Finite Group Databasebeta

← C109×#24124 #42142118

Subgroups — C109×#24124 #42142118

Order 27904.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C109C211yesmaximal, characteristic, complemented
2C2×#478×C109C211yesmaximal, characteristic, complemented
3C2×C4×D8×C109C211yesmaximal, characteristic, complemented
4C109×#2535C211yesmaximal, characteristic, complemented
5C109×#2034C211yesmaximal, characteristic, complemented
6C109×#2033C211yesmaximal, characteristic, complemented
7C109×#1999C211yesmaximal, characteristic, complemented
8C109×#1999C211yesmaximal, characteristic, complemented
9C109×#1991C211yesmaximal, characteristic, complemented
10C109×#1954C211yesmaximal, characteristic, complemented
11C109×#1875C211yesmaximal, characteristic, complemented
12C109×#1874C211yesmaximal, characteristic, complemented
13C109×#1854C211yesmaximal, characteristic, complemented
14C109×#1852C211yesmaximal, characteristic, complemented
15C109×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C109C2211yescharacteristic
17#553×C109—24no—
18#553×C109—24no—
19C2×#126×C109—21no—
20C2×#125×C109C2211yescharacteristic
21C2×#123×C109—21no—
22C2×#121×C109—21no—
23C2×#121×C109C2211yescharacteristic
24C2×#121×C109C2211yescharacteristic
25C2×#121×C109C2211yescharacteristic
26C2×#121×C109C2211yescharacteristic
27C2×C4×D4×C109—21no—
28C2×C4×D4×C109C2211yescharacteristic
29C2×C4×D4×C109C2211yescharacteristic
30C2×C4×D4×C109C2211yescharacteristic
31C2×#117×C109C2211yescharacteristic
32C22×C4⋊C4×C109C2211yescharacteristic
33#478×C109—24no—
34C4×D8×C109—24no—
35C2×#107×C109C2211yescharacteristic
36C2×#107×C109C2211yescharacteristic
37C2×#106×C109C2211yescharacteristic
38C2×C4⋊C8×C109C2211yescharacteristic
39C2×#102×C109C2211yescharacteristic
40C2×#102×C109C2211yescharacteristic
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×C22⋊C8×C109C2211yescharacteristic
46C2×C22⋊C8×C109C2211yescharacteristic
47C2×C22⋊C8×C109C2211yescharacteristic
48C2×C22⋊C8×C109C2211yescharacteristic
49C2×C4×C8×C109C2211yescharacteristic
50#397×C109—21no—
51#392×C109—21no—
52#386×C109—21no—
53#386×C109—21no—
54#382×C109C2211yescharacteristic
55#380×C109C2211yescharacteristic
56#380×C109C2211yescharacteristic
57#340×C109C2211yescharacteristic
58#340×C109C2211yescharacteristic
59#340×C109C2211yescharacteristic
60#340×C109C2211yescharacteristic
61#340×C109C2211yescharacteristic
62#340×C109C2211yescharacteristic
63C22×D4×C109—21no—
64C22×D4×C109—21no—
65C22×D4×C109—21no—
66C22×D4×C109—21no—
67C22×D4×C109D411yescharacteristic
68C22×D4×C109C2311yescharacteristic
69C22×D4×C109C2311yescharacteristic
70C23×C4×C109—21no—
71C23×C4×C109—21no—
72C23×C4×C109—21no—
73C23×C4×C109C2311yescharacteristic
74C23×C4×C109C2311yescharacteristic
75C2×D8×C109—22no—
76C2×D8×C109—22no—
77C2×D8×C109—22no—
78C22×C8×C109C2311yescharacteristic
79C22×C8×C109C2311yescharacteristic
80C22×C8×C109C2311yescharacteristic
81C22×C8×C109C2311yescharacteristic
82#126×C109—28no—
83#125×C109—22no—
84#125×C109D414yescomplemented
85#123×C109—28no—
86#121×C109—28no—
87#121×C109—22no—
88#121×C109—22no—
89#121×C109—22no—
90#121×C109—22no—
91#121×C109—22no—
92#121×C109—22no—
93#121×C109—41no—
94#121×C109—41no—
95C4×D4×C109—28no—
96C4×D4×C109—22no—
97C4×D4×C109—22no—
98C4×D4×C109—22no—
99C4×D4×C109—22no—
