Finite Group Databasebeta

← C109×#24034 #42142028

Subgroups — C109×#24034 #42142028

Order 27904.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C109C211yesmaximal, characteristic
2C2×#482×C109C211yesmaximal, characteristic, complemented
3C2×#416×C109C211yesmaximal, characteristic, complemented
4C109×#2485C211yesmaximal, characteristic, complemented
5C109×#2041C211yesmaximal, characteristic, complemented
6C109×#2041C211yesmaximal, characteristic, complemented
7C109×#2034C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#1893C211yesmaximal, characteristic, complemented
10C109×#1869C211yesmaximal, characteristic, complemented
11C109×#1865C211yesmaximal, characteristic, complemented
12C109×#1863C211yesmaximal, characteristic, complemented
13C109×#1788C211yesmaximal, characteristic, complemented
14C109×#1788C211yesmaximal, characteristic, complemented
15C109×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×#41×C109C2211yescharacteristic
18C23×C8×C109C2211yescharacteristic
19#550×C109—24no—
20#550×C109—24no—
21C2×#127×C109—21no—
22C2×#127×C109C2211yescharacteristic
23C2×#121×C109—21no—
24C2×#121×C109—21no—
25C2×#121×C109C2211yescharacteristic
26C2×#121×C109C2211yescharacteristic
27C2×C4×Q8×C109C2211yescharacteristic
28C2×C4×D4×C109—21no—
29C2×C4×D4×C109C2211yescharacteristic
30C2×#117×C109C2211yescharacteristic
31#482×C109—24no—
32C2×#107×C109C2211yescharacteristic
33C2×#106×C109C2211yescharacteristic
34#416×C109—24no—
35C2×#103×C109C2211yescharacteristic
36C2×#103×C109C2211yescharacteristic
37C2×#103×C109C2211yescharacteristic
38C2×#103×C109C2211yescharacteristic
39C2×#102×C109C2211yescharacteristic
40C2×#102×C109C2211yescharacteristic
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×C22⋊C8×C109C2211yescharacteristic
48C2×C22⋊C8×C109C2211yescharacteristic
49C2×C22⋊C8×C109C2211yescharacteristic
50#397×C109—21no—
51#394×C109—21no—
52#389×C109C2211yescharacteristic
53#389×C109C2211yescharacteristic
54#388×C109—21no—
55#387×C109—21no—
56#380×C109C2211yescharacteristic
57#380×C109C2211yescharacteristic
58#380×C109C2211yescharacteristic
59#340×C109C2211yescharacteristic
60#340×C109C2211yescharacteristic
61#336×C109C2211yescharacteristic
62#336×C109C2211yescharacteristic
63C2×#41×C109—22no—
64C2×#41×C109—22no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—22no—
69C2×#41×C109—22no—
70C2×#41×C109—41no—
71C2×#41×C109—41no—
72C2×#41×C109—41no—
73C2×#41×C109—41no—
74C2×#41×C109D414yes—
75C22×Q8×C109C2311yescharacteristic
76C22×D4×C109—21no—
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109—21no—
82C22×D4×C109D411yescharacteristic
83C22×D4×C109C2311yescharacteristic
84C22×D4×C109C2311yescharacteristic
85C23×C4×C109—21no—
86C23×C4×C109—21no—
87C23×C4×C109C2311yescharacteristic
88C23×C4×C109C2311yescharacteristic
89C22×C8×C109—22no—
90C22×C8×C109—41no—
91C22×C8×C109—41no—
92C22×C8×C109C2311yescharacteristic
93C22×C8×C109C2311yescharacteristic
94C22×C8×C109C2311yescharacteristic
95C22×C8×C109C2311yescharacteristic
96#127×C109—28no—
97#127×C109—22no—
98#127×C109—22no—
99#121×C109—28no—
100#121×C109—28no—
101#121×C109—22no—
102#121×C109—22no—
103#121×C109—22no—
104#121×C109D414yes—
105C4×Q8×C109—22no—
106C4×Q8×C109—22no—
107C4×D4×C109—28no—
108C4×D4×C109—22no—
109C4×D4×C109—22no—
110#117×C109—22no—
111#117×C109—22no—
