Finite Group Databasebeta

← C73×#24791 #32934195

Subgroups — C73×#24791 #32934195

Order 18688.

962 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#470×C73C211yesmaximal, characteristic, complemented
2C2×#467×C73C211yesmaximal, characteristic, complemented
3C2×#435×C73C211yesmaximal, characteristic
4C2×#428×C73C211yesmaximal, characteristic, complemented
5C73×#2417C211yesmaximal, characteristic
6C73×#2415C211yesmaximal, characteristic
7C73×#2068C211yesmaximal, characteristic, complemented
8C73×#2066C211yesmaximal, characteristic, complemented
9C73×#2036C211yesmaximal, characteristic, complemented
10C73×#2035C211yesmaximal, characteristic, complemented
11C73×#1971C211yesmaximal, characteristic, complemented
12C73×#1943C211yesmaximal, characteristic, complemented
13C73×#1873C211yesmaximal, characteristic, complemented
14C73×#1872C211yesmaximal, characteristic, complemented
15C73×#1807C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C23×C8×C73C2211yescharacteristic
19C2×C22⋊Q8×C73C2211yescharacteristic
20C2×C22⋊Q8×C73C2211yescharacteristic
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×C4×D4×C73C2211yescharacteristic
24C2×#117×C73C2211yescharacteristic
25C22×C4⋊C4×C73C2211yescharacteristic
26#470×C73—24no—
27#467×C73—24no—
28#435×C73—24no—
29#428×C73—24no—
30C2×#107×C73C2211yescharacteristic
31C2×#107×C73C2211yescharacteristic
32C2×#106×C73C2211yescharacteristic
33C2×#106×C73C2211yescharacteristic
34C2×#106×C73C2211yescharacteristic
35C2×C4⋊C8×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#103×C73C2211yescharacteristic
41C2×#103×C73C2211yescharacteristic
42C2×C22⋊C8×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×#97×C73C2211yescharacteristic
45#398×C73—21no—
46#397×C73—21no—
47#396×C73—21no—
48#394×C73—21no—
49#391×C73C2211yescharacteristic
50#391×C73C2211yescharacteristic
51#389×C73—21no—
52#389×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#388×C73—21no—
55#386×C73—21no—
56#380×C73—21no—
57#380×C73C2211yescharacteristic
58#380×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C22×Q8×C73C2311yescharacteristic
65C22×D4×C73D411yescharacteristic
66C23×C4×C73—21no—
67C23×C4×C73C2311yescharacteristic
68C23×C4×C73C2311yescharacteristic
69C2×Q16×C73—22no—
70C2×Q16×C73—22no—
71C2×Q16×C73—22no—
72C2×M16×C73—22no—
73C2×M16×C73—22no—
74C2×M16×C73D414yes—
75C22×C8×C73—22no—
76C22×C8×C73—22no—
77C22×C8×C73—22no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22⋊Q8×C73—22no—
83C22⋊Q8×C73—22no—
84C22⋊Q8×C73—22no—
85C22⋊Q8×C73—22no—
86C22⋊Q8×C73—22no—
87C22⋊Q8×C73—22no—
88C22⋊Q8×C73—41no—
89C22⋊Q8×C73—41no—
90C4×D4×C73—22no—
91C4×D4×C73—22no—
92#117×C73—22no—
93#117×C73—41no—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—41no—
103C2×C4⋊C4×C73D411yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73D411yescharacteristic
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C42×C73—21no—
120C2×C42×C73C2311yescharacteristic
121#107×C73—22no—
122#107×C73D414yescomplemented
123#106×C73—22no—
124#106×C73—22no—
125#106×C73—22no—
126C4⋊C8×C73—22no—
127#103×C73—22no—
128#103×C73—22no—
129#103×C73—22no—
130#103×C73—22no—
131#103×C73—41no—
132#103×C73—41no—
133C22⋊C8×C73—22no—
134C22⋊C8×C73—22no—
135#97×C73—22no—
136#95×C73—21no—
137#95×C73—21no—
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73—21no—
142#95×C73—21no—
143#95×C73—21no—
144C24×C73C2×D411yescharacteristic
145C24×C73C2×D411yescharacteristic
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×Q8×C73—21no—
153C2×Q8×C73—21no—
154C2×Q8×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×D4×C73—22no—
159C2×D4×C73—22no—
160C2×D4×C73—41no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—42no—
180C22×C4×C73—42no—
181C22×C4×C73—81no—
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73C2×D412yes—
187C22×C4×C73#4112yes—
188C22×C4×C73C2411yescharacteristic
189Q16×C73—44no—
190M16×C73—28no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—44no—
200C2×C8×C73C2×D412yes—
201C2×C8×C73C2×D412yes—
202C2×C8×C73C2×D412yes—
203C2×C8×C73#4112yes—
204C4⋊C4×C73—22no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73—42no—
218C4⋊C4×C73—42no—
219C4⋊C4×C73—42no—
220C4⋊C4×C73—42no—
221C4⋊C4×C73—81no—
222C4⋊C4×C73C2×D412yes—
223C4⋊C4×C73C2×D412yes—
224C22⋊C4×C73—22no—
225C22⋊C4×C73—22no—
226C22⋊C4×C73—42no—
227C22⋊C4×C73—42no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—81no—
233C42×C73—21no—
234C42×C73—21no—