100C4×D4×C109—22no—
101C4×D4×C109D414yescomplemented
102#117×C109—22no—
103#117×C109—22no—
104C2×C4⋊C4×C109—21no—
105C2×C4⋊C4×C109—21no—
106C2×C4⋊C4×C109—21no—
107C2×C4⋊C4×C109—22no—
108C2×C4⋊C4×C109—22no—
109C2×C4⋊C4×C109D411yescharacteristic
110C2×C4⋊C4×C109C2311yescharacteristic
111C2×C4⋊C4×C109C2311yescharacteristic
112C2×C4⋊C4×C109C2311yescharacteristic
113C2×C4⋊C4×C109C2311yescharacteristic
114C2×C4⋊C4×C109C2311yescharacteristic
115C2×C4⋊C4×C109C2311yescharacteristic
116C2×C22⋊C4×C109—21no—
117C2×C22⋊C4×C109—21no—
118C2×C22⋊C4×C109—21no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109D411yescharacteristic
126C2×C22⋊C4×C109D411yescharacteristic
127C2×C42×C109—21no—
128C2×C42×C109C2311yescharacteristic
129#107×C109—22no—
130#107×C109—22no—
131#106×C109—22no—
132C4⋊C8×C109—22no—
133#102×C109—22no—
134#102×C109—22no—
135#102×C109—22no—
136#102×C109—22no—
137#102×C109—41no—
138#102×C109—41no—
139C22⋊C8×C109—22no—
140C22⋊C8×C109—22no—
141C22⋊C8×C109—41no—
142C22⋊C8×C109—41no—
143C4×C8×C109—22no—
144#95×C109—21no—
145#95×C109—21no—
146#95×C109—21no—
147#95×C109—21no—
148C24×C109—21no—
149C24×C109—21no—
150C24×C109C2×D411yescharacteristic
151C24×C109C2×D411yescharacteristic
152C2×D4×C109—24no—
153C2×D4×C109—22no—
154C2×D4×C109—24no—
155C2×D4×C109—22no—
156C2×D4×C109—21no—
157C2×D4×C109—21no—
158C2×D4×C109—21no—
159C2×D4×C109—21no—
160C2×D4×C109—21no—
161C2×D4×C109—21no—
162C2×D4×C109—21no—
163C2×D4×C109—21no—
164C2×D4×C109—21no—
165C2×D4×C109—21no—
166C2×D4×C109—41no—
167C2×D4×C109—42no—
168C2×D4×C109—42no—
169C2×D4×C109—42no—
170C2×D4×C109—42no—
171C2×D4×C109—42no—
172C2×D4×C109—42no—
173C2×D4×C109—81no—
174C2×D4×C109—81no—
175C2×D4×C109—81no—
176C2×D4×C109—81no—
177C2×D4×C109C2×D412yes—
178C2×D4×C109#4112yes—
179C22×C4×C109—21no—
180C22×C4×C109—21no—
181C22×C4×C109—21no—
182C22×C4×C109—24no—
183C22×C4×C109—21no—
184C22×C4×C109—21no—
185C22×C4×C109—21no—
186C22×C4×C109—21no—
187C22×C4×C109—21no—
188C22×C4×C109—21no—
189C22×C4×C109—21no—
190C22×C4×C109—21no—
191C22×C4×C109—21no—
192C22×C4×C109—21no—
193C22×C4×C109—21no—
194C22×C4×C109—21no—
195C22×C4×C109—24no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—21no—
199C22×C4×C109—42no—
200C22×C4×C109—81no—
201C22×C4×C109—81no—
202C22×C4×C109—81no—
203C22×C4×C109—81no—
204C22×C4×C109—81no—
205C22×C4×C109—81no—
206C22×C4×C109C2×D411yescharacteristic
207C22×C4×C109C2×D411yescharacteristic
208C22×C4×C109C2×D411yescharacteristic
209C22×C4×C109C2×D411yescharacteristic
210C22×C4×C109C2411yescharacteristic
211D8×C109—28no—
212C2×C8×C109—21no—
213C2×C8×C109—21no—
214C2×C8×C109—21no—
215C2×C8×C109—21no—
216C2×C8×C109—21no—
217C2×C8×C109—21no—
218C2×C8×C109—21no—
219C2×C8×C109—21no—
220C2×C8×C109—21no—
221C2×C8×C109—21no—
222C2×C8×C109—21no—
223C2×C8×C109#4112yes—
224C4⋊C4×C109—24no—
225C4⋊C4×C109—24no—
226C4⋊C4×C109—24no—
227C4⋊C4×C109—22no—
228C4⋊C4×C109—21no—
229C4⋊C4×C109—21no—
230C4⋊C4×C109—21no—
231C4⋊C4×C109—21no—
232C4⋊C4×C109—21no—
233C4⋊C4×C109—21no—
234C4⋊C4×C109—21no—
235C4⋊C4×C109—21no—
236C4⋊C4×C109—21no—
237C4⋊C4×C109C2×D412yes—
238C4⋊C4×C109C2×D412yes—
239C4⋊C4×C109C2×D412yes—
240C22⋊C4×C109—24no—
241C22⋊C4×C109—24no—
242C22⋊C4×C109—24no—
243C22⋊C4×C109—24no—
244C22⋊C4×C109—22no—
245C22⋊C4×C109—22no—
246C22⋊C4×C109—42no—
247C22⋊C4×C109—42no—
