Finite Group Databasebeta

← C73×#23036 #32932440

Subgroups — C73×#23036 #32932440

Order 18688.

942 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#470×C73C211yesmaximal, characteristic
2C2×C4×Q16×C73C211yesmaximal, characteristic, complemented
3C2×#428×C73C211yesmaximal, characteristic
4C73×#2362C211yesmaximal, characteristic
5C73×#2360C211yesmaximal, characteristic
6C73×#1971C211yesmaximal, characteristic, complemented
7C73×#1941C211yesmaximal, characteristic, complemented
8C73×#1928C211yesmaximal, characteristic, complemented
9C73×#1927C211yesmaximal, characteristic, complemented
10C73×#1873C211yesmaximal, characteristic
11C73×#1872C211yesmaximal, characteristic
12C73×#1865C211yesmaximal, characteristic, complemented
13C73×#1863C211yesmaximal, characteristic, complemented
14C73×#1776C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic
16C22×Q16×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×C22⋊Q8×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic
21C2×C4×Q8×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24#470×C73C418yescomplemented
25C4×Q16×C73—24no—
26#428×C73—24no—
27C2×#107×C73C2211yescharacteristic
28C2×#107×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31C2×#106×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40C2×C4×C8×C73C2211yescharacteristic
41#391×C73C2211yescharacteristic
42#391×C73C2211yescharacteristic
43#389×C73—21no—
44#389×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic
46#388×C73—21no—
47#388×C73—21no—
48#387×C73—21no—
49#387×C73—21no—
50#385×C73—21no—
51C4×C4⋊C4×C73—21no—
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C22⋊C4×C73—21no—
55C4×C22⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C23×C4×C73—21no—
65C23×C4×C73C2311yescharacteristic
66C2×Q16×C73—22no—
67C2×Q16×C73—22no—
68C2×Q16×C73C2×C414yescomplemented
69C2×M16×C73—22no—
70C2×M16×C73—22no—
71C2×M16×C73C2×C414yes—
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22⋊Q8×C73—22no—
77C22⋊Q8×C73—22no—
78C22⋊Q8×C73C2×C414yes—
79C22⋊Q8×C73C2×C414yes—
80C4×Q8×C73—22no—
81C4×Q8×C73—22no—
82C4×Q8×C73—41no—
83C4×Q8×C73—41no—
84#117×C73—22no—
85#117×C73—41no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—41no—
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73D411yescharacteristic
105C2×C22⋊C4×C73D411yescharacteristic
106C2×C42×C73—21no—
107C2×C42×C73—21no—
108C2×C42×C73—21no—
109C2×C42×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113#107×C73—22no—
114#107×C73D414yes—
115#106×C73—22no—
116#106×C73—22no—
117#106×C73C2×C414yescomplemented
118#103×C73—22no—
119#103×C73—22no—
120#103×C73—41no—
121#103×C73—41no—
122#103×C73C2×C414yescomplemented
123#103×C73C2×C414yescomplemented
124C22⋊C8×C73—22no—
125#97×C73—22no—
126C4×C8×C73—22no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73D411yescharacteristic
136#95×C73D411yescharacteristic
137C24×C73C2×D411yescharacteristic
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73C22×C412yes—
149C2×Q8×C73C22×C412yes—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—42no—
163C22×C4×C73—42no—
164C22×C4×C73—81no—
165C22×C4×C73C22×C412yes—
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73#4112yes—
172C22×C4×C73C2411yescharacteristic
173Q16×C73—28no—
174M16×C73—28no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73C22×C412yes—
184C2×C8×C73C22×C412yes—
185C2×C8×C73C2×D412yes—
186C2×C8×C73#4112yes—
187C4⋊C4×C73—24no—
188C4⋊C4×C73—24no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—42no—
199C4⋊C4×C73—42no—
200C4⋊C4×C73—42no—
201C4⋊C4×C73—81no—
202C4⋊C4×C73C22×C412yes—
203C4⋊C4×C73C22×C412yes—
204C4⋊C4×C73C2×D412yes—
205C4⋊C4×C73C2×D412yes—
206C22⋊C4×C73—24no—
207C22⋊C4×C73—24no—
208C22⋊C4×C73—22no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73—42no—
211C42×C73—21no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—42no—
216C42×C73—42no—
217C42×C73—42no—
218C42×C73—42no—
219C42×C73—81no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73C4×D412yes—
227C23×C73C22×D411yescharacteristic
228Q8×C73—22no—
229Q8×C73—22no—
230Q8×C73—22no—
231Q8×C73—22no—
232Q8×C73—41no—
233Q8×C73—41no—
234Q8×C73—41no—
235Q8×C73—41no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—22no—
241C2×C4×C73—22no—
242C2×C4×C73—22no—
