Finite Group Databasebeta

← #11889122

Subgroups — #11889122

Order 1152.

955 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595288C211yesmaximal, characteristic
2#10594456C211yesmaximal, characteristic, complemented
3#10592463C211yesmaximal, characteristic, complemented
4C3×#4778C211yesmaximal, characteristic, complemented
5C3×#4770C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591444C211yesmaximal, characteristic, complemented
8#10591413C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590850C211yesmaximal, characteristic, complemented
11#10590743C211yesmaximal, characteristic, complemented
12#10590722C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590474C211yesmaximal, characteristic, complemented
15#10590425C211yesmaximal, characteristic, complemented
16#80685—31nomaximal
17#78934—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21#64149C2211yescharacteristic
22#64099C2211yescharacteristic, complemented
23C3×#938C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic, complemented
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×#897C2211yescharacteristic, complemented
28C3×#892C2211yescharacteristic, complemented
29#63983—21no—
30#63977—21no—
31#63971—21no—
32#63909C2211yescharacteristic
33C4×#625C2211yescharacteristic
34#63898C2211yescharacteristic
35#63891—21no—
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37#63877—21no—
38#63869—21no—
39#63858—21no—
40#63856C2211yescharacteristic, complemented
41#63843C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63648C2211yescharacteristic, complemented
47#63642C2211yescharacteristic, complemented
48#63636C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61D4×#67—31no—
62#5642—31no—
63#5609—31no—
64#5529—31no—
65C3×#465—31no—
66C3×#418—31no—
67#5218—31no—
68#5169—31no—
69#5163—31no—
70#5134—31no—
71#5127—31no—
72C2×#821—31no—
73#5111—31no—
74#5046—31no—
75#5033—31no—
76#5003—31no—
77#4871—31no—
78#4866—31no—
79#4817—31no—
80#4812—31no—
81#4778D311yescharacteristic, complemented
82#4776—31no—
83#4774—31no—
84#4770D311yescharacteristic, complemented
85D3×#102—31no—
86#4766—31no—
87#4764—31no—
88#4764—31no—
89#4764—61no—
90#4762—31no—
91#4757—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106D3×#67—44no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#625D411yescharacteristic
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#214—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×ΓL(1,𝔽25)—41no—
132C3×D3×C8—41no—
133#3724—21no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3717—41no—
144#3715—22no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×D3×D4C2×D311yescharacteristic
151C22×D12—31no—
152C2×C3×SD16—31no—
153C2×C3×M16—31no—
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×#117—31no—
158#953—61no—
159#946—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162C2×#215—31no—
163#940—31no—
164#940—31no—
165#940—61no—
166#939—61no—
167#938C2×D311yescharacteristic
168#937—61no—
169#937—61no—
170D4×Dic3—31no—
171C2×#214—31no—
172C2×#214C2×D311yescharacteristic, complemented
173#930—31no—
174C4×#67—31no—
175C4×#67—31no—
176C2×C4⋊Dic3—31no—
177#924—31no—
178C2×#204—31no—
179C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
180C2×D3×C8C2×D311yescharacteristic, complemented
181#898—61no—
182#897C2×D311yescharacteristic, complemented
183#895—31no—
184#893—31no—
185#892C2×D311yescharacteristic, complemented
186D3×C4⋊C4—31no—
187#890—31no—
188#890—31no—
189#890—61no—
190#890—61no—
191#887—31no—
192#886—61no—
193#884—61no—
194#883—61no—
195#882—61no—
196#879—61no—
197#877—61no—
198#872—61no—
199#870—61no—
200C3×#106—31no—
201C3×#103—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic, complemented
207C3×#102C2×D311yescharacteristic, complemented
208#832—31no—
209#832—31no—
210#832—31no—
211#832—61no—
212#832C2×D311yescharacteristic, complemented
213#830—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#816C2×D311yescharacteristic, complemented
225#815—31no—
226#815—31no—
227#815—61no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#808C2×D311yescharacteristic, complemented
236#807—31no—
237#807—31no—
238#807—31no—
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255#638—81no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C3×#67—42no—