248C22⋊C4×C109—42no—
249C22⋊C4×C109—81no—
250C22⋊C4×C109—81no—
251C42×C109—24no—
252C42×C109C2×D412yes—
253C42×C109C2×D412yes—
254C23×C109—21no—
255C23×C109—21no—
256C23×C109—21no—
257C23×C109—21no—
258C23×C109—21no—
259C23×C109—21no—
260C23×C109—21no—
261C23×C109—22no—
262C23×C109—22no—
263C23×C109—21no—
264C23×C109—21no—
265C23×C109—21no—
266C23×C109—21no—
267C23×C109—21no—
268C23×C109—21no—
269C23×C109—41no—
270C23×C109—41no—
271C23×C109—41no—
272C23×C109—41no—
273C23×C109—41no—
274C23×C109—41no—
275C23×C109—41no—
276C23×C109—41no—
277C23×C109—41no—
278C23×C109—41no—
279C23×C109—41no—
280C23×C109—41no—
281C23×C109#13512yes—
282C23×C109C22×D411yescharacteristic
283D4×C109—22no—
284D4×C109—22no—
285D4×C109—22no—
286D4×C109—22no—
287D4×C109—44no—
288D4×C109—48no—
289D4×C109—41no—
290D4×C109—41no—
291D4×C109—41no—
292D4×C109—41no—
293D4×C109—84no—
294D4×C109—84no—
295D4×C109—84no—
296C2×C4×C109—21no—
297C2×C4×C109—21no—
298C2×C4×C109—21no—
299C2×C4×C109—21no—
300C2×C4×C109—21no—
301C2×C4×C109—22no—
302C2×C4×C109—22no—
303C2×C4×C109—21no—
304C2×C4×C109—22no—
305C2×C4×C109—21no—
306C2×C4×C109—21no—
307C2×C4×C109—21no—
308C2×C4×C109—21no—
309C2×C4×C109—41no—
310C2×C4×C109—41no—
311C2×C4×C109—41no—
312C2×C4×C109—41no—
313C2×C4×C109—41no—
314C2×C4×C109—41no—
315C2×C4×C109—41no—
316C2×C4×C109—41no—
317C2×C4×C109—41no—
318C2×C4×C109—41no—
319C2×C4×C109—41no—
320C2×C4×C109—41no—
321C2×C4×C109—41no—
322C2×C4×C109—41no—
323C2×C4×C109—41no—
324C2×C4×C109—41no—
325C2×C4×C109—41no—
326C2×C4×C109—41no—
327C2×C4×C109—41no—
328C2×C4×C109—41no—
329C2×C4×C109—41no—
330C2×C4×C109—41no—
331C2×C4×C109—41no—
332C2×C4×C109—84no—
333C2×C4×C109—84no—
334C2×C4×C109—84no—
335C2×C4×C109#12012yes—
336C2×C4×C109#12012yes—
337C2×C4×C109C22×D411yescharacteristic
338C2×C4×C109C22×D411yescharacteristic
339C2×C4×C109C2×#4111yescharacteristic
340C2×C4×C109C2×#4111yescharacteristic
341C2×C4×C109H(5,𝔽2)11yescharacteristic
342C2×C4×C1092−1+411yescharacteristic
343C8×C109—22no—
344C8×C109—41no—
345C8×C109—41no—
346C8×C109—41no—
347C22×C109—22no—
348C22×C109—22no—
349C22×C109—22no—
350C22×C109—41no—
351C22×C109—41no—
352C22×C109—41no—
353C22×C109—41no—
354C22×C109—41no—
355C22×C109—41no—
356C22×C109—41no—
357C22×C109—42no—
358C22×C109—42no—
359C22×C109—41no—
360C22×C109—42no—
361C22×C109—42no—
362C22×C109—41no—
363C22×C109—42no—
364C22×C109—41no—
365C22×C109—41no—
366C22×C109—42no—
367C22×C109—81no—
368C22×C109—81no—
369C22×C109—81no—
370C22×C109—81no—
371C22×C109—81no—
372C22×C109—81no—
373C22×C109—81no—
374C22×C109—81no—
375C22×C109C2×#12011yescharacteristic
376C22×C109#54611yescharacteristic
377C22×C109#54711yescharacteristic
378C22×C109C2×#13511yescharacteristic
379C22×C109#57511yescharacteristic
380C22×C109#57611yescharacteristic
381C22×C109#57611yescharacteristic
382C4×C109—22no—
383C4×C109—22no—
384C4×C109—41no—
385C4×C109—41no—
386C4×C109—42no—
387C4×C109—42no—
388C4×C109—42no—
389C4×C109—81no—
390C4×C109—81no—
391C4×C109—81no—
392C4×C109#52511yescharacteristic
393C4×C109#53711yescharacteristic
394C4×C109#54811yescharacteristic
395C4×C109#55011yescharacteristic
396#24124C10911yesmaximal, characteristic, direct product factor, Sylow
397C2×C109—42no—
398C2×C109—81no—
399C2×C109—82no—
400C2×C109—82no—
401C2×C109#240711yescharacteristic
