Finite Group Databasebeta

← #11861160

Subgroups — #11861160

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5750C211yesmaximal, characteristic, complemented
2#10595453C211yesmaximal, characteristic
3#10594668C211yesmaximal, characteristic, complemented
4#10592843C211yesmaximal, characteristic, complemented
5C3×#5145C211yesmaximal, characteristic, complemented
6#10591673C211yesmaximal, characteristic, complemented
7D3×#837C211yesmaximal, characteristic, complemented
8#10591663C211yesmaximal, characteristic, complemented
9D3×#825C211yesmaximal, characteristic, complemented
10#10590995C211yesmaximal, characteristic, complemented
11#10590976C211yesmaximal, characteristic, complemented
12#10590973C211yesmaximal, characteristic, complemented
13#10590924C211yesmaximal, characteristic, complemented
14#10590921C211yesmaximal, characteristic, complemented
15#10590667C211yesmaximal, characteristic, complemented
16#83811—31nomaximal
17#79898—31nomaximal
18C3×D3×#41C2211yescharacteristic
19D3×#235C2211yescharacteristic
20C32×#131C2211yescharacteristic, complemented
21#64159C2211yescharacteristic
22#64110C2211yescharacteristic, complemented
23C3×#950C2211yescharacteristic
24C3×#948C2211yescharacteristic, complemented
25C3×#907—21no—
26C3×#907C2211yescharacteristic, complemented
27C3×D3×M16—21no—
28C3×D3×M16C2211yescharacteristic
29C3×#901—21no—
30C3×#901C2211yescharacteristic, complemented
31C3×#901C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)—21no—
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34#63948C411yescharacteristic, complemented
35#63946C411yescharacteristic, complemented
36#63943C411yescharacteristic, complemented
37#63939C411yescharacteristic, complemented
38#63934C411yescharacteristic, complemented
39#63932C411yescharacteristic, complemented
40#63929C411yescharacteristic, complemented
41#63925C411yescharacteristic, complemented
42C4×D3×Dic3C2211yescharacteristic
43#63829C2211yescharacteristic
44#63822C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63817C2211yescharacteristic, complemented
47#63814C2211yescharacteristic, complemented
48D3×#208C2211yescharacteristic
49#63805—21no—
50#63804—21no—
51#63791—21no—
52D3×ΓL(1,𝔽25)—21no—
53#63664C2211yescharacteristic, complemented
54#63652C2211yescharacteristic, complemented
55#63649C2211yescharacteristic, complemented
56C8×C3⋊Dic3C2211yescharacteristic, complemented
57C3×#837C2211yescharacteristic, complemented
58C3×#825C2211yescharacteristic, complemented
59C3×#822C2211yescharacteristic, complemented
60C3×#815C2211yescharacteristic, complemented
61#63578C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63570C2211yescharacteristic, complemented
64#63569C2211yescharacteristic, complemented
65#63568C2211yescharacteristic, complemented
66#63568C2211yescharacteristic, complemented
67#63554C2211yescharacteristic, complemented
68#63553C2211yescharacteristic, complemented
69C3×#568—31no—
70#5822—31no—
71#5768—31no—
72#5750—31no—
73#5750D311yescharacteristic, complemented
74#5745—31no—
75C3×#444—31no—
76C2×#837—31no—
77#5196—31no—
78#5145—31no—
79#5145—31no—
80#5145—31no—
81#5145D311yescharacteristic, complemented
82#5144—31no—