243C2×C4×C73—22no—
244C2×C4×C73—22no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—22no—
248C2×C4×C73—21no—
249C2×C4×C73—22no—
250C2×C4×C73—22no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—84no—
278C2×C4×C73C4×D412yes—
279C2×C4×C73#13712yes—
280C2×C4×C73C23×C411yescharacteristic
281C2×C4×C73C22×D411yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×C4×C73H(5,𝔽2)11yescharacteristic
285C2×C4×C732−1+411yescharacteristic
286C8×C73—22no—
287C8×C73—41no—
288C8×C73—41no—
289C8×C73C4×D414yes—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—41no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73—41no—
297C22×C73C2×C4×D411yescharacteristic
298C22×C73D4211yescharacteristic
299C22×C73#54711yescharacteristic
300C22×C73C2×#13711yescharacteristic
301C22×C73#57511yescharacteristic
302C22×C73#57711yescharacteristic
303C22×C73#57811yescharacteristic
304C4×C73—22no—
305C4×C73—22no—
306C4×C73—41no—
307C4×C73—41no—
308C4×C73—42no—
309C4×C73—42no—
310C4×C73—42no—
311C4×C73—42no—
312C4×C73—41no—
313C4×C73—42no—
314C4×C73—42no—
315C4×C73—81no—
316C4×C73—81no—
317C4×C73C2×C4×D411yescharacteristic
318C4×C73#52011yescharacteristic
319C4×C73#54811yescharacteristic
320C4×C73#55311yescharacteristic
321#23036C7311yesmaximal, characteristic, direct product factor, Sylow
322C2×C73—42no—
323C2×C73#236111yescharacteristic
324C2×C73C4×#13711yescharacteristic
325C2×C73#294711yescharacteristic
326C2×C73#326711yescharacteristic
327C2×C73#327011yescharacteristic
328C2×C73#335211yescharacteristic
329C2×C73#335611yescharacteristic
330C2×#470C2×C7311yescharacteristic
331C2×C4×Q16C2×C7311yescharacteristic, complemented
332C2×#428C2×C7311yescharacteristic
333#2362C2×C7311yescharacteristic
334#2360C2×C7311yescharacteristic
335#1971C2×C7311yescharacteristic, complemented
336#1941C2×C7311yescharacteristic, complemented
337#1928C2×C7311yescharacteristic, complemented
338#1927C2×C7311yescharacteristic, complemented
339#1873C2×C7311yescharacteristic
340#1872C2×C7311yescharacteristic
341#1865C2×C7311yescharacteristic, complemented
342#1863C2×C7311yescharacteristic, complemented
343#1776C2×C7311yescharacteristic, complemented
344#1753C2×C7311yescharacteristic
345C73#2303611yescharacteristic, direct product factor, Sylow
346C22×Q16C22×C7311yescharacteristic
347C22×M16C22×C7311yescharacteristic
348C2×C22⋊Q8C22×C7311yescharacteristic
349C2×C22⋊Q8C22×C7311yescharacteristic
350C2×C4×Q8C22×C7311yescharacteristic
351C2×C4×Q8C22×C7311yescharacteristic
352C2×#117C22×C7311yescharacteristic
353C22×C4⋊C4C22×C7311yescharacteristic
354#470C4×C7318yescomplemented
355C4×Q16—24no—
356#428—24no—
357C2×#107C22×C7311yescharacteristic
358C2×#107C22×C7311yescharacteristic
359C2×#106C22×C7311yescharacteristic
360C2×#106C22×C7311yescharacteristic
361C2×#106C22×C7311yescharacteristic
362C2×#103C22×C7311yescharacteristic
363C2×#103C22×C7311yescharacteristic
364C2×#103C22×C7311yescharacteristic
365C2×#103C22×C7311yescharacteristic
366C2×#103C22×C7311yescharacteristic
367C2×#103C22×C7311yescharacteristic
368C2×C22⋊C8C22×C7311yescharacteristic
369C2×#97C22×C7311yescharacteristic
370C2×C4×C8C22×C7311yescharacteristic
371#391C22×C7311yescharacteristic
372#391C22×C7311yescharacteristic
373#389—21no—
374#389C22×C7311yescharacteristic
375#389C22×C7311yescharacteristic
376#388—21no—
377#388—21no—
378#387—21no—
379#387—21no—
380#385—21no—
381C4×C4⋊C4—21no—
382C4×C4⋊C4C22×C7311yescharacteristic
383C4×C4⋊C4C22×C7311yescharacteristic
384C4×C22⋊C4—21no—
385C4×C22⋊C4C22×C7311yescharacteristic
386#340C22×C7311yescharacteristic
387#340C22×C7311yescharacteristic
388#340C22×C7311yescharacteristic
389#340C22×C7311yescharacteristic
390#336C22×C7311yescharacteristic
391#336C22×C7311yescharacteristic
392C22×Q8C23×C7311yescharacteristic
393C22×Q8C23×C7311yescharacteristic
394C23×C4—21no—
395C23×C4C23×C7311yescharacteristic
396C2×Q16—22no—
397C2×Q16—22no—
398C2×Q16C2×C4×C7314yescomplemented
399C2×M16—22no—
400C2×M16—22no—
401C2×M16C2×C4×C7314yes—
402C22×C8C23×C7311yescharacteristic
403C22×C8C23×C7311yescharacteristic
404C22×C8C23×C7311yescharacteristic
405C22×C8C23×C7311yescharacteristic
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8C2×C4×C7314yes—
409C22⋊Q8C2×C4×C7314yes—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—41no—