402C2×C109#300211yescharacteristic
403C2×C109#300811yescharacteristic
404C2×C109#329711yescharacteristic
405C2×C109#332211yescharacteristic
406C2×C109#333911yescharacteristic
407C2×C109#335511yescharacteristic
408C2×#553C2×C10911yescharacteristic, complemented
409C2×#478C2×C10911yescharacteristic, complemented
410C2×C4×D8C2×C10911yescharacteristic, complemented
411#2535C2×C10911yescharacteristic, complemented
412#2034C2×C10911yescharacteristic, complemented
413#2033C2×C10911yescharacteristic, complemented
414#1999C2×C10911yescharacteristic, complemented
415#1999C2×C10911yescharacteristic, complemented
416#1991C2×C10911yescharacteristic, complemented
417#1954C2×C10911yescharacteristic, complemented
418#1875C2×C10911yescharacteristic, complemented
419#1874C2×C10911yescharacteristic, complemented
420#1854C2×C10911yescharacteristic, complemented
421#1852C2×C10911yescharacteristic, complemented
422#1804C2×C10911yescharacteristic, complemented
423C109#2412411yescharacteristic, direct product factor, Sylow
424C22×D8C22×C10911yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C10911yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C10911yescharacteristic
432C2×#121C22×C10911yescharacteristic
433C2×#121C22×C10911yescharacteristic
434C2×#121C22×C10911yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C10911yescharacteristic
437C2×C4×D4C22×C10911yescharacteristic
438C2×C4×D4C22×C10911yescharacteristic
439C2×#117C22×C10911yescharacteristic
440C22×C4⋊C4C22×C10911yescharacteristic
441#478—24no—
442C4×D8—24no—
443C2×#107C22×C10911yescharacteristic
444C2×#107C22×C10911yescharacteristic
445C2×#106C22×C10911yescharacteristic
446C2×C4⋊C8C22×C10911yescharacteristic
447C2×#102C22×C10911yescharacteristic
448C2×#102C22×C10911yescharacteristic
449C2×#102C22×C10911yescharacteristic
450C2×#102C22×C10911yescharacteristic
451C2×#102C22×C10911yescharacteristic
452C2×#102C22×C10911yescharacteristic
453C2×C22⋊C8C22×C10911yescharacteristic
454C2×C22⋊C8C22×C10911yescharacteristic
455C2×C22⋊C8C22×C10911yescharacteristic
456C2×C22⋊C8C22×C10911yescharacteristic
457C2×C4×C8C22×C10911yescharacteristic
458#397—21no—
459#392—21no—
460#386—21no—
461#386—21no—
462#382C22×C10911yescharacteristic
463#380C22×C10911yescharacteristic
464#380C22×C10911yescharacteristic
465#340C22×C10911yescharacteristic
466#340C22×C10911yescharacteristic
467#340C22×C10911yescharacteristic
468#340C22×C10911yescharacteristic
469#340C22×C10911yescharacteristic
470#340C22×C10911yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C10911yescharacteristic
476C22×D4C23×C10911yescharacteristic
477C22×D4C23×C10911yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C10911yescharacteristic
482C23×C4C23×C10911yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C10911yescharacteristic
487C22×C8C23×C10911yescharacteristic
488C22×C8C23×C10911yescharacteristic
489C22×C8C23×C10911yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C10914yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C10914yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C10911yescharacteristic
518C2×C4⋊C4C23×C10911yescharacteristic
519C2×C4⋊C4C23×C10911yescharacteristic
520C2×C4⋊C4C23×C10911yescharacteristic
521C2×C4⋊C4C23×C10911yescharacteristic
522C2×C4⋊C4C23×C10911yescharacteristic