83#5144—31no—
84#5144—31no—
85#5144—31no—
86#5144—31no—
87#5144—31no—
88#5144—61no—
89C2×#825—31no—
90#5124—31no—
91Dic3×M16—31no—
92#4895—31no—
93#4893—31no—
94#4823—31no—
95#4823—31no—
96D3×#104—31no—
97D3×#104—31no—
98#4717—31no—
99#4707—31no—
100C32×#41C2311yescharacteristic
101#3828C2311yescharacteristic
102C3×#239C2×C411yescharacteristic
103C3×D3×Q8C2×C411yescharacteristic
104C3×#237—21no—
105C3×#237C2×C411yescharacteristic
106C3×D3×D4—21no—
107C3×D3×D4C2×C411yescharacteristic
108C3×#235—21no—
109C3×#235C2311yescharacteristic
110C3×#235C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113D3×#67—21no—
114#3804—21no—
115C2×D3×Dic3—21no—
116D3×D12C2×C411yescharacteristic
117C4×D32—21no—
118#3799C2×C411yescharacteristic
119#3798—21no—
120#3795C2×C411yescharacteristic
121D3×Dic6C2×C411yescharacteristic
122C32×M16—21no—
123C32×M16C2311yescharacteristic
124C2×C32×C8—21no—
125C2×C32×C8C2311yescharacteristic
126#3756C2×C411yescharacteristic, complemented
127#3755C2×C411yescharacteristic, complemented
128#3754C2×C411yescharacteristic, complemented
129#3753C2×C411yescharacteristic, complemented
130C4×C3⋊Dic3C2311yescharacteristic
131#3748C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3743—21no—
134C8×C3⋊D3—21no—
135C3×#216C2×C411yescharacteristic, complemented
136C3×#215C2×C411yescharacteristic, complemented
137C3×#214C2×C411yescharacteristic, complemented
138C3×#213C2×C411yescharacteristic, complemented
139C3×C4×Dic3C2311yescharacteristic
140C3×#208—21no—
141C3×#208C2311yescharacteristic
142C3×#208C2311yescharacteristic
143C2×C3×C3⋊C8—21no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C3×ΓL(1,𝔽25)—21no—
147C3×ΓL(1,𝔽25)—21no—
148C3×ΓL(1,𝔽25)—21no—
149C3×ΓL(1,𝔽25)—21no—
150C3×ΓL(1,𝔽25)D411yescharacteristic
151C3×ΓL(1,𝔽25)D411yescharacteristic
152C3×ΓL(1,𝔽25)D411yescharacteristic
153C3×ΓL(1,𝔽25)D411yescharacteristic
154C3×D3×C8—21no—
155C3×D3×C8—21no—
156C3×D3×C8—21no—
157C3×D3×C8—21no—
158Dic32—21no—
159#3719C2×C411yescharacteristic, complemented
160#3718C2×C411yescharacteristic, complemented
161#3717C2×C411yescharacteristic, complemented
162#3716C2×C411yescharacteristic, complemented
163#3715C2×C411yescharacteristic, complemented
164#3715C2×C411yescharacteristic, complemented
165#3714C2×C411yescharacteristic, complemented
166#3713C2×C411yescharacteristic, complemented
167#3712—21no—
168#3711—21no—
169#3711—21no—
170#3711C2×C411yescharacteristic
171#3711C2×C411yescharacteristic
172#3711C2×C411yescharacteristic
173#3711C2×C411yescharacteristic
174#3710—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#2956—91noSylow
178C2×C3×#41—31no—
179D3×#41—31no—
180D3×#41C2×D311yescharacteristic
181C2×#235—31no—
182C3×#135—31no—
183C3×#131—21no—
184C3×#131—31no—
185C3×#131—31no—
186C3×#131—31no—
187C3×#131—31no—
188C3×#131—61no—
189C3×#131—61no—
190C3×#131C2×D311yescharacteristic, complemented
191C3×#131C2×D311yescharacteristic, complemented
192C2×C3×M16—31no—
193C2×C3×M16—31no—
194C2×C3×M16—61no—
195C2×C3×M16—61no—
196#951—31no—
197#951—31no—
198#950—31no—
199#950—31no—
200#950—31no—
201#950—31no—
202#950—31no—
203#950—61no—
204#950C2×D311yescharacteristic
205#949—31no—
206#949—31no—
207#948—31no—
