Finite Group Databasebeta

← C109×#32735 #42150729

Subgroups — C109×#32735 #42150729

Order 27904.

766 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2624C211yesmaximal, characteristic, complemented
2C109×#2620C211yesmaximal, characteristic, complemented
3C109×#2100C211yesmaximal, characteristic, complemented
4C109×#2093C211yesmaximal, characteristic, complemented
5C109×#2068C211yesmaximal, characteristic, complemented
6C109×#2067C211yesmaximal, characteristic, complemented
7C109×#2055C211yesmaximal, characteristic, complemented
8C109×#2054C211yesmaximal, characteristic, complemented
9C109×#2042C211yesmaximal, characteristic, complemented
10C109×#2036C211yesmaximal, characteristic, complemented
11C109×#2033C211yesmaximal, characteristic, complemented
12C109×#2012C211yesmaximal, characteristic, complemented
13C109×#2000C211yesmaximal, characteristic, complemented
14C109×#1999C211yesmaximal, characteristic
15C109×#1798C211yesmaximal, characteristic, complemented
16C22×SD16×C109C2211yescharacteristic
17C22×D8×C109C2211yescharacteristic
18C2×#124×C109C2211yescharacteristic
19C2×C22⋊Q8×C109C2211yescharacteristic
20C2×#121×C109C2211yescharacteristic
21C2×#121×C109C2211yescharacteristic
22C2×#117×C109C2211yescharacteristic
23C2×#107×C109C2211yescharacteristic
24C2×#107×C109C2211yescharacteristic
25C2×C4⋊C8×C109C2211yescharacteristic
26C2×C4⋊C8×C109C2211yescharacteristic
27C2×#103×C109C2211yescharacteristic
28C2×#103×C109C2211yescharacteristic
29C2×#103×C109C2211yescharacteristic
30C2×#102×C109C2211yescharacteristic
31C2×#102×C109C2211yescharacteristic
32C2×#102×C109C2211yescharacteristic
33C2×#102×C109C2211yescharacteristic
34C2×#102×C109C2211yescharacteristic
35C2×C22⋊C8×C109C2211yescharacteristic
36C2×C22⋊C8×C109C2211yescharacteristic
37#399×C109—21no—
38#397×C109—21no—
39#396×C109—21no—
40#396×C109—21no—
41#394×C109—21no—
42#394×C109—21no—
43#394×C109—21no—
44#394×C109—21no—
45#391×C109C2211yescharacteristic
46#390×C109C2211yescharacteristic
47#390×C109C2211yescharacteristic
48#390×C109C2211yescharacteristic
49#389×C109C2211yescharacteristic
50#389×C109C2211yescharacteristic
51#384×C109C2211yescharacteristic
52#380×C109C2211yescharacteristic
53#340×C109C2211yescharacteristic
54#340×C109C2211yescharacteristic
55#340×C109C2211yescharacteristic
56#340×C109C2211yescharacteristic
57#336×C109C2211yescharacteristic
58#336×C109C2211yescharacteristic
59C22×Q8×C109C2311yescharacteristic
60C22×D4×C109—21no—
61C22×D4×C109—21no—
62C22×D4×C109C2311yescharacteristic
63C22×D4×C109C2311yescharacteristic
64C23×C4×C109C2311yescharacteristic
65C2×SD16×C109—41no—
66C2×SD16×C109—41no—
67C2×SD16×C109—41no—
68C2×D8×C109—41no—
69C2×D8×C109—41no—
70C2×D8×C109—41no—
71C22×C8×C109C2311yescharacteristic
72C22×C8×C109C2311yescharacteristic
73C22×C8×C109C2311yescharacteristic
74C22×C8×C109C2311yescharacteristic
75#124×C109—41no—
76#124×C109—41no—
77C22⋊Q8×C109—41no—
78C22⋊Q8×C109—41no—
79#121×C109—41no—
80#121×C109—41no—
81#121×C109—41no—
82#121×C109—41no—
83#117×C109—41no—
84#117×C109—41no—
85C2×C4⋊C4×C109—21no—
86C2×C4⋊C4×C109—21no—
87C2×C4⋊C4×C109—21no—
88C2×C4⋊C4×C109—21no—