523C2×C4⋊C4C23×C10911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4D4×C10911yescharacteristic
534C2×C22⋊C4D4×C10911yescharacteristic
535C2×C42—21no—
536C2×C42C23×C10911yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C10911yescharacteristic
559C24C2×D4×C10911yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C10912yes—
586C2×D4#41×C10912yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C10911yescharacteristic
615C22×C4C2×D4×C10911yescharacteristic
616C22×C4C2×D4×C10911yescharacteristic
617C22×C4C2×D4×C10911yescharacteristic
618C22×C4C24×C10911yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C10912yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C10912yes—
646C4⋊C4C2×D4×C10912yes—
647C4⋊C4C2×D4×C10912yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C10912yes—
661C42C2×D4×C10912yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#135×C10912yes—
690C23C22×D4×C10911yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C10912yes—
744C2×C4#120×C10912yes—
745C2×C4C22×D4×C10911yescharacteristic
746C2×C4C22×D4×C10911yescharacteristic
747C2×C4C2×#41×C10911yescharacteristic
748C2×C4C2×#41×C10911yescharacteristic
749C2×C4H(5,𝔽2)×C10911yescharacteristic
750C2×C42−1+4×C10911yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C10911yescharacteristic
784C22#546×C10911yescharacteristic
785C22#547×C10911yescharacteristic
786C22C2×#135×C10911yescharacteristic
787C22#575×C10911yescharacteristic
788C22#576×C10911yescharacteristic
789C22#576×C10911yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4#525×C10911yescharacteristic
801C4#537×C10911yescharacteristic
802C4#548×C10911yescharacteristic
803C4#550×C10911yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C109×#240711yescharacteristic
809C2C109×#300211yescharacteristic
810C2C109×#300811yescharacteristic
811C2C109×#329711yescharacteristic
812C2C109×#332211yescharacteristic
813C2C109×#333911yescharacteristic
814C2C109×#335511yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
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
1. C2×#553×C109C2semidirect
2. C2×#478×C109C2semidirect
3. C2×C4×D8×C109C2semidirect
4. C109×#2535C2semidirect
5. C109×#2034C2semidirect
6. C109×#2033C2semidirect
7. C109×#1999C2semidirect
8. C109×#1999C2semidirect
9. C109×#1991C2semidirect
10. C109×#1954C2semidirect
11. C109×#1875C2semidirect
12. C109×#1874C2semidirect
13. C109×#1854C2semidirect
14. C109×#1852C2semidirect
15. C109×#1804C2semidirect
84. #125×C109D4semidirect
101. C4×D4×C109D4semidirect
396. #24124C109direct (N × H)
408. C2×#553C2×C109semidirect
409. C2×#478C2×C109semidirect
410. C2×C4×D8C2×C109semidirect
411. #2535C2×C109semidirect
412. #2034C2×C109semidirect
413. #2033C2×C109semidirect
414. #1999C2×C109semidirect
415. #1999C2×C109semidirect
416. #1991C2×C109semidirect
417. #1954C2×C109semidirect
418. #1875C2×C109semidirect
419. #1874C2×C109semidirect
420. #1854C2×C109semidirect
421. #1852C2×C109semidirect
422. #1804C2×C109semidirect
423. C109#24124direct (N × H)
492. #125D4×C109semidirect
509. C4×D4D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1092
C2×#478×C1092
C2×C4×D8×C1092
C109×#25352
C109×#20342
C109×#20332
C109×#19992
C109×#19912
C109×#19542
C109×#18752
C109×#18742
C109×#18542
C109×#18522
C109×#18042
#24124109