Finite Group Databasebeta

← C109×#23580 #42141574

Subgroups — C109×#23580 #42141574

Order 27904.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C109C211yesmaximal, characteristic, complemented
2C2×#442×C109C211yesmaximal, characteristic, complemented
3C2×C4×D8×C109C211yesmaximal, characteristic, complemented
4C109×#2324C211yesmaximal, characteristic, complemented
5C109×#2059C211yesmaximal, characteristic, complemented
6C109×#2041C211yesmaximal, characteristic, complemented
7C109×#2034C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#2025C211yesmaximal, characteristic, complemented
10C109×#2011C211yesmaximal, characteristic, complemented
11C109×#1999C211yesmaximal, characteristic, complemented
12C109×#1999C211yesmaximal, characteristic, complemented
13C109×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C109C211yesmaximal, characteristic, complemented
15C109×#1750C211yesmaximal, characteristic, complemented
16C22×D8×C109C2211yescharacteristic
17C22×D8×C109C2211yescharacteristic
18#540×C109—24no—
19#540×C109—24no—
20C2×#127×C109C2211yescharacteristic
21C2×#125×C109C2211yescharacteristic
22C2×#123×C109—21no—
23C2×#123×C109—21no—
24C2×#121×C109—21no—
25C2×#121×C109—21no—
26C2×#121×C109C2211yescharacteristic
27C2×#121×C109C2211yescharacteristic
28C2×#121×C109C2211yescharacteristic
29C2×C4×D4×C109C2211yescharacteristic
30C2×C4×D4×C109C2211yescharacteristic
31C2×C4×D4×C109C2211yescharacteristic
32C2×#117×C109C2211yescharacteristic
33#442×C109—24no—
34C4×D8×C109—24no—
35C2×#107×C109C2211yescharacteristic
36C2×#106×C109C2211yescharacteristic
37C2×#102×C109C2211yescharacteristic
38C2×#102×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×#97×C109C2211yescharacteristic
48C2×C4×C8×C109C2211yescharacteristic
49#390×C109—21no—
50#390×C109C2211yescharacteristic
51#389×C109C2211yescharacteristic
52#388×C109—21no—
53#386×C109—21no—
54#385×C109—21no—
55#380×C109C2211yescharacteristic
56C4×C4⋊C4×C109C2211yescharacteristic
57#340×C109C2211yescharacteristic
58#340×C109C2211yescharacteristic
59#340×C109C2211yescharacteristic
60#340×C109C2211yescharacteristic
61#336×C109C2211yescharacteristic
62#336×C109C2211yescharacteristic
63C22×D4×C109—21no—
64C22×D4×C109—21no—
65C22×D4×C109—21no—
66C22×D4×C109—21no—
67C22×D4×C109—21no—
68C22×D4×C109C2311yescharacteristic
69C22×D4×C109C2311yescharacteristic
70C22×D4×C109C2311yescharacteristic
71C23×C4×C109—21no—
72C23×C4×C109—21no—
73C23×C4×C109—21no—
74C23×C4×C109C2311yescharacteristic
75C2×D8×C109—22no—
76C2×D8×C109—22no—
77C2×D8×C109—22no—
78C2×D8×C109—22no—
79C2×D8×C109—22no—
80C2×D8×C109—22no—
81C22×C8×C109C2311yescharacteristic
82C22×C8×C109C2311yescharacteristic
83C22×C8×C109C2311yescharacteristic
84C22×C8×C109C2311yescharacteristic
85#127×C109—22no—
86#127×C109—22no—
87#125×C109—22no—
88#125×C109—22no—
89#123×C109—28no—
90#123×C109—28no—
91#121×C109—28no—
92#121×C109—28no—
93#121×C109—22no—
94#121×C109—22no—
95#121×C109—22no—
96#121×C109—22no—
97#121×C109—22no—
98#121×C109—22no—
99C4×D4×C109—22no—
100C4×D4×C109—22no—
101C4×D4×C109—22no—
102C4×D4×C109—22no—
103C4×D4×C109D414yescomplemented