262C3×#67—42no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12#4112yes—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#626—42no—
277#626—42no—
278#625—22no—
279D3×Dic3—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—31no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—31no—
299C2×#102—91no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—121no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C22×D311yescharacteristic
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C2×#67—21no—
316C2×#67—21no—
317C2×#67—31no—
318C2×#67—31no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—121no—
326C2×#67—121no—
327C2×#67—124no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330D3×D4—22no—
331D3×D4—41no—
332D3×D4—62no—
333D3×D4—121no—
334D3×D4—124no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—61no—
338C2×D12—62no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—121no—
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—121no—
349C3×M16—121no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—121no—
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—61no—
366#217—21no—
367#217—31no—
368#217—31no—
369#217—61no—
370#217—61no—
371#215—62no—
372#215—121no—
373#214—41no—
374#214—62no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383C4⋊Dic3—21no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—121no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—121no—
403C4×Dic3—21no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—121no—
415ΓL(1,𝔽25)—41no—
416D3×C8—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—84no—
433C2×C3×D3AGL(1,ℤ/8)12yes—
434D32—84no—
435C32×C4—41no—
436C32×C4C2×#4111yescharacteristic
437C32×C4H(5,𝔽2)11yescharacteristic
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—31no—
447C22×D4—91no—
448C22×D4—181no—
449C2×SD16—31no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×M16—31no—
453C22×C8—31no—
454#127—91no—
455#126—181no—
456#125—91no—
457#125—181no—
458#123—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461#121—31no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—91no—
467C4×D4—91no—
468C4×D4—91no—
469#117—31no—
470#117—181no—
471C2×C4⋊C4—91no—
472#107—91no—
473#107—91no—
474#106—31no—
475C4⋊C8—91no—
476#103—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102D3211yescharacteristic, complemented
486C22⋊C8—91no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—31no—
493C23×C3—41no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C23×C3—241no—
498C22×D3—21no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—81no—
504C22×D3—121no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3D3×D411yescharacteristic
512C22×D3D3×D411yescharacteristic
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—32no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—61no—
523C3×D4—122no—
524C3×D4—122no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—42no—
541#67—42no—
542#67—62no—
543#67—62no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—242no—
549#67—241no—
550#67—241no—
551#67—242no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3—122no—
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568D12—21no—
569D12—61no—
570D12—61no—
571D12—61no—
572D12—61no—
573D12—121no—
574D12—121no—
575D12—122no—
576D12—122no—
577D12#23512yes—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—122no—
583C4×D3—122no—
584Dic6—21no—
585Dic6—21no—
586C3×C8—21no—
587C3×C8—21no—
588C3×C8—41no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—61no—
594C3⋊C8—61no—
595C3⋊C8—121no—
596C2×C32—81no—
597C2×C32#54611yescharacteristic
598C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
599C2×C32#57711yescharacteristic
600C3⋊D3—81no—
601C3×D3—22no—
602C3×D3—42no—
603C3×D3—41no—
604C24—61no—
605C24—181no—
606C2×Q8—31no—
607C2×D4—31no—
608C2×D4—61no—
609C2×D4—62no—
610C2×D4—61no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—121no—
614C2×D4—181no—
615C2×D4—182no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—361no—
620C2×D4—364no—
621C2×D4C2×D3211yescharacteristic
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—181no—
625C22×C4—181no—
626SD16—121no—
627SD16—182no—
628SD16—361no—
629M16—121no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—121no—
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4—181no—
645C4⋊C4C2×D3211yescharacteristic
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—91no—