112C2×C4⋊C4×C109—21no—
113C2×C4⋊C4×C109—21no—
114C2×C4⋊C4×C109—21no—
115C2×C4⋊C4×C109D411yescharacteristic
116C2×C4⋊C4×C109C2311yescharacteristic
117C2×C4⋊C4×C109C2311yescharacteristic
118C2×C4⋊C4×C109C2311yescharacteristic
119C2×C4⋊C4×C109C2311yescharacteristic
120C2×C4⋊C4×C109C2311yescharacteristic
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109D411yescharacteristic
128C2×C22⋊C4×C109D411yescharacteristic
129C2×C42×C109—21no—
130C2×C42×C109—21no—
131C2×C42×C109C2311yescharacteristic
132#107×C109—22no—
133#106×C109—22no—
134#103×C109—22no—
135#103×C109—22no—
136#103×C109—22no—
137#103×C109—22no—
138#102×C109—22no—
139#102×C109—22no—
140#102×C109—22no—
141#102×C109—22no—
142#102×C109—41no—
143#102×C109—41no—
144#102×C109—41no—
145#102×C109—41no—
146C22⋊C8×C109—22no—
147C22⋊C8×C109—41no—
148C22⋊C8×C109—41no—
149#95×C109—21no—
150#95×C109—21no—
151#95×C109—21no—
152#95×C109—21no—
153#95×C109—21no—
154C24×C109—21no—
155C24×C109—21no—
156C24×C109C2×D411yescharacteristic
157C24×C109C2×D411yescharacteristic
158#41×C109—28no—
159#41×C109—44no—
160#41×C109—44no—
161#41×C109—44no—
162#41×C109—44no—
163#41×C109—44no—
164#41×C109—44no—
165#41×C109—44no—
166C2×Q8×C109—21no—
167C2×Q8×C109—21no—
168C2×Q8×C109—21no—
169C2×Q8×C109C2×D412yes—
170C2×Q8×C109#4112yes—
171C2×Q8×C109#4112yes—
172C2×D4×C109—24no—
173C2×D4×C109—24no—
174C2×D4×C109—22no—
175C2×D4×C109—24no—
176C2×D4×C109—24no—
177C2×D4×C109—24no—
178C2×D4×C109—24no—
179C2×D4×C109—22no—
180C2×D4×C109—21no—
181C2×D4×C109—21no—
182C2×D4×C109—21no—
183C2×D4×C109—21no—
184C2×D4×C109—21no—
185C2×D4×C109—21no—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—21no—
189C2×D4×C109—21no—
190C2×D4×C109—41no—
191C2×D4×C109—42no—
192C2×D4×C109—42no—
193C2×D4×C109—42no—
194C2×D4×C109—42no—
195C2×D4×C109—42no—
196C2×D4×C109—42no—
197C2×D4×C109—81no—
198C2×D4×C109—81no—
199C2×D4×C109—81no—
200C2×D4×C109—81no—
201C2×D4×C109—81no—
202C2×D4×C109—81no—
203C2×D4×C109C2×D412yes—
204C2×D4×C109C2×D412yes—
205C22×C4×C109—21no—
206C22×C4×C109—21no—
207C22×C4×C109—21no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—24no—
211C22×C4×C109—21no—
212C22×C4×C109—24no—
213C22×C4×C109—21no—
214C22×C4×C109—21no—
215C22×C4×C109—21no—
216C22×C4×C109—21no—
217C22×C4×C109—21no—
218C22×C4×C109—21no—
219C22×C4×C109—21no—
220C22×C4×C109—21no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—42no—
224C22×C4×C109—42no—
225C22×C4×C109—42no—
226C22×C4×C109—42no—
227C22×C4×C109C2×D411yescharacteristic
228C22×C4×C109C2×D411yescharacteristic
229C22×C4×C109C2×D411yescharacteristic
230C22×C4×C109C2×D412yes—
231C22×C4×C109C2×D412yes—
232C22×C4×C109C2×D411yescharacteristic
233C22×C4×C109C2411yescharacteristic
234C2×C8×C109—21no—
235C2×C8×C109—21no—
236C2×C8×C109—21no—
237C2×C8×C109—21no—
238C2×C8×C109—21no—
239C2×C8×C109—21no—
240C2×C8×C109—21no—
241C2×C8×C109—21no—
242C2×C8×C109—21no—
243C2×C8×C109—21no—
244C2×C8×C109—21no—
245C2×C8×C109—21no—
246C2×C8×C109—44no—
247C4⋊C4×C109—24no—
248C4⋊C4×C109—22no—
249C4⋊C4×C109—21no—
250C4⋊C4×C109—21no—
251C4⋊C4×C109—21no—
252C4⋊C4×C109—21no—
253C4⋊C4×C109—21no—
254C4⋊C4×C109—21no—
255C4⋊C4×C109—21no—
256C4⋊C4×C109—21no—
257C4⋊C4×C109—21no—
258C4⋊C4×C109—42no—
259C4⋊C4×C109—81no—
260C4⋊C4×C109C2×D412yes—
261C22⋊C4×C109—24no—
262C22⋊C4×C109—22no—
263C22⋊C4×C109—24no—