104C4×D4×C109D414yescomplemented
105#117×C109—22no—
106#117×C109—22no—
107C2×C4⋊C4×C109—21no—
108C2×C4⋊C4×C109—21no—
109C2×C4⋊C4×C109—21no—
110C2×C4⋊C4×C109D411yescharacteristic
111C2×C4⋊C4×C109D411yescharacteristic
112C2×C4⋊C4×C109C2311yescharacteristic
113C2×C4⋊C4×C109C2311yescharacteristic
114C2×C4⋊C4×C109C2311yescharacteristic
115C2×C4⋊C4×C109C2311yescharacteristic
116C2×C4⋊C4×C109C2311yescharacteristic
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×C109—21no—
126C2×C22⋊C4×C109D411yescharacteristic
127C2×C22⋊C4×C109D411yescharacteristic
128C2×C42×C109—21no—
129C2×C42×C109C2311yescharacteristic
130C2×C42×C109C2311yescharacteristic
131#107×C109—22no—
132#106×C109—22no—
133#102×C109—22no—
134#102×C109—22no—
135#102×C109—22no—
136#102×C109—22no—
137#102×C109—22no—
138#102×C109—22no—
139#102×C109—22no—
140#102×C109—22no—
141C22⋊C8×C109—22no—
142C22⋊C8×C109—22no—
143#97×C109—22no—
144C4×C8×C109—22no—
145#95×C109—21no—
146#95×C109—21no—
147#95×C109—21no—
148C24×C109—21no—
149C24×C109—21no—
150C24×C109—21no—
151C24×C109C2×D411yescharacteristic
152C2×D4×C109—24no—
153C2×D4×C109—24no—
154C2×D4×C109—24no—
155C2×D4×C109—24no—
156C2×D4×C109—24no—
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—21no—
167C2×D4×C109—21no—
168C2×D4×C109—21no—
169C2×D4×C109—21no—
170C2×D4×C109—21no—
171C2×D4×C109—21no—
172C2×D4×C109—81no—
173C2×D4×C109—81no—
174C2×D4×C109—81no—
175C2×D4×C109—81no—
176C2×D4×C109—81no—
177C2×D4×C109—81no—
178C2×D4×C109—81no—
179C2×D4×C109—81no—
180C2×D4×C109—81no—
181C2×D4×C109—81no—
182C2×D4×C109C2×D412yes—
183C2×D4×C109C2×D412yes—
184C2×D4×C109#4112yes—
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—24no—
195C22×C4×C109—24no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—42no—
199C22×C4×C109—81no—
200C22×C4×C109—81no—
201C22×C4×C109—81no—
202C22×C4×C109—81no—
203C22×C4×C109—81no—
204C22×C4×C109—81no—
205C22×C4×C109C2×D411yescharacteristic
206C22×C4×C109C2×D411yescharacteristic
207C22×C4×C109C2×D411yescharacteristic
208C22×C4×C109C2×D411yescharacteristic
209C22×C4×C109C2×D411yescharacteristic
210C22×C4×C109C2411yescharacteristic
211D8×C109—28no—
212D8×C109—28no—
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—
224C2×C8×C109#4112yes—
225C4⋊C4×C109—24no—
226C4⋊C4×C109—24no—
227C4⋊C4×C109—22no—
228C4⋊C4×C109—22no—
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—81no—
237C4⋊C4×C109C2×D412yes—
238C4⋊C4×C109C2×D412yes—
239C4⋊C4×C109#4112yes—
240C22⋊C4×C109—24no—
241C22⋊C4×C109—24no—
242C22⋊C4×C109—24no—
243C22⋊C4×C109—24no—
244C22⋊C4×C109—24no—
245C22⋊C4×C109—22no—
246C22⋊C4×C109—22no—
247C22⋊C4×C109—42no—
248C22⋊C4×C109—81no—
249C22⋊C4×C109—81no—
250C22⋊C4×C109—81no—
251C42×C109—21no—
252C42×C109—21no—
253C42×C109—81no—
254C42×C109C2×D412yes—
255C42×C109C2×D412yes—
256C23×C109—21no—
257C23×C109—22no—
258C23×C109—22no—
259C23×C109—22no—
260C23×C109—21no—
261C23×C109—21no—
262C23×C109—21no—
263C23×C109—21no—
264C23×C109—21no—
265C23×C109—21no—
266C23×C109—41no—
267C23×C109—41no—
268C23×C109—41no—
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—41no—
282C23×C109—41no—
283C23×C109—41no—
