669D12—21no—
670D12—41no—
671D12—41no—
672D12C2×C3×D411yescharacteristic
673C4×D3—21no—
674C4×D3—21no—
675C4×D3—21no—
676C4×D3—41no—
677C4×D3—41no—
678C4×D3—41no—
679C4×D3—41no—
680C4×D3C2×C3×D411yescharacteristic
681C4×D3C2×C3×D411yescharacteristic
682C4×D3C2×C3×D411yescharacteristic
683C4×D3C2×C3×D411yescharacteristic
684Dic6—21no—
685Dic6—21no—
686Dic6—21no—
687Dic6—41no—
688Dic6—41no—
689Dic6C2×C3×D411yescharacteristic
690C3×C8—21no—
691C3×C8—21no—
692C3×C8—21no—
693C3×C8—21no—
694C3×C8—21no—
695C3×C8—21no—
696C3×C8—21no—
697C3×C8—21no—
698C3×C8—31no—
699C3×C8—31no—
700C3×C8—41no—
701C3×C8—41no—
702C3×C8—41no—
703C3×C8—61no—
704C3×C8—61no—
705C3×C8—61no—
706C3×C8D3×D411yescharacteristic
707C3×C8D3×D411yescharacteristic
708C3×C8C2×C3×D411yescharacteristic
709C3×C8C2×C3×D411yescharacteristic
710C3⋊C8—21no—
711C3⋊C8—21no—
712C3⋊C8—21no—
713C3⋊C8C2×C3×D411yescharacteristic
714C3⋊C8C2×C3×D411yescharacteristic
715C2×C32—21no—
716C2×C32—41no—
717C2×C32C2×#12111yescharacteristic
718C3×D3—21no—
719C3×D3—21no—
720C3×D3—41no—
721C3×D3—81no—
722#41—31no—
723#41—31no—
724#41—31no—
725#41—61no—
726#41—61no—
727#41—61no—
728#41—61no—
729#41—61no—
730#41—61no—
731#41C22×C3×D311yescharacteristic
732C2×Q8—31no—
733C2×Q8—31no—
734C2×Q8—61no—
735C2×Q8—61no—
736C2×Q8—61no—
737C2×Q8—61no—
738C2×Q8—61no—
739C2×Q8C22×C3×D311yescharacteristic
740C2×Q8C22×C3×D311yescharacteristic
741C2×D4—31no—
742C2×D4—31no—
743C2×D4—61no—
744C2×D4—61no—
745C22×C4—31no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749Q16—21no—
750Q16—21no—
751Q16—21no—
752Q16—21no—
753Q16—61no—
754Q16—61no—
755Q16—61no—
756Q16—61no—
757Q16—61no—
758Q16—61no—
759SD16—21no—
760SD16—21no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—61no—
766SD16—61no—
767SD16—61no—
768SD16—61no—
769SD16—61no—
770SD16—61no—
771D8—61no—
772D8—61no—
773M16—21no—
774M16—31no—
775M16—31no—
776M16—31no—
777M16—31no—
778M16—31no—
779M16—31no—
780M16—31no—
781M16—61no—
782M16—61no—
783M16—61no—
784M16—61no—
785M16—61no—
786M16—61no—
787M16C22×C3×D311yescharacteristic
788M16C22×C3×D311yescharacteristic
789M16C22×C3×D311yescharacteristic
790C2×C8—21no—
791C2×C8—31no—
792C2×C8—61no—
793C2×C8—61no—
794C2×C8—61no—
795C2×C8—61no—
796C2×C8—61no—
797C2×C8—61no—
798C2×C8C22×C3×D311yescharacteristic
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—31no—
803C22×C3—31no—
804C22×C3—41no—
805C22×C3—61no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—241no—
809C22×C3—241no—
810C22×C3D3×#4111yescharacteristic
811C22×C3C2×C3×#4111yescharacteristic
812C2×D3—21no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—81no—
816C2×D3—81no—
817C2×D3C3×#12111yescharacteristic
818C2×D3C3×#12111yescharacteristic
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—31no—
824C3×C4—31no—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—41no—
830C3×C4—61no—
831C3×C4—81no—
832C3×C4—81no—
833C3×C4—121no—
834C3×C4C2×D3×D411yescharacteristic
835C3×C4C2×D3×D411yescharacteristic
836C3×C4C22×C3×D411yescharacteristic
837C3×C4C22×C3×D411yescharacteristic
838Dic3—21no—
839Dic3—41no—
840Dic3C3×#12111yescharacteristic
841Dic3C3×#12111yescharacteristic
842C32#306911yescharacteristic, complemented, Sylow
843C23—31no—
844C23—61no—
845C23—61no—
846Q8—21no—
847Q8—21no—
848Q8—21no—
849Q8—21no—
850Q8—31no—
851Q8—61no—
852Q8—61no—
853Q8—61no—
854Q8—121no—
855Q8—121no—
856Q8C3×D3×D411yescharacteristic
857D4—21no—
858D4—31no—
859D4—61no—
860D4—61no—
861D4—61no—
862D4—61no—
863D4—61no—
864D4—61no—
865D4—121no—
866D4—121no—
867D4C3×D3×D411yescharacteristic
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—31no—
872C2×C4—31no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—31no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—121no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4C23×C3×D311yescharacteristic
886C8—21no—
887C8—21no—
888C8—21no—
889C8—31no—
890C8—31no—
891C8—61no—
892C8—61no—
893C8—61no—
894C8C3×D3×D411yescharacteristic
895C8C3×D3×D411yescharacteristic
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—41no—
900C2×C3—41no—
901C2×C3—41no—
902C2×C3—61no—
903C2×C3—61no—
904C2×C3—81no—
905C2×C3—121no—
906C2×C3—241no—
907C2×C3D3×#12111yescharacteristic
908C2×C3C2×C3×#12111yescharacteristic
909D3—21no—
910D3—21no—
911D3—41no—
912D3—81no—
913C22—21no—
914C22—31no—
915C22—31no—
916C22—61no—
917C22—121no—
918C22—121no—
919C22—241no—
920C22—241no—
921C22C3×D3×#4111yescharacteristic
922C4—21no—
923C4—31no—
924C4—31no—
925C4—41no—
926C4—41no—
927C4—61no—
928C4—121no—
929C4C2×C3×D3×D411yescharacteristic
930C4C2×C3×D3×D411yescharacteristic
931C3—21no—
932C3#8094411yescharacteristic, direct product factor
933C3C3×#306911yescharacteristic, complemented
934C2—21no—
935C2—41no—
936C2—61no—
937C2—61no—
938C2—121no—
939C2—241no—
940C2C3×D3×#12111yescharacteristic
subgroupG/H
centerC2×C3D3×#121
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#473C2
socleC2×C32C2×#121
prime radicalC3×#5777C2
hypercenterC3×#473D3
hypocenterC3C3×#3069
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#473