89C2×C4⋊C4×C109—21no—
90C2×C4⋊C4×C109D411yescharacteristic
91C2×C4⋊C4×C109D411yescharacteristic
92C2×C4⋊C4×C109C2311yescharacteristic
93C2×C4⋊C4×C109C2311yescharacteristic
94C2×C4⋊C4×C109C2311yescharacteristic
95C2×C4⋊C4×C109C2311yescharacteristic
96C2×C4⋊C4×C109C2311yescharacteristic
97C2×C22⋊C4×C109—21no—
98C2×C22⋊C4×C109—21no—
99C2×C22⋊C4×C109—21no—
100C2×C22⋊C4×C109—21no—
101C2×C22⋊C4×C109—21no—
102C2×C22⋊C4×C109—21no—
103C2×C22⋊C4×C109—21no—
104C2×C22⋊C4×C109—21no—
105C2×C22⋊C4×C109—21no—
106C2×C22⋊C4×C109—21no—
107C2×C22⋊C4×C109—21no—
108C2×C22⋊C4×C109—21no—
109C2×C22⋊C4×C109D411yescharacteristic
110C2×C22⋊C4×C109D411yescharacteristic
111C2×C42×C109C2311yescharacteristic
112C2×C42×C109C2311yescharacteristic
113#107×C109—41no—
114#107×C109—41no—
115C4⋊C8×C109—41no—
116C4⋊C8×C109—41no—
117#103×C109—41no—
118#103×C109—41no—
119#103×C109—41no—
120#102×C109—41no—
121#102×C109—41no—
122#102×C109—41no—
123#102×C109—41no—
124#102×C109—41no—
125C22⋊C8×C109—41no—
126C22⋊C8×C109—41no—
127#95×C109—21no—
128#95×C109—21no—
129#95×C109—21no—
130#95×C109—21no—
131#95×C109—21no—
132C24×C109—21no—
133C24×C109—21no—
134C24×C109C2×D411yescharacteristic
135C2×Q8×C109—21no—
136C2×Q8×C109—21no—
137C2×Q8×C109—21no—
138C2×Q8×C109—21no—
139C2×Q8×C109—21no—
140C2×Q8×C109—21no—
141C2×D4×C109—21no—
142C2×D4×C109—21no—
143C2×D4×C109—21no—
144C2×D4×C109—21no—
145C2×D4×C109—21no—
146C2×D4×C109—21no—
147C2×D4×C109—21no—
148C2×D4×C109—21no—
149C2×D4×C109—21no—
150C2×D4×C109—21no—
151C2×D4×C109—21no—
152C2×D4×C109—21no—
153C2×D4×C109—42no—
154C2×D4×C109—42no—
155C2×D4×C109—81no—
156C2×D4×C109—81no—
157C2×D4×C109—81no—
158C2×D4×C109—81no—
159C22×C4×C109—21no—
160C22×C4×C109—21no—
161C22×C4×C109—21no—
162C22×C4×C109—21no—
163C22×C4×C109—21no—
164C22×C4×C109—21no—
165C22×C4×C109—21no—
166C22×C4×C109—21no—
167C22×C4×C109—21no—
168C22×C4×C109—21no—
169C22×C4×C109—21no—
170C22×C4×C109—21no—
171C22×C4×C109C2×D411yescharacteristic
172C22×C4×C109C2×D411yescharacteristic
173C22×C4×C109C2×D411yescharacteristic
174C22×C4×C109C2×D411yescharacteristic
175C22×C4×C109C2×D411yescharacteristic
176C22×C4×C109C2411yescharacteristic
177SD16×C109—44no—
178D8×C109—44no—
179C2×C8×C109—21no—
180C2×C8×C109—21no—
181C2×C8×C109—21no—
182C2×C8×C109—21no—
183C2×C8×C109—21no—
184C2×C8×C109—21no—
185C2×C8×C109—21no—
186C2×C8×C109—21no—
187C2×C8×C109—21no—
188C2×C8×C109—21no—
189C2×C8×C109—21no—
190C2×C8×C109—21no—
191C4⋊C4×C109—21no—
192C4⋊C4×C109—21no—
193C4⋊C4×C109—21no—
194C4⋊C4×C109—21no—
195C4⋊C4×C109—21no—
196C4⋊C4×C109—21no—
197C4⋊C4×C109—21no—
198C4⋊C4×C109—21no—
199C4⋊C4×C109—21no—
200C4⋊C4×C109—21no—
201C4⋊C4×C109—41no—
202C4⋊C4×C109—41no—
203C4⋊C4×C109—42no—
204C4⋊C4×C109—81no—
205C4⋊C4×C109—81no—
206C4⋊C4×C109—81no—
207C4⋊C4×C109—81no—
208C22⋊C4×C109—41no—
209C22⋊C4×C109—41no—
210C22⋊C4×C109—42no—
211C22⋊C4×C109—42no—
212C22⋊C4×C109—42no—
213C22⋊C4×C109—42no—
214C22⋊C4×C109—42no—
215C22⋊C4×C109—81no—
216C22⋊C4×C109—81no—
217C22⋊C4×C109—81no—
218C22⋊C4×C109—81no—
219C22⋊C4×C109—81no—
220C22⋊C4×C109—81no—
221C22⋊C4×C109—81no—
222C42×C109—21no—
223C42×C109—21no—
224C42×C109—21no—
225C42×C109—21no—