284C23×C109C22×D411yescharacteristic
285D4×C109—22no—
286D4×C109—22no—
287D4×C109—22no—
288D4×C109—22no—
289D4×C109—22no—
290D4×C109—22no—
291D4×C109—41no—
292D4×C109—41no—
293D4×C109—41no—
294D4×C109—41no—
295D4×C109—41no—
296D4×C109—41no—
297D4×C109—84no—
298D4×C109—84no—
299D4×C109—84no—
300D4×C109—84no—
301D4×C109—84no—
302C2×C4×C109—21no—
303C2×C4×C109—21no—
304C2×C4×C109—21no—
305C2×C4×C109—21no—
306C2×C4×C109—21no—
307C2×C4×C109—21no—
308C2×C4×C109—21no—
309C2×C4×C109—22no—
310C2×C4×C109—22no—
311C2×C4×C109—21no—
312C2×C4×C109—22no—
313C2×C4×C109—21no—
314C2×C4×C109—21no—
315C2×C4×C109—21no—
316C2×C4×C109—21no—
317C2×C4×C109—21no—
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—41no—
333C2×C4×C109—41no—
334C2×C4×C109—84no—
335C2×C4×C109—84no—
336C2×C4×C109—84no—
337C2×C4×C109#12012yes—
338C2×C4×C109#12012yes—
339C2×C4×C109C22×D411yescharacteristic
340C2×C4×C109C22×D411yescharacteristic
341C2×C4×C109C2×#4111yescharacteristic
342C2×C4×C109C2×#4111yescharacteristic
343C2×C4×C109C2×#4111yescharacteristic
344C2×C4×C109C2×#4111yescharacteristic
345C8×C109—22no—
346C8×C109—22no—
347C8×C109—41no—
348C8×C109—41no—
349C22×C109—41no—
350C22×C109—42no—
351C22×C109—41no—
352C22×C109—42no—
353C22×C109—41no—
354C22×C109—42no—
355C22×C109—42no—
356C22×C109—42no—
357C22×C109—41no—
358C22×C109—41no—
359C22×C109—42no—
360C22×C109—41no—
361C22×C109—42no—
362C22×C109—42no—
363C22×C109—41no—
364C22×C109—42no—
365C22×C109—81no—
366C22×C109—81no—
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×C109—81no—
376C22×C109—81no—
377C22×C109C2×#12011yescharacteristic
378C22×C109#52511yescharacteristic
379C22×C109#53211yescharacteristic
380C22×C109#57611yescharacteristic
381C22×C109#57611yescharacteristic
382C22×C109#57611yescharacteristic
383C22×C109#57711yescharacteristic
384C4×C109—22no—
385C4×C109—22no—
386C4×C109—42no—
387C4×C109—41no—
388C4×C109—41no—
389C4×C109—42no—
390C4×C109—41no—
391C4×C109—42no—
392C4×C109—81no—
393C4×C109—81no—
394C4×C109#52511yescharacteristic
395C4×C109#52511yescharacteristic
396C4×C109#53211yescharacteristic
397C4×C109#53211yescharacteristic
398#23580C10911yesmaximal, characteristic, direct product factor, Sylow
399C2×C109—81no—
400C2×C109—82no—
401C2×C109—82no—
402C2×C109—82no—
403C2×C109#238811yescharacteristic
404C2×C109#300811yescharacteristic
405C2×C109#301211yescharacteristic
406C2×C109#311911yescharacteristic
407C2×C109#312211yescharacteristic
408C2×C109#317611yescharacteristic
409C2×C109#317911yescharacteristic
410C2×#540C2×C10911yescharacteristic, complemented
411C2×#442C2×C10911yescharacteristic, complemented
412C2×C4×D8C2×C10911yescharacteristic, complemented
413#2324C2×C10911yescharacteristic, complemented
414#2059C2×C10911yescharacteristic, complemented
415#2041C2×C10911yescharacteristic, complemented
416#2034C2×C10911yescharacteristic, complemented
417#2033C2×C10911yescharacteristic, complemented
418#2025C2×C10911yescharacteristic, complemented
419#2011C2×C10911yescharacteristic, complemented
420#1999C2×C10911yescharacteristic, complemented
421#1999C2×C10911yescharacteristic, complemented