Complements

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

NH ≅ G/Ntype
2. C3×D3×#137C2semidirect
3. C2×C3×#918C2semidirect
4. C3×#5750C2semidirect
5. C32×#473C2semidirect
6. C3×#5204C2semidirect
7. C3×#5203C2semidirect
8. C3×#5192C2semidirect
9. C3×#5141C2semidirect
10. C3×#4898C2semidirect
11. C3×#4893C2semidirect
12. C3×#4755C2semidirect
13. C3×#4754C2semidirect
14. C3×#4751C2semidirect
15. C3×D3×#101C2semidirect
17. #80944C3direct (N × H)
23. C2×C32×Q16C22semidirect
28. C2×C3×#216C22semidirect
31. C2×C3×#215C22semidirect
52. C2×C3×#204C22semidirect
57. C32×#108C22semidirect
58. C32×#101C22semidirect
59. C32×#101C22semidirect
60. C3×#836C22semidirect
61. C3×#836C22semidirect
62. C3×#824C22semidirect
63. C3×#824C22semidirect
64. C3×#823C22semidirect
65. C3×#823C22semidirect
66. C3×#822C22semidirect
67. C3×#822C22semidirect
68. C3×#819C22semidirect
74. D3×#137C2×C3semidirect
75. C2×#918C2×C3semidirect
76. #5750C2×C3semidirect
81. C3×#473D3semidirect
82. C3×#473C2×C3semidirect
90. #5204C2×C3semidirect
91. #5203C2×C3semidirect
92. #5192C2×C3semidirect
93. #5141C2×C3semidirect
94. #4898C2×C3semidirect
95. #4893C2×C3semidirect
96. #4755C2×C3semidirect
97. #4754C2×C3semidirect
98. #4751C2×C3semidirect
99. D3×#101C2×C3semidirect
209. C2×C3×Q16C2×D3semidirect
210. C2×C3×Q16C22×C3semidirect
231. C2×#216C22×C3semidirect
234. C2×#215C22×C3semidirect
255. C2×#204C22×C3semidirect
264. C3×#108C2×D3semidirect
265. C3×#108C22×C3semidirect
272. C3×#101C2×D3semidirect
273. C3×#101C2×D3semidirect
274. C3×#101C22×C3semidirect
275. C3×#101C22×C3semidirect
278. #836C22×C3semidirect
279. #836C22×C3semidirect
280. #824C22×C3semidirect
281. #824C22×C3semidirect
282. #823C22×C3semidirect
283. #823C22×C3semidirect
284. #822C22×C3semidirect
285. #822C22×C3semidirect
286. #819C22×C3semidirect
347. #473C3×D3semidirect
565. C2×Q16C2×C3×D3semidirect
584. #108C2×C3×D3semidirect
589. #101C2×C3×D3semidirect
590. #101C2×C3×D3semidirect
842. C32#3069semidirect
932. C3#80944direct (N × H)
933. C3C3×#3069semidirect

Maximal subgroups

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

subgroupindex
C3×#57772
C3×D3×#1372
C2×C3×#9182
C3×#57502
C32×#4732
C3×#52042
C3×#52032
C3×#51922
C3×#51412
C3×#48982
C3×#48932
C3×#47552
C3×#47542
C3×#47512
C3×D3×#1012
C3×#30693
#809443