208#948C2×D311yescharacteristic, complemented
209#942—31no—
210#942—31no—
211#932—31no—
212#932—31no—
213C2×C4×Dic3—31no—
214C2×#208—31no—
215C2×#208—31no—
216#918—31no—
217#918—31no—
218#915—31no—
219#915—31no—
220#914—31no—
221#914—31no—
222#911—31no—
223#911—31no—
224#907—21no—
225#907—31no—
226#907—61no—
227#907—61no—
228#907—61no—
229#907C2×D311yescharacteristic, complemented
230D3×M16—21no—
231D3×M16—31no—
232D3×M16—61no—
233D3×M16—61no—
234D3×M16—61no—
235D3×M16C2×D311yescharacteristic
236#904—31no—
237#901—21no—
238#901—31no—
239#901—31no—
240#901—31no—
241#901—31no—
242#901—61no—
243#901—61no—
244#901C2×D311yescharacteristic, complemented
245#901C2×D311yescharacteristic, complemented
246C2×ΓL(1,𝔽25)—21no—
247C2×ΓL(1,𝔽25)—31no—
248C2×ΓL(1,𝔽25)—61no—
249C2×ΓL(1,𝔽25)C2×D311yescharacteristic
250C42×D3—31no—
251C3×#108—31no—
252C3×#104—31no—
253C3×#104—31no—
254C3×#97—31no—
255#837—31no—
256#837—31no—
257#837—31no—
258#837—31no—
259#837—31no—
260#837—61no—
261#837C2×D311yescharacteristic, complemented
262#825—31no—
263#825—31no—
264#825—31no—
265#825—31no—
266#825—31no—
267#825—61no—
268#825C2×D311yescharacteristic, complemented
269#822—31no—
270#822—31no—
271#822—31no—
272#822—31no—
273#822—31no—
274#822—61no—
275#822C2×D311yescharacteristic, complemented
276#819—31no—
277#815—31no—
278#815C2×D311yescharacteristic, complemented
279C8×Dic3—31no—
280C8×Dic3—31no—
281C8×Dic3—31no—
282C8×Dic3—31no—
283C8×Dic3—61no—
284#805—31no—
285#805—31no—
286#803—31no—
287C22×C3×D3—21no—
288C22×C3×D3#4111yescharacteristic
289C2×D32—21no—
290C32×Q8C22×C411yescharacteristic
291C32×D4—21no—
292C32×D4C22×C411yescharacteristic
293C2×C32×C4—21no—
294C2×C32×C4C2411yescharacteristic
295#638—21no—
296C2×C3⋊Dic3—21no—
297C4⋊(C3⋊D3)C22×C411yescharacteristic
298C4×C3⋊D3—21no—
299#634C22×C411yescharacteristic
300C3×#67—21no—
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×D12C22×C411yescharacteristic
309C3×D12C22×C411yescharacteristic
310C3×C4×D3—21no—
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3C22×C411yescharacteristic
315C3×C4×D3C22×C411yescharacteristic
316C3×C4×D3C2×D411yescharacteristic
317C3×C4×D3C2×D411yescharacteristic
318C3×Dic6—21no—
319C3×Dic6C22×C411yescharacteristic
320C3×Dic6C22×C411yescharacteristic
321#627—21no—
322#626—21no—
323#626—21no—
324#625—21no—
325#624—21no—
326D3×Dic3—21no—
327D3×Dic3—21no—
328D3×Dic3—42no—
329C32×C8—21no—
330C32×C8C2×D411yescharacteristic
331C32×C8C2×D411yescharacteristic
332C3⋊(C3⋊C8)—21no—
333C3⋊(C3⋊C8)C22×C411yescharacteristic
334C3⋊(C3⋊C8)C22×C411yescharacteristic
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8C22×C411yescharacteristic
338C3×C3⋊C8C22×C411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341#575—91no—
342#568—31no—
343#568—91no—
344#444—31no—
345#444—91no—
346#444—91no—
347#444—91no—
348#443—91no—
349#443—91no—
350#443—91no—
351#443—91no—
352#430—91no—
353C2×#104—91no—
354C2×#104—91no—
355C4×M16—91no—
356C3×#41—21no—
357C3×#41—31no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41C22×D311yescharacteristic
364C3×#41C22×D311yescharacteristic
365C2×C3×Q8—31no—
366C2×C3×D4—31no—
367C2×C3×D4—61no—
368C22×C3×C4—31no—
369C22×C3×C4—61no—
370C2×#67—61no—