650C22⋊C4—91no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—61no—
655C42—91no—
656C42—181no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—62no—
670C22×C3—61no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—244no—
677C22×C3C2×D3×D411yescharacteristic
678C22×C3C2×D3×D411yescharacteristic
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—22no—
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—84no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—241no—
695C2×D3—241no—
696C2×D3—241no—
697C2×D3—244no—
698C2×D3—244no—
699C2×D3#91412yes—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C2×#23511yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4#100411yescharacteristic
713C3×C4D3×#4111yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—41no—
717Dic3—41no—
718Dic3—41no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—241no—
728C32#331011yescharacteristic, complemented, Sylow
729C23—21no—
730C23—31no—
731C23—31no—
732C23—61no—
733C23—122no—
734C23—122no—
735C23—181no—
736C23—241no—
737C23—362no—
738C23—362no—
739C23—721no—
740Q8—61no—
741Q8—61no—
742D4—21no—
743D4—21no—
744D4—32no—
745D4—61no—
746D4—122no—
747D4—122no—
748D4—182no—
749D4—181no—
750D4—181no—
751D4—362no—
752D4—362no—
753D4—362no—
754D4—721no—
755C2×C4—21no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—181no—
768C2×C4—362no—
769C2×C4—362no—
770C2×C4C22×D3211yescharacteristic
771C8—21no—
772C8—61no—
773C8—61no—
774C8—181no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—62no—
779C2×C3—81no—
780C2×C3—81no—
781C2×C3—122no—
782C2×C3—121no—
783C2×C3—161no—
784C2×C3#549011yescharacteristic
785C2×C3#561011yescharacteristic
786C2×C3C2×#91411yescharacteristic
787C2×C3#577011yescharacteristic
788C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
789C2×C3#577511yescharacteristic
790D3—22no—
791D3—41no—
792D3—42no—
793D3—241no—
794D3—241no—
795D3—481no—
796C22—32no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—61no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—61no—
805C22—62no—
806C22—121no—
807C22—121no—
808C22—244no—
809C22—361no—
810C22—361no—
811C22—361no—
812C22—724no—
813C22D32×D411yescharacteristic
814C4—41no—
815C4—61no—
816C4—61no—
817C4—121no—
818C4—121no—
819C4—121no—
820C4—181no—
821C4—181no—
822C4—361no—
823C4D3×#23511yescharacteristic
824C4#6431311yescharacteristic
825C3—21no—
826C3#7893411yescharacteristic, complemented
827C3#8068511yescharacteristic, complemented
828C2—62no—
829C2—81no—
830C2—121no—
831C2—122no—
832C2—721no—
833C2#1059427311yescharacteristic
834C2#1059473611yescharacteristic
835C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595288C2
hypercenter#102D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594456C2semidirect
3. #10592463C2semidirect
4. C3×#4778C2semidirect
5. C3×#4770C2semidirect
6. #10591458C2semidirect
7. #10591444C2semidirect
8. #10591413C2semidirect
9. D3×#821C2semidirect
10. #10590850C2semidirect
11. #10590743C2semidirect
12. #10590722C2semidirect
13. #10590596C2semidirect
14. #10590474C2semidirect
15. #10590425C2semidirect
22. #64099C22semidirect
24. C2×C3×#214C22semidirect
25. C2×C3×ΓL(1,𝔽25)C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×#897C22semidirect
28. C3×#892C22semidirect
36. D3×C4⋊Dic3C22semidirect
40. #63856C22semidirect
41. #63843C22semidirect
42. C2×#3717C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
46. #63648C22semidirect
47. #63642C22semidirect
48. #63636C22semidirect
49. C3×#832C22semidirect
51. C3×#816C22semidirect
53. C3×#808C22semidirect
54. #63576C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
57. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
81. #4778D3semidirect
84. #4770D3semidirect
172. C2×#214C2×D3semidirect
179. C2×ΓL(1,𝔽25)C2×D3semidirect
180. C2×D3×C8C2×D3semidirect
182. #897C2×D3semidirect
185. #892C2×D3semidirect
206. C3×#102C2×D3semidirect
207. C3×#102C2×D3semidirect
212. #832C2×D3semidirect
224. #816C2×D3semidirect
235. #808C2×D3semidirect
485. #102D32semidirect
728. C32#3310semidirect
826. C3#78934semidirect
827. C3#80685semidirect

Maximal subgroups

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

subgroupindex
#105952882
#105944562
#105924632
C3×#47782
C3×#47702
#105914582
#105914442
#105914132
D3×#8212
#105908502
#105907432
#105907222
#105905962
#105904742
#105904252
#806853
#789343