422#1762C2×C10911yescharacteristic, complemented
423C4×#102C2×C10911yescharacteristic, complemented
424#1750C2×C10911yescharacteristic, complemented
425C109#2358011yescharacteristic, direct product factor, Sylow
426C22×D8C22×C10911yescharacteristic
427C22×D8C22×C10911yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C10911yescharacteristic
431C2×#125C22×C10911yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C10911yescharacteristic
437C2×#121C22×C10911yescharacteristic
438C2×#121C22×C10911yescharacteristic
439C2×C4×D4C22×C10911yescharacteristic
440C2×C4×D4C22×C10911yescharacteristic
441C2×C4×D4C22×C10911yescharacteristic
442C2×#117C22×C10911yescharacteristic
443#442—24no—
444C4×D8—24no—
445C2×#107C22×C10911yescharacteristic
446C2×#106C22×C10911yescharacteristic
447C2×#102C22×C10911yescharacteristic
448C2×#102C22×C10911yescharacteristic
449C2×#102C22×C10911yescharacteristic
450C2×#102C22×C10911yescharacteristic
451C2×#102C22×C10911yescharacteristic
452C2×#102C22×C10911yescharacteristic
453C2×#102C22×C10911yescharacteristic
454C2×#102C22×C10911yescharacteristic
455C2×C22⋊C8C22×C10911yescharacteristic
456C2×C22⋊C8C22×C10911yescharacteristic
457C2×#97C22×C10911yescharacteristic
458C2×C4×C8C22×C10911yescharacteristic
459#390—21no—
460#390C22×C10911yescharacteristic
461#389C22×C10911yescharacteristic
462#388—21no—
463#386—21no—
464#385—21no—
465#380C22×C10911yescharacteristic
466C4×C4⋊C4C22×C10911yescharacteristic
467#340C22×C10911yescharacteristic
468#340C22×C10911yescharacteristic
469#340C22×C10911yescharacteristic
470#340C22×C10911yescharacteristic
471#336C22×C10911yescharacteristic
472#336C22×C10911yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C10911yescharacteristic
479C22×D4C23×C10911yescharacteristic
480C22×D4C23×C10911yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C10911yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C10911yescharacteristic
492C22×C8C23×C10911yescharacteristic
493C22×C8C23×C10911yescharacteristic
494C22×C8C23×C10911yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C10914yescomplemented
514C4×D4D4×C10914yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C10911yescharacteristic
521C2×C4⋊C4D4×C10911yescharacteristic
522C2×C4⋊C4C23×C10911yescharacteristic
523C2×C4⋊C4C23×C10911yescharacteristic
524C2×C4⋊C4C23×C10911yescharacteristic
525C2×C4⋊C4C23×C10911yescharacteristic
526C2×C4⋊C4C23×C10911yescharacteristic
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⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C10911yescharacteristic
537C2×C22⋊C4D4×C10911yescharacteristic
538C2×C42—21no—
539C2×C42C23×C10911yescharacteristic
540C2×C42C23×C10911yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C10911yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C10912yes—
593C2×D4C2×D4×C10912yes—
594C2×D4#41×C10912yes—
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—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C10911yescharacteristic
616C22×C4C2×D4×C10911yescharacteristic
617C22×C4C2×D4×C10911yescharacteristic
618C22×C4C2×D4×C10911yescharacteristic
619C22×C4C2×D4×C10911yescharacteristic