371C22×Dic3—61no—
372#239—31no—
373#239C4×D311yescharacteristic
374D3×Q8—31no—
375D3×Q8C4×D311yescharacteristic
376#237—21no—
377#237—31no—
378#237—61no—
379#237C4×D311yescharacteristic
380D3×D4—21no—
381D3×D4—31no—
382D3×D4—61no—
383D3×D4C4×D311yescharacteristic
384#235—21no—
385#235—31no—
386#235—31no—
387#235—31no—
388#235—31no—
389#235—61no—
390#235—61no—
391#235—61no—
392#235—61no—
393#235C22×D311yescharacteristic
394#235C22×D311yescharacteristic
395C2×D12—31no—
396C2×C4×D3—21no—
397C2×C4×D3—61no—
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×C4×D3C22×D311yescharacteristic
401C2×Dic6—31no—
402C3×Q16—31no—
403C3×SD16—31no—
404C3×SD16—31no—
405C3×D8—31no—
406C3×M16—21no—
407C3×M16—21no—
408C3×M16—21no—
409C3×M16—31no—
410C3×M16—31no—
411C3×M16—31no—
412C3×M16—31no—
413C3×M16—31no—
414C3×M16—31no—
415C3×M16—41no—
416C3×M16—61no—
417C3×M16—61no—
418C3×M16—61no—
419C3×M16—61no—
420C3×M16—61no—
421C3×M16C22×D311yescharacteristic
422C3×M16C22×D311yescharacteristic
423C2×C3×C8—21no—
424C2×C3×C8—21no—
425C2×C3×C8—21no—
426C2×C3×C8—31no—
427C2×C3×C8—31no—
428C2×C3×C8—41no—
429C2×C3×C8—61no—
430C2×C3×C8—61no—
431C2×C3×C8—61no—
432C2×C3×C8—61no—
433C2×C3×C8—61no—
434C2×C3×C8C22×D311yescharacteristic
435C2×C3×C8C22×D311yescharacteristic
436C3×C42—31no—
437#216—31no—
438#216—31no—
439#216—31no—
440#216—31no—
441#216—31no—
442#216—61no—
443#216C4×D311yescharacteristic, complemented
444#215—31no—
445#215—31no—
446#215—31no—
447#215—31no—
448#215—31no—
449#215—61no—
450#215C4×D311yescharacteristic, complemented
451#214—31no—
452#214—31no—
453#214—31no—
454#214—31no—
455#214—31no—
456#214—61no—
457#214C4×D311yescharacteristic, complemented
458#213—31no—
459#213—31no—
460#213—31no—
461#213—31no—
462#213—31no—
463#213—61no—
464#213C4×D311yescharacteristic, complemented
465C4×Dic3—31no—
466C4×Dic3—31no—
467C4×Dic3—61no—
468C4×Dic3—61no—
469C4×Dic3—61no—
470C4×Dic3C22×D311yescharacteristic
471#208—21no—
472#208—31no—
473#208—31no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—31no—
478#208—61no—
479#208—61no—
480#208—61no—
481#208C22×D311yescharacteristic
482#208C22×D311yescharacteristic
483C2×C3⋊C8—21no—
484C2×C3⋊C8—31no—
485C2×C3⋊C8—31no—
486C2×C3⋊C8—61no—
487C2×C3⋊C8—61no—
488C2×C3⋊C8—61no—
489C2×C3⋊C8C22×D311yescharacteristic
490C2×C3⋊C8C22×D311yescharacteristic
491Dic12—31no—
492D24—31no—
493#204—31no—
494#204—31no—
495ΓL(1,𝔽25)—21no—
496ΓL(1,𝔽25)—21no—
497ΓL(1,𝔽25)—21no—
498ΓL(1,𝔽25)—21no—
499ΓL(1,𝔽25)—31no—
500ΓL(1,𝔽25)—31no—
501ΓL(1,𝔽25)—31no—
502ΓL(1,𝔽25)—31no—
503ΓL(1,𝔽25)—61no—
504ΓL(1,𝔽25)—61no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—61no—
509ΓL(1,𝔽25)—121no—
510ΓL(1,𝔽25)#6711yescharacteristic
511ΓL(1,𝔽25)#6711yescharacteristic
512ΓL(1,𝔽25)#6711yescharacteristic
513ΓL(1,𝔽25)#6711yescharacteristic
514D3×C8—21no—
515D3×C8—21no—
516D3×C8—21no—
517D3×C8—21no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—121no—
525C22×C32—21no—
526C22×C32C2×#4111yescharacteristic
527C2×C3⋊D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—81no—
532C2×C3×D3C4×D411yescharacteristic
533C2×C3×D3C4×D411yescharacteristic
534D32—81no—
535C32×C4—21no—
536C32×C4C23×C411yescharacteristic