264C22⋊C4×C109—22no—
265C22⋊C4×C109—42no—
266C22⋊C4×C109—42no—
267C22⋊C4×C109—81no—
268C22⋊C4×C109—81no—
269C42×C109—24no—
270C42×C109—21no—
271C42×C109—21no—
272C42×C109—42no—
273C23×C109—21no—
274C23×C109—21no—
275C23×C109—21no—
276C23×C109—21no—
277C23×C109—21no—
278C23×C109—21no—
279C23×C109—21no—
280C23×C109—22no—
281C23×C109—22no—
282C23×C109—21no—
283C23×C109—21no—
284C23×C109—21no—
285C23×C109—21no—
286C23×C109—21no—
287C23×C109—21no—
288C23×C109—41no—
289C23×C109—41no—
290C23×C109—41no—
291C23×C109—41no—
292C23×C109—41no—
293C23×C109—41no—
294C23×C109—41no—
295C23×C109—41no—
296C23×C109—41no—
297C23×C109—41no—
298C23×C109—41no—
299C23×C109—41no—
300C23×C109#12012yes—
301C23×C109C22×D411yescharacteristic
302Q8×C109—22no—
303Q8×C109—22no—
304Q8×C109—22no—
305Q8×C109#12314yes—
306D4×C109—22no—
307D4×C109—22no—
308D4×C109—22no—
309D4×C109—22no—
310D4×C109—44no—
311D4×C109—48no—
312D4×C109—48no—
313D4×C109—48no—
314D4×C109—41no—
315D4×C109—41no—
316D4×C109—41no—
317D4×C109—41no—
318D4×C109—84no—
319D4×C109—84no—
320D4×C109—84no—
321C2×C4×C109—21no—
322C2×C4×C109—22no—
323C2×C4×C109—21no—
324C2×C4×C109—21no—
325C2×C4×C109—22no—
326C2×C4×C109—22no—
327C2×C4×C109—21no—
328C2×C4×C109—22no—
329C2×C4×C109—22no—
330C2×C4×C109—22no—
331C2×C4×C109—22no—
332C2×C4×C109—21no—
333C2×C4×C109—22no—
334C2×C4×C109—21no—
335C2×C4×C109—21no—
336C2×C4×C109—21no—
337C2×C4×C109—21no—
338C2×C4×C109—21no—
339C2×C4×C109—48no—
340C2×C4×C109—48no—
341C2×C4×C109—41no—
342C2×C4×C109—41no—
343C2×C4×C109—41no—
344C2×C4×C109—41no—
345C2×C4×C109—41no—
346C2×C4×C109—41no—
347C2×C4×C109—41no—
348C2×C4×C109—41no—
349C2×C4×C109—41no—
350C2×C4×C109—41no—
351C2×C4×C109—41no—
352C2×C4×C109—41no—
353C2×C4×C109—41no—
354C2×C4×C109—41no—
355C2×C4×C109—41no—
356C2×C4×C109—41no—
357C2×C4×C109—41no—
358C2×C4×C109—41no—
359C2×C4×C109#12012yes—
360C2×C4×C109#13512yes—
361C2×C4×C109C22×D411yescharacteristic
362C2×C4×C109C22×D411yescharacteristic
363C2×C4×C109C2×#4111yescharacteristic
364C2×C4×C109C2×#4111yescharacteristic
365C2×C4×C109H(5,𝔽2)11yescharacteristic
366C2×C4×C109H(5,𝔽2)11yescharacteristic
367C8×C109—41no—
368C8×C109—41no—
369C8×C109—41no—
370C8×C109—41no—
371C22×C109—22no—
372C22×C109—22no—
373C22×C109—22no—
374C22×C109—41no—
375C22×C109—41no—
376C22×C109—41no—
377C22×C109—41no—
378C22×C109—42no—
379C22×C109—42no—
380C22×C109—41no—
381C22×C109—41no—
382C22×C109—42no—
383C22×C109—42no—
384C22×C109—41no—
385C22×C109—42no—
386C22×C109—42no—
387C22×C109—41no—
388C22×C109—41no—
389C22×C109—41no—
390C22×C109—41no—
391C22×C109—81no—
392C22×C109—81no—
393C22×C109—81no—
394C22×C109—81no—
395C22×C109—81no—
396C22×C109—81no—
397C22×C109—81no—
398C22×C109—81no—
399C22×C109C2×#12011yescharacteristic
400C22×C109#54611yescharacteristic
401C22×C109#54611yescharacteristic
402C22×C109C2×#13511yescharacteristic
403C22×C109#57511yescharacteristic
404C22×C109#57611yescharacteristic
405C22×C109#57711yescharacteristic
406C4×C109—22no—
407C4×C109—24no—
408C4×C109—22no—
409C4×C109—41no—
410C4×C109—41no—
411C4×C109—42no—
412C4×C109—81no—
413C4×C109—81no—
414C4×C109—81no—
415C4×C109—81no—
416C4×C109C2×#12311yescharacteristic
417C4×C109#53411yescharacteristic
418C4×C109#54611yescharacteristic
419C4×C109#54611yescharacteristic
420#24034C10911yesmaximal, characteristic, direct product factor, Sylow