226C23×C109—21no—
227C23×C109—21no—
228C23×C109—21no—
229C23×C109—21no—
230C23×C109—21no—
231C23×C109—21no—
232C23×C109—21no—
233C23×C109—41no—
234C23×C109—41no—
235C23×C109—41no—
236C23×C109—41no—
237C23×C109—41no—
238C23×C109—41no—
239C23×C109—41no—
240C23×C109—41no—
241C23×C109—41no—
242C23×C109—41no—
243C23×C109—41no—
244C23×C109—41no—
245C23×C109—41no—
246C23×C109—41no—
247C23×C109C22×D411yescharacteristic
248Q8×C109—41no—
249Q8×C109—41no—
250Q8×C109—41no—
251Q8×C109—41no—
252D4×C109—41no—
253D4×C109—41no—
254D4×C109—41no—
255D4×C109—41no—
256D4×C109—41no—
257D4×C109—41no—
258D4×C109—41no—
259D4×C109—41no—
260D4×C109—84no—
261D4×C109—84no—
262C2×C4×C109—21no—
263C2×C4×C109—21no—
264C2×C4×C109—21no—
265C2×C4×C109—21no—
266C2×C4×C109—21no—
267C2×C4×C109—21no—
268C2×C4×C109—21no—
269C2×C4×C109—21no—
270C2×C4×C109—21no—
271C2×C4×C109—21no—
272C2×C4×C109—21no—
273C2×C4×C109—21no—
274C2×C4×C109—21no—
275C2×C4×C109—21no—
276C2×C4×C109—21no—
277C2×C4×C109—41no—
278C2×C4×C109—41no—
279C2×C4×C109—41no—
280C2×C4×C109—41no—
281C2×C4×C109—41no—
282C2×C4×C109—41no—
283C2×C4×C109—41no—
284C2×C4×C109—41no—
285C2×C4×C109—41no—
286C2×C4×C109—41no—
287C2×C4×C109—41no—
288C2×C4×C109—41no—
289C2×C4×C109—41no—
290C2×C4×C109—41no—
291C2×C4×C109—41no—
292C2×C4×C109—41no—
293C2×C4×C109—41no—
294C2×C4×C109—41no—
295C2×C4×C109—41no—
296C2×C4×C109—41no—
297C2×C4×C109—41no—
298C2×C4×C109—41no—
299C2×C4×C109H(5,𝔽2)11yescharacteristic
300C2×C4×C109H(5,𝔽2)11yescharacteristic
301C2×C4×C109H(5,𝔽2)11yescharacteristic
302C2×C4×C109H(5,𝔽2)11yescharacteristic
303C2×C4×C109H(5,𝔽2)11yescharacteristic
304C2×C4×C1092−1+411yescharacteristic
305C8×C109—41no—
306C8×C109—41no—
307C8×C109—41no—
308C8×C109—41no—
309C22×C109—41no—
310C22×C109—41no—
311C22×C109—41no—
312C22×C109—41no—
313C22×C109—41no—
314C22×C109—41no—
315C22×C109—41no—
316C22×C109—81no—
317C22×C109—81no—
318C22×C109—81no—
319C22×C109—81no—
320C22×C109—81no—
321C22×C109—81no—
322C22×C109—81no—
323C22×C109—81no—
324C22×C109—81no—
325C22×C109—81no—
326C22×C109—81no—
327C22×C109—81no—
328C22×C109—81no—
329C22×C109—81no—
330C22×C109#53411yescharacteristic
331C22×C109#53511yescharacteristic
332C22×C109#53711yescharacteristic
333C22×C109#57611yescharacteristic
334C22×C109#57611yescharacteristic
335C22×C109#57711yescharacteristic
336C22×C109#57811yescharacteristic
337C4×C109—41no—
338C4×C109—41no—
339C4×C109—41no—
340C4×C109—41no—
341C4×C109—41no—
342C4×C109—81no—
343C4×C109—81no—
344C4×C109—81no—
345C4×C109—81no—
346C4×C109—81no—
347C4×C109—81no—
348C4×C109#56011yescharacteristic
349C4×C109#56011yescharacteristic
350C4×C109#56211yescharacteristic
351C4×C109#56211yescharacteristic
352#32735C10911yesmaximal, characteristic, direct product factor, Sylow
353C2×C109—81no—
354C2×C109—161no—
355C2×C109—161no—
356C2×C109#281311yescharacteristic
357C2×C109#319811yescharacteristic
358C2×C109#320311yescharacteristic
359C2×C109#322011yescharacteristic
360C2×C109#322511yescharacteristic
361C2×C109#325711yescharacteristic
362C2×C109#326211yescharacteristic
363#2624C2×C10911yescharacteristic, complemented
364#2620C2×C10911yescharacteristic, complemented