537C32×C4C22×D411yescharacteristic
538C3⋊Dic3—22no—
539C3⋊Dic3—21no—
540C3×Dic3—21no—
541C3×Dic3—21no—
542C3×Dic3—41no—
543C3×Dic3C4×D411yescharacteristic
544C3×Dic3C4×D411yescharacteristic
545C2×#41—31no—
546C2×#41—91no—
547#137—91no—
548#137—91no—
549#137—91no—
550#137—91no—
551AGL(1,ℤ/8)—91no—
552AGL(1,ℤ/8)—91no—
553AGL(1,ℤ/8)—91no—
554AGL(1,ℤ/8)—91no—
555#135—31no—
556#135—91no—
557#135—91no—
558#135—91no—
559#131—31no—
560#131—31no—
561#131—31no—
562#131—31no—
563#131—61no—
564#131—61no—
565#131—91no—
566#131—91no—
567#131—91no—
568#131—181no—
569#131—181no—
570#131D3211yescharacteristic, complemented
571C2×M16—31no—
572C2×M16—31no—
573C2×M16—61no—
574C2×M16—61no—
575C2×M16—91no—
576C2×M16—91no—
577C2×M16—181no—
578C2×M16—181no—
579C2×C42—91no—
580#108—31no—
581#108—91no—
582#108—91no—
583#108—91no—
584#104—31no—
585#104—31no—
586#104—91no—
587#104—91no—
588#104—91no—
589#104—91no—
590#104—91no—
591#104—91no—
592#97—31no—
593#97—91no—
594C4×C8—91no—
595C4×C8—91no—
596C23×C3—31no—
597C23×C3—61no—
598C22×D3—21no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3#23511yescharacteristic
602C3×Q8—21no—
603C3×Q8—31no—
604C3×Q8—31no—
605C3×Q8—61no—
606C3×Q8C2×C4×D311yescharacteristic
607C3×Q8C2×C4×D311yescharacteristic
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—31no—
612C3×D4—31no—
613C3×D4—41no—
614C3×D4—61no—
615C3×D4—61no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4—61no—
619C3×D4C2×C4×D311yescharacteristic
620C3×D4C2×C4×D311yescharacteristic
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—31no—
625C2×C3×C4—31no—
626C2×C3×C4—31no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—41no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638#67—21no—
639#67—21no—
640#67—21no—
641#67—21no—
642#67—61no—
643#67—61no—
644#67—61no—
645#67—61no—
646#67—61no—
647#67—61no—
648#67—121no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—121no—
656C2×Dic3—122no—
657C2×Dic3#23511yescharacteristic
658D12—21no—
659D12—31no—
660D12—31no—
661D12—61no—
662D12—61no—
663D12—61no—
664D12C2×C4×D311yescharacteristic
665D12C2×C4×D311yescharacteristic
666C4×D3—21no—
667C4×D3—21no—
668C4×D3—21no—
669C4×D3—21no—
670C4×D3—61no—
671C4×D3—61no—
672C4×D3—61no—
673C4×D3—61no—
674C4×D3—61no—
675C4×D3—61no—
676C4×D3—121no—
677C4×D3—122no—
678C4×D3C2×C4×D311yescharacteristic
679C4×D3C2×C4×D311yescharacteristic
680C4×D3C2×#6711yescharacteristic
681C4×D3C2×#6711yescharacteristic
682Dic6—21no—
683Dic6—31no—
684Dic6—31no—
685Dic6—61no—
686Dic6—61no—
687Dic6—61no—
688Dic6C2×C4×D311yescharacteristic
689Dic6C2×C4×D311yescharacteristic
690C3×C8—21no—
691C3×C8—21no—
692C3×C8—21no—
693C3×C8—21no—
694C3×C8—31no—
695C3×C8—31no—
696C3×C8—31no—
697C3×C8—31no—
698C3×C8—41no—
699C3×C8—61no—
700C3×C8—61no—
701C3×C8D3×D411yescharacteristic
702C3×C8D3×D411yescharacteristic
703C3×C8C2×#6711yescharacteristic
704C3×C8C2×#6711yescharacteristic
705C3⋊C8—21no—
706C3⋊C8—21no—
707C3⋊C8—31no—
708C3⋊C8—31no—
709C3⋊C8—31no—
710C3⋊C8—31no—
711C3⋊C8—61no—
712C3⋊C8—61no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—121no—
716C3⋊C8C2×C4×D311yescharacteristic
717C3⋊C8C2×C4×D311yescharacteristic
718C3⋊C8C2×#6711yescharacteristic