620C22×C4C24×C10911yescharacteristic
621D8—28no—
622D8—28no—
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—21no—
632C2×C8—21no—
633C2×C8#41×C10912yes—
634C2×C8#41×C10912yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C10912yes—
648C4⋊C4C2×D4×C10912yes—
649C4⋊C4#41×C10912yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C10912yes—
665C42C2×D4×C10912yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
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—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C10911yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
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—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C10912yes—
748C2×C4#120×C10912yes—
749C2×C4C22×D4×C10911yescharacteristic
750C2×C4C22×D4×C10911yescharacteristic
751C2×C4C2×#41×C10911yescharacteristic
752C2×C4C2×#41×C10911yescharacteristic
753C2×C4C2×#41×C10911yescharacteristic
754C2×C4C2×#41×C10911yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C10911yescharacteristic
788C22#525×C10911yescharacteristic
789C22#532×C10911yescharacteristic
790C22#576×C10911yescharacteristic
791C22#576×C10911yescharacteristic
792C22#576×C10911yescharacteristic
793C22#577×C10911yescharacteristic
794C4—22no—
795C4—22no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—42no—
800C4—42no—
801C4—41no—
802C4—81no—
803C4—81no—
804C4#525×C10911yescharacteristic
805C4#525×C10911yescharacteristic
806C4#532×C10911yescharacteristic
807C4#532×C10911yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C109×#238811yescharacteristic
813C2C109×#300811yescharacteristic
814C2C109×#301211yescharacteristic
815C2C109×#311911yescharacteristic
816C2C109×#312211yescharacteristic
817C2C109×#317611yescharacteristic
818C2C109×#317911yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×#117×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C109C2semidirect
2. C2×#442×C109C2semidirect
3. C2×C4×D8×C109C2semidirect
4. C109×#2324C2semidirect
5. C109×#2059C2semidirect
6. C109×#2041C2semidirect
7. C109×#2034C2semidirect
8. C109×#2033C2semidirect
9. C109×#2025C2semidirect
10. C109×#2011C2semidirect
11. C109×#1999C2semidirect
12. C109×#1999C2semidirect
13. C109×#1762C2semidirect
14. C4×#102×C109C2semidirect
15. C109×#1750C2semidirect
103. C4×D4×C109D4semidirect
104. C4×D4×C109D4semidirect
398. #23580C109direct (N × H)
410. C2×#540C2×C109semidirect
411. C2×#442C2×C109semidirect
412. C2×C4×D8C2×C109semidirect
413. #2324C2×C109semidirect
414. #2059C2×C109semidirect
415. #2041C2×C109semidirect
416. #2034C2×C109semidirect
417. #2033C2×C109semidirect
418. #2025C2×C109semidirect
419. #2011C2×C109semidirect
420. #1999C2×C109semidirect
421. #1999C2×C109semidirect
422. #1762C2×C109semidirect
423. C4×#102C2×C109semidirect
424. #1750C2×C109semidirect
425. C109#23580direct (N × H)
513. C4×D4D4×C109semidirect
514. C4×D4D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C1092
C2×#442×C1092
C2×C4×D8×C1092
C109×#23242
C109×#20592
C109×#20412
C109×#20342
C109×#20332
C109×#20252
C109×#20112
C109×#19992
C109×#17622
C4×#102×C1092
C109×#17502
#23580109