365#2100C2×C10911yescharacteristic, complemented
366#2093C2×C10911yescharacteristic, complemented
367#2068C2×C10911yescharacteristic, complemented
368#2067C2×C10911yescharacteristic, complemented
369#2055C2×C10911yescharacteristic, complemented
370#2054C2×C10911yescharacteristic, complemented
371#2042C2×C10911yescharacteristic, complemented
372#2036C2×C10911yescharacteristic, complemented
373#2033C2×C10911yescharacteristic, complemented
374#2012C2×C10911yescharacteristic, complemented
375#2000C2×C10911yescharacteristic, complemented
376#1999C2×C10911yescharacteristic
377#1798C2×C10911yescharacteristic, complemented
378C109#3273511yescharacteristic, direct product factor, Sylow
379C22×SD16C22×C10911yescharacteristic
380C22×D8C22×C10911yescharacteristic
381C2×#124C22×C10911yescharacteristic
382C2×C22⋊Q8C22×C10911yescharacteristic
383C2×#121C22×C10911yescharacteristic
384C2×#121C22×C10911yescharacteristic
385C2×#117C22×C10911yescharacteristic
386C2×#107C22×C10911yescharacteristic
387C2×#107C22×C10911yescharacteristic
388C2×C4⋊C8C22×C10911yescharacteristic
389C2×C4⋊C8C22×C10911yescharacteristic
390C2×#103C22×C10911yescharacteristic
391C2×#103C22×C10911yescharacteristic
392C2×#103C22×C10911yescharacteristic
393C2×#102C22×C10911yescharacteristic
394C2×#102C22×C10911yescharacteristic
395C2×#102C22×C10911yescharacteristic
396C2×#102C22×C10911yescharacteristic
397C2×#102C22×C10911yescharacteristic
398C2×C22⋊C8C22×C10911yescharacteristic
399C2×C22⋊C8C22×C10911yescharacteristic
400#399—21no—
401#397—21no—
402#396—21no—
403#396—21no—
404#394—21no—
405#394—21no—
406#394—21no—
407#394—21no—
408#391C22×C10911yescharacteristic
409#390C22×C10911yescharacteristic
410#390C22×C10911yescharacteristic
411#390C22×C10911yescharacteristic
412#389C22×C10911yescharacteristic
413#389C22×C10911yescharacteristic
414#384C22×C10911yescharacteristic
415#380C22×C10911yescharacteristic
416#340C22×C10911yescharacteristic
417#340C22×C10911yescharacteristic
418#340C22×C10911yescharacteristic
419#340C22×C10911yescharacteristic
420#336C22×C10911yescharacteristic
421#336C22×C10911yescharacteristic
422C22×Q8C23×C10911yescharacteristic
423C22×D4—21no—
424C22×D4—21no—
425C22×D4C23×C10911yescharacteristic
426C22×D4C23×C10911yescharacteristic
427C23×C4C23×C10911yescharacteristic
428C2×SD16—41no—
429C2×SD16—41no—
430C2×SD16—41no—
431C2×D8—41no—
432C2×D8—41no—
433C2×D8—41no—
434C22×C8C23×C10911yescharacteristic
435C22×C8C23×C10911yescharacteristic
436C22×C8C23×C10911yescharacteristic
437C22×C8C23×C10911yescharacteristic
438#124—41no—
439#124—41no—
440C22⋊Q8—41no—
441C22⋊Q8—41no—
442#121—41no—
443#121—41no—
444#121—41no—
445#121—41no—
446#117—41no—
447#117—41no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4D4×C10911yescharacteristic
454C2×C4⋊C4D4×C10911yescharacteristic
455C2×C4⋊C4C23×C10911yescharacteristic
456C2×C4⋊C4C23×C10911yescharacteristic
457C2×C4⋊C4C23×C10911yescharacteristic
458C2×C4⋊C4C23×C10911yescharacteristic
459C2×C4⋊C4C23×C10911yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4D4×C10911yescharacteristic
473C2×C22⋊C4D4×C10911yescharacteristic