413C4×Q8—41no—
414#117—22no—
415#117—41no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4C23×C7311yescharacteristic
426C2×C4⋊C4C23×C7311yescharacteristic
427C2×C4⋊C4C23×C7311yescharacteristic
428C2×C4⋊C4C23×C7311yescharacteristic
429C2×C4⋊C4C23×C7311yescharacteristic
430C2×C4⋊C4C23×C7311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4D4×C7311yescharacteristic
435C2×C22⋊C4D4×C7311yescharacteristic
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42C23×C7311yescharacteristic
442C2×C42C23×C7311yescharacteristic
443#107—22no—
444#107D4×C7314yes—
445#106—22no—
446#106—22no—
447#106C2×C4×C7314yescomplemented
448#103—22no—
449#103—22no—
450#103—41no—
451#103—41no—
452#103C2×C4×C7314yescomplemented
453#103C2×C4×C7314yescomplemented
454C22⋊C8—22no—
455#97—22no—
456C4×C8—22no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95D4×C7311yescharacteristic
466#95D4×C7311yescharacteristic
467C24C2×D4×C7311yescharacteristic
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8C22×C4×C7312yes—
479C2×Q8C22×C4×C7312yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—81no—
495C22×C4C22×C4×C7312yes—
496C22×C4C2×D4×C7311yescharacteristic
497C22×C4C2×D4×C7311yescharacteristic
498C22×C4C2×D4×C7311yescharacteristic
499C22×C4C2×D4×C7311yescharacteristic
500C22×C4C2×D4×C7311yescharacteristic
501C22×C4#41×C7312yes—
502C22×C4C24×C7311yescharacteristic
503Q16—28no—
504M16—28no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8C22×C4×C7312yes—
514C2×C8C22×C4×C7312yes—
515C2×C8C2×D4×C7312yes—
516C2×C8#41×C7312yes—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—81no—
532C4⋊C4C22×C4×C7312yes—
533C4⋊C4C22×C4×C7312yes—
534C4⋊C4C2×D4×C7312yes—
535C4⋊C4C2×D4×C7312yes—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—42no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—42no—
547C42—42no—
548C42—42no—
549C42—81no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23C4×D4×C7312yes—
557C23C22×D4×C7311yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—84no—
608C2×C4C4×D4×C7312yes—
609C2×C4#137×C7312yes—
610C2×C4C23×C4×C7311yescharacteristic
611C2×C4C22×D4×C7311yescharacteristic
612C2×C4C2×#41×C7311yescharacteristic
613C2×C4C2×#41×C7311yescharacteristic
614C2×C4H(5,𝔽2)×C7311yescharacteristic
615C2×C42−1+4×C7311yescharacteristic
616C8—22no—
617C8—41no—
618C8—41no—
619C8C4×D4×C7314yes—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22C2×C4×D4×C7311yescharacteristic
628C22D42×C7311yescharacteristic
629C22#547×C7311yescharacteristic
630C22C2×#137×C7311yescharacteristic
631C22#575×C7311yescharacteristic
632C22#577×C7311yescharacteristic
633C22#578×C7311yescharacteristic
634C4—22no—
635C4—22no—
636C4—41no—
637C4—42no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4C2×C4×D4×C7311yescharacteristic
648C4#520×C7311yescharacteristic
649C4#548×C7311yescharacteristic
650C4#553×C7311yescharacteristic
651C2—42no—
652C2C73×#236111yescharacteristic
653C2C4×#137×C7311yescharacteristic
654C2C73×#294711yescharacteristic
655C2C73×#326711yescharacteristic
656C2C73×#327011yescharacteristic
657C2C73×#335211yescharacteristic
658C2C73×#335611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC24×C73C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q16×C73C2semidirect
6. C73×#1971C2semidirect
7. C73×#1941C2semidirect
8. C73×#1928C2semidirect
9. C73×#1927C2semidirect
12. C73×#1865C2semidirect
13. C73×#1863C2semidirect
14. C73×#1776C2semidirect
24. #470×C73C4semidirect
68. C2×Q16×C73C2×C4semidirect
117. #106×C73C2×C4semidirect
122. #103×C73C2×C4semidirect
123. #103×C73C2×C4semidirect
321. #23036C73direct (N × H)
331. C2×C4×Q16C2×C73semidirect
335. #1971C2×C73semidirect
336. #1941C2×C73semidirect
337. #1928C2×C73semidirect
338. #1927C2×C73semidirect
341. #1865C2×C73semidirect
342. #1863C2×C73semidirect
343. #1776C2×C73semidirect
345. C73#23036direct (N × H)
354. #470C4×C73semidirect
398. C2×Q16C2×C4×C73semidirect
447. #106C2×C4×C73semidirect
452. #103C2×C4×C73semidirect
453. #103C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#470×C732
C2×C4×Q16×C732
C2×#428×C732
C73×#23622
C73×#23602
C73×#19712
C73×#19412
C73×#19282
C73×#19272
C73×#18732
C73×#18722
C73×#18652
C73×#18632
C73×#17762
C73×#17532
#2303673