719C3⋊C8C2×#6711yescharacteristic
720C2×C32—21no—
721C2×C32—41no—
722C2×C32C2×C4×D411yescharacteristic
723C3⋊D3—41no—
724C3×D3—21no—
725C3×D3—21no—
726C3×D3—41no—
727C3×D3—41no—
728#41—31no—
729#41—31no—
730#41—31no—
731#41—31no—
732#41—61no—
733#41—61no—
734#41—91no—
735#41—91no—
736#41—91no—
737#41—181no—
738#41—181no—
739#41C2×D3211yescharacteristic
740C2×Q8—31no—
741C2×Q8—91no—
742C2×D4—31no—
743C2×D4—61no—
744C2×D4—91no—
745C2×D4—181no—
746C22×C4—31no—
747C22×C4—61no—
748C22×C4—181no—
749C22×C4—181no—
750Q16—31no—
751Q16—91no—
752Q16—91no—
753Q16—91no—
754SD16—31no—
755SD16—31no—
756SD16—91no—
757SD16—91no—
758SD16—91no—
759SD16—91no—
760SD16—91no—
761SD16—91no—
762D8—31no—
763D8—91no—
764D8—91no—
765D8—91no—
766M16—21no—
767M16—31no—
768M16—31no—
769M16—31no—
770M16—31no—
771M16—31no—
772M16—31no—
773M16—61no—
774M16—61no—
775M16—61no—
776M16—61no—
777M16—61no—
778M16—91no—
779M16—91no—
780M16—91no—
781M16—91no—
782M16—91no—
783M16—181no—
784M16—181no—
785M16—181no—
786M16—181no—
787M16C2×D3211yescharacteristic
788C2×C8—21no—
789C2×C8—31no—
790C2×C8—31no—
791C2×C8—61no—
792C2×C8—61no—
793C2×C8—61no—
794C2×C8—61no—
795C2×C8—61no—
796C2×C8—91no—
797C2×C8—181no—
798C2×C8—181no—
799C2×C8—181no—
800C2×C8—181no—
801C2×C8C2×D3211yescharacteristic
802C42—31no—
803C42—91no—
804C42—181no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—31no—
809C22×C3—31no—
810C22×C3—41no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—121no—
814C22×C3—241no—
815C22×C3C2×#23511yescharacteristic
816C22×C3D3×#4111yescharacteristic
817C2×D3—21no—
818C2×D3—21no—
819C2×D3—41no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—81no—
823C2×D3—121no—
824C2×D3—241no—
825C2×D3—241no—
826C2×D3C4×#6711yescharacteristic
827C2×D3C4×#6711yescharacteristic
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—21no—
831C3×C4—21no—
832C3×C4—31no—
833C3×C4—31no—
834C3×C4—41no—
835C3×C4—61no—
836C3×C4—61no—
837C3×C4—121no—
838C3×C4C22×C4×D311yescharacteristic
839C3×C4C22×C4×D311yescharacteristic
840C3×C4C2×D3×D411yescharacteristic
841C3×C4C22×#6711yescharacteristic
842Dic3—21no—
843Dic3—21no—
844Dic3—41no—
845Dic3—62no—
846Dic3—62no—
847Dic3—61no—
848Dic3—61no—
849Dic3—121no—
850Dic3—122no—
851Dic3C4×#6711yescharacteristic
852Dic3C4×#6711yescharacteristic
853C32#295611yescharacteristic, complemented, Sylow
854C23—31no—
855C23—61no—
856C23—181no—
857Q8—31no—
858Q8—31no—
859Q8—61no—
860Q8—91no—
861Q8—181no—
862Q8C4×D3211yescharacteristic
863D4—21no—
864D4—31no—
865D4—31no—
866D4—61no—
867D4—61no—
868D4—61no—
869D4—61no—
870D4—61no—
871D4—91no—
872D4—181no—
873D4—181no—
874D4—181no—
875D4—181no—
876D4C4×D3211yescharacteristic
877C2×C4—21no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—31no—
882C2×C4—31no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—362no—
895C2×C4C22×D3211yescharacteristic
896C8—21no—
897C8—31no—
898C8—31no—
899C8—31no—
900C8—31no—
901C8—61no—
902C8—61no—
903C8—91no—
904C8—91no—
905C8—181no—
906C8D3×#6711yescharacteristic
907C8D3×#6711yescharacteristic
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—41no—
912C2×C3—41no—
913C2×C3—41no—
914C2×C3—61no—
915C2×C3—61no—
916C2×C3—81no—
917C2×C3—121no—
918C2×C3—121no—