421C2×C109—42no—
422C2×C109—81no—
423C2×C109—82no—
424C2×C109—82no—
425C2×C109#240511yescharacteristic
426C2×C109#300211yescharacteristic
427C2×C109#301211yescharacteristic
428C2×C109#330411yescharacteristic
429C2×C109#330511yescharacteristic
430C2×C109#330911yescharacteristic
431C2×C109#331711yescharacteristic
432C2×#550C2×C10911yescharacteristic
433C2×#482C2×C10911yescharacteristic, complemented
434C2×#416C2×C10911yescharacteristic, complemented
435#2485C2×C10911yescharacteristic, complemented
436#2041C2×C10911yescharacteristic, complemented
437#2041C2×C10911yescharacteristic, complemented
438#2034C2×C10911yescharacteristic, complemented
439#2033C2×C10911yescharacteristic, complemented
440#1893C2×C10911yescharacteristic, complemented
441#1869C2×C10911yescharacteristic, complemented
442#1865C2×C10911yescharacteristic, complemented
443#1863C2×C10911yescharacteristic, complemented
444#1788C2×C10911yescharacteristic, complemented
445#1788C2×C10911yescharacteristic, complemented
446#1788C2×C10911yescharacteristic, complemented
447C109#2403411yescharacteristic, direct product factor, Sylow
448C22×#41C22×C10911yescharacteristic
449C22×#41C22×C10911yescharacteristic
450C23×C8C22×C10911yescharacteristic
451#550—24no—
452#550—24no—
453C2×#127—21no—
454C2×#127C22×C10911yescharacteristic
455C2×#121—21no—
456C2×#121—21no—
457C2×#121C22×C10911yescharacteristic
458C2×#121C22×C10911yescharacteristic
459C2×C4×Q8C22×C10911yescharacteristic
460C2×C4×D4—21no—
461C2×C4×D4C22×C10911yescharacteristic
462C2×#117C22×C10911yescharacteristic
463#482—24no—
464C2×#107C22×C10911yescharacteristic
465C2×#106C22×C10911yescharacteristic
466#416—24no—
467C2×#103C22×C10911yescharacteristic
468C2×#103C22×C10911yescharacteristic
469C2×#103C22×C10911yescharacteristic
470C2×#103C22×C10911yescharacteristic
471C2×#102C22×C10911yescharacteristic
472C2×#102C22×C10911yescharacteristic
473C2×#102C22×C10911yescharacteristic
474C2×#102C22×C10911yescharacteristic
475C2×#102C22×C10911yescharacteristic
476C2×#102C22×C10911yescharacteristic
477C2×#102C22×C10911yescharacteristic
478C2×#102C22×C10911yescharacteristic
479C2×C22⋊C8C22×C10911yescharacteristic
480C2×C22⋊C8C22×C10911yescharacteristic
481C2×C22⋊C8C22×C10911yescharacteristic
482#397—21no—
483#394—21no—
484#389C22×C10911yescharacteristic
485#389C22×C10911yescharacteristic
486#388—21no—
487#387—21no—
488#380C22×C10911yescharacteristic
489#380C22×C10911yescharacteristic
490#380C22×C10911yescharacteristic
491#340C22×C10911yescharacteristic
492#340C22×C10911yescharacteristic
493#336C22×C10911yescharacteristic
494#336C22×C10911yescharacteristic
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C10914yes—
507C22×Q8C23×C10911yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C10911yescharacteristic
515C22×D4C23×C10911yescharacteristic
516C22×D4C23×C10911yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C10911yescharacteristic
520C23×C4C23×C10911yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C10911yescharacteristic
525C22×C8C23×C10911yescharacteristic
526C22×C8C23×C10911yescharacteristic
527C22×C8C23×C10911yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C10914yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C10911yescharacteristic
548C2×C4⋊C4C23×C10911yescharacteristic