474C2×C42C23×C10911yescharacteristic
475C2×C42C23×C10911yescharacteristic
476#107—41no—
477#107—41no—
478C4⋊C8—41no—
479C4⋊C8—41no—
480#103—41no—
481#103—41no—
482#103—41no—
483#102—41no—
484#102—41no—
485#102—41no—
486#102—41no—
487#102—41no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C24—21no—
496C24—21no—
497C24C2×D4×C10911yescharacteristic
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4—81no—
520C2×D4—81no—
521C2×D4—81no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4C2×D4×C10911yescharacteristic
535C22×C4C2×D4×C10911yescharacteristic
536C22×C4C2×D4×C10911yescharacteristic
537C22×C4C2×D4×C10911yescharacteristic
538C22×C4C2×D4×C10911yescharacteristic
539C22×C4C24×C10911yescharacteristic
540SD16—44no—
541D8—44no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—42no—
567C4⋊C4—81no—
568C4⋊C4—81no—
569C4⋊C4—81no—
570C4⋊C4—81no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C22×D4×C10911yescharacteristic
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4H(5,𝔽2)×C10911yescharacteristic
663C2×C4H(5,𝔽2)×C10911yescharacteristic
664C2×C4H(5,𝔽2)×C10911yescharacteristic
665C2×C4H(5,𝔽2)×C10911yescharacteristic
666C2×C4H(5,𝔽2)×C10911yescharacteristic
667C2×C42−1+4×C10911yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22#534×C10911yescharacteristic
694C22#535×C10911yescharacteristic
695C22#537×C10911yescharacteristic
696C22#576×C10911yescharacteristic
697C22#576×C10911yescharacteristic
698C22#577×C10911yescharacteristic
699C22#578×C10911yescharacteristic
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4#560×C10911yescharacteristic
712C4#560×C10911yescharacteristic
713C4#562×C10911yescharacteristic
714C4#562×C10911yescharacteristic
715C2—81no—
716C2—161no—
717C2—161no—
718C2C109×#281311yescharacteristic
719C2C109×#319811yescharacteristic
720C2C109×#320311yescharacteristic
721C2C109×#322011yescharacteristic
722C2C109×#322511yescharacteristic
723C2C109×#325711yescharacteristic
724C2C109×#326211yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#1999C2
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. C109×#2624C2semidirect
2. C109×#2620C2semidirect
3. C109×#2100C2semidirect
4. C109×#2093C2semidirect
5. C109×#2068C2semidirect
6. C109×#2067C2semidirect
7. C109×#2055C2semidirect
8. C109×#2054C2semidirect
9. C109×#2042C2semidirect
10. C109×#2036C2semidirect
11. C109×#2033C2semidirect
12. C109×#2012C2semidirect
13. C109×#2000C2semidirect
15. C109×#1798C2semidirect
352. #32735C109direct (N × H)
363. #2624C2×C109semidirect
364. #2620C2×C109semidirect
365. #2100C2×C109semidirect
366. #2093C2×C109semidirect
367. #2068C2×C109semidirect
368. #2067C2×C109semidirect
369. #2055C2×C109semidirect
370. #2054C2×C109semidirect
371. #2042C2×C109semidirect
372. #2036C2×C109semidirect
373. #2033C2×C109semidirect
374. #2012C2×C109semidirect
375. #2000C2×C109semidirect
377. #1798C2×C109semidirect
378. C109#32735direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#26242
C109×#26202
C109×#21002
C109×#20932
C109×#20682
C109×#20672
C109×#20552
C109×#20542
C109×#20422
C109×#20362
C109×#20332
C109×#20122
C109×#20002
C109×#19992
C109×#17982
#32735109