919C2×C3C4×D3×D411yescharacteristic
920C2×C3C2×C4×#6711yescharacteristic
921D3—21no—
922D3—21no—
923D3—41no—
924D3—41no—
925D3—121no—
926D3—121no—
927D3—241no—
928C22—21no—
929C22—31no—
930C22—31no—
931C22—61no—
932C22—61no—
933C22—121no—
934C22—181no—
935C22—241no—
936C22—721no—
937C22D3×#23511yescharacteristic
938C4—21no—
939C4—31no—
940C4—31no—
941C4—61no—
942C4—61no—
943C4—121no—
944C4—182no—
945C4—181no—
946C4C2×C4×D3211yescharacteristic
947C4C2×D3×#6711yescharacteristic
948C3—21no—
949C3#7989811yescharacteristic, complemented
950C3#8381111yescharacteristic, complemented
951C2—21no—
952C2—41no—
953C2—61no—
954C2—61no—
955C2—121no—
956C2—121no—
957C2—361no—
958C2C4×D3×#6711yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32C2×C4×D4
prime radical#10595453C2
cosocleC2×C32×C4C24
hypercenter#131D32
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C3×#5750C2semidirect
3. #10594668C2semidirect
4. #10592843C2semidirect
5. C3×#5145C2semidirect
6. #10591673C2semidirect
7. D3×#837C2semidirect
8. #10591663C2semidirect
9. D3×#825C2semidirect
10. #10590995C2semidirect
11. #10590976C2semidirect
12. #10590973C2semidirect
13. #10590924C2semidirect
14. #10590921C2semidirect
15. #10590667C2semidirect
20. C32×#131C22semidirect
22. #64110C22semidirect
24. C3×#948C22semidirect
26. C3×#907C22semidirect
30. C3×#901C22semidirect
31. C3×#901C22semidirect
34. #63948C4semidirect
35. #63946C4semidirect
36. #63943C4semidirect
37. #63939C4semidirect
38. #63934C4semidirect
39. #63932C4semidirect
40. #63929C4semidirect
41. #63925C4semidirect
46. #63817C22semidirect
47. #63814C22semidirect
53. #63664C22semidirect
54. #63652C22semidirect
55. #63649C22semidirect
56. C8×C3⋊Dic3C22semidirect
57. C3×#837C22semidirect
58. C3×#825C22semidirect
59. C3×#822C22semidirect
60. C3×#815C22semidirect
61. #63578C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63569C22semidirect
65. #63568C22semidirect
66. #63568C22semidirect
67. #63554C22semidirect
68. #63553C22semidirect
73. #5750D3semidirect
81. #5145D3semidirect
126. #3756C2×C4semidirect
127. #3755C2×C4semidirect
128. #3754C2×C4semidirect
129. #3753C2×C4semidirect
135. C3×#216C2×C4semidirect
136. C3×#215C2×C4semidirect
137. C3×#214C2×C4semidirect
138. C3×#213C2×C4semidirect
159. #3719C2×C4semidirect
160. #3718C2×C4semidirect
161. #3717C2×C4semidirect
162. #3716C2×C4semidirect
163. #3715C2×C4semidirect
164. #3715C2×C4semidirect
165. #3714C2×C4semidirect
166. #3713C2×C4semidirect
190. C3×#131C2×D3semidirect
191. C3×#131C2×D3semidirect
208. #948C2×D3semidirect
229. #907C2×D3semidirect
244. #901C2×D3semidirect
245. #901C2×D3semidirect
261. #837C2×D3semidirect
268. #825C2×D3semidirect
275. #822C2×D3semidirect
278. #815C2×D3semidirect
443. #216C4×D3semidirect
450. #215C4×D3semidirect
457. #214C4×D3semidirect
464. #213C4×D3semidirect
570. #131D32semidirect
853. C32#2956semidirect
949. C3#79898semidirect
950. C3#83811semidirect

Maximal subgroups

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

subgroupindex
C3×#57502
#105954532
#105946682
#105928432
C3×#51452
#105916732
D3×#8372
#105916632
D3×#8252
#105909952
#105909762
#105909732
#105909242
#105909212
#105906672
#838113
#798983