549C2×C4⋊C4C23×C10911yescharacteristic
550C2×C4⋊C4C23×C10911yescharacteristic
551C2×C4⋊C4C23×C10911yescharacteristic
552C2×C4⋊C4C23×C10911yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C10911yescharacteristic
560C2×C22⋊C4D4×C10911yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C10911yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C10911yescharacteristic
589C24C2×D4×C10911yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C10912yes—
602C2×Q8#41×C10912yes—
603C2×Q8#41×C10912yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C10912yes—
636C2×D4C2×D4×C10912yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C10911yescharacteristic
660C22×C4C2×D4×C10911yescharacteristic
661C22×C4C2×D4×C10911yescharacteristic
662C22×C4C2×D4×C10912yes—
663C22×C4C2×D4×C10912yes—
664C22×C4C2×D4×C10911yescharacteristic
665C22×C4C24×C10911yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C10912yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C10912yes—
733C23C22×D4×C10911yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C10914yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#120×C10912yes—
792C2×C4#135×C10912yes—
793C2×C4C22×D4×C10911yescharacteristic
794C2×C4C22×D4×C10911yescharacteristic
795C2×C4C2×#41×C10911yescharacteristic
796C2×C4C2×#41×C10911yescharacteristic
797C2×C4H(5,𝔽2)×C10911yescharacteristic
798C2×C4H(5,𝔽2)×C10911yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C10911yescharacteristic
832C22#546×C10911yescharacteristic
833C22#546×C10911yescharacteristic
834C22C2×#135×C10911yescharacteristic
835C22#575×C10911yescharacteristic
836C22#576×C10911yescharacteristic
837C22#577×C10911yescharacteristic
838C4—22no—
839C4—22no—
840C4—24no—
841C4—41no—
842C4—42no—
843C4—41no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C10911yescharacteristic
849C4#534×C10911yescharacteristic
850C4#546×C10911yescharacteristic
851C4#546×C10911yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C109×#240511yescharacteristic
857C2C109×#300211yescharacteristic
858C2C109×#301211yescharacteristic
859C2C109×#330411yescharacteristic
860C2C109×#330511yescharacteristic
861C2C109×#330911yescharacteristic
862C2C109×#331711yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC2×#550×C109C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#482×C109C2semidirect
3. C2×#416×C109C2semidirect
4. C109×#2485C2semidirect
5. C109×#2041C2semidirect
6. C109×#2041C2semidirect
7. C109×#2034C2semidirect
8. C109×#2033C2semidirect
9. C109×#1893C2semidirect
10. C109×#1869C2semidirect
11. C109×#1865C2semidirect
12. C109×#1863C2semidirect
13. C109×#1788C2semidirect
14. C109×#1788C2semidirect
15. C109×#1788C2semidirect
420. #24034C109direct (N × H)
433. C2×#482C2×C109semidirect
434. C2×#416C2×C109semidirect
435. #2485C2×C109semidirect
436. #2041C2×C109semidirect
437. #2041C2×C109semidirect
438. #2034C2×C109semidirect
439. #2033C2×C109semidirect
440. #1893C2×C109semidirect
441. #1869C2×C109semidirect
442. #1865C2×C109semidirect
443. #1863C2×C109semidirect
444. #1788C2×C109semidirect
445. #1788C2×C109semidirect
446. #1788C2×C109semidirect
447. C109#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#550×C1092
C2×#482×C1092
C2×#416×C1092
C109×#24852
C109×#20412
C109×#20342
C109×#20332
C109×#18932
C109×#18692
C109×#18652
C109×#18632
C109×#17882
#24034109