235C42×C73—42no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73#12112yes—
249C23×C73#13712yes—
250C23×C73C22×D411yescharacteristic
251Q8×C73—41no—
252Q8×C73—41no—
253Q8×C73—41no—
254Q8×C73—41no—
255Q8×C73—41no—
256Q8×C73—41no—
257Q8×C73—41no—
258Q8×C73—41no—
259D4×C73—44no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—84no—
304C2×C4×C73#12112yes—
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C22×D411yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C73C2×#4111yescharacteristic
309C2×C4×C73H(5,𝔽2)11yescharacteristic
310C2×C4×C732−1+411yescharacteristic
311C8×C73—22no—
312C8×C73—41no—
313C8×C73—41no—
314C8×C73#12114yes—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—22no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73C2×#12111yescharacteristic
330C22×C73D4211yescharacteristic
331C22×C73#54711yescharacteristic
332C22×C73C2×#13711yescharacteristic
333C22×C73#57511yescharacteristic
334C22×C73#57711yescharacteristic
335C22×C73#57811yescharacteristic
336C4×C73—22no—
337C4×C73—41no—
338C4×C73—42no—
339C4×C73—42no—
340C4×C73—41no—
341C4×C73—41no—
342C4×C73—81no—
343C4×C73—81no—
344C4×C73—81no—
345C4×C73—81no—
346C4×C73—81no—
347C4×C73—81no—
348C4×C73C2×#12111yescharacteristic
349C4×C73#53711yescharacteristic
350C4×C73#54811yescharacteristic
351C4×C73#55311yescharacteristic
352#24791C7311yesmaximal, characteristic, direct product factor, Sylow
353C2×C73—42no—
354C2×C73—42no—
355C2×C73#241611yescharacteristic
356C2×C73#305611yescharacteristic
357C2×C73#306311yescharacteristic
358C2×C73#326711yescharacteristic
359C2×C73#327011yescharacteristic
360C2×C73#334411yescharacteristic
361C2×C73#334911yescharacteristic
362C2×#470C2×C7311yescharacteristic, complemented
363C2×#467C2×C7311yescharacteristic, complemented
364C2×#435C2×C7311yescharacteristic
365C2×#428C2×C7311yescharacteristic, complemented
366#2417C2×C7311yescharacteristic
367#2415C2×C7311yescharacteristic
368#2068C2×C7311yescharacteristic, complemented
369#2066C2×C7311yescharacteristic, complemented
370#2036C2×C7311yescharacteristic, complemented
371#2035C2×C7311yescharacteristic, complemented
372#1971C2×C7311yescharacteristic, complemented
373#1943C2×C7311yescharacteristic, complemented
374#1873C2×C7311yescharacteristic, complemented
375#1872C2×C7311yescharacteristic, complemented
376#1807C2×C7311yescharacteristic, complemented
377C73#2479111yescharacteristic, direct product factor, Sylow
378C22×Q16C22×C7311yescharacteristic
379C22×M16C22×C7311yescharacteristic
380C23×C8C22×C7311yescharacteristic
381C2×C22⋊Q8C22×C7311yescharacteristic
382C2×C22⋊Q8C22×C7311yescharacteristic
383C2×C22⋊Q8C22×C7311yescharacteristic
384C2×C22⋊Q8C22×C7311yescharacteristic
385C2×C4×D4C22×C7311yescharacteristic
386C2×#117C22×C7311yescharacteristic
387C22×C4⋊C4C22×C7311yescharacteristic
388#470—24no—
389#467—24no—
390#435—24no—
391#428—24no—
392C2×#107C22×C7311yescharacteristic
393C2×#107C22×C7311yescharacteristic
394C2×#106C22×C7311yescharacteristic
395C2×#106C22×C7311yescharacteristic
396C2×#106C22×C7311yescharacteristic
397C2×C4⋊C8C22×C7311yescharacteristic
398C2×#103C22×C7311yescharacteristic
399C2×#103C22×C7311yescharacteristic
400C2×#103C22×C7311yescharacteristic
401C2×#103C22×C7311yescharacteristic
402C2×#103C22×C7311yescharacteristic
403C2×#103C22×C7311yescharacteristic
404C2×C22⋊C8C22×C7311yescharacteristic
405C2×C22⋊C8C22×C7311yescharacteristic
406C2×#97C22×C7311yescharacteristic
407#398—21no—
408#397—21no—
409#396—21no—
410#394—21no—
411#391C22×C7311yescharacteristic
412#391C22×C7311yescharacteristic
413#389—21no—
414#389C22×C7311yescharacteristic
415#389C22×C7311yescharacteristic
416#388—21no—
417#386—21no—
418#380—21no—
419#380C22×C7311yescharacteristic
420#380C22×C7311yescharacteristic
421#340C22×C7311yescharacteristic
422#340C22×C7311yescharacteristic
423#340C22×C7311yescharacteristic
424#340C22×C7311yescharacteristic
425C22×Q8C23×C7311yescharacteristic
426C22×Q8C23×C7311yescharacteristic
427C22×D4D4×C7311yescharacteristic
428C23×C4—21no—
429C23×C4C23×C7311yescharacteristic
430C23×C4C23×C7311yescharacteristic
431C2×Q16—22no—
432C2×Q16—22no—
433C2×Q16—22no—
434C2×M16—22no—
435C2×M16—22no—
436C2×M16D4×C7314yes—
437C22×C8—22no—
438C22×C8—22no—
439C22×C8—22no—
440C22×C8C23×C7311yescharacteristic
441C22×C8C23×C7311yescharacteristic
442C22×C8C23×C7311yescharacteristic
443C22×C8C23×C7311yescharacteristic
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—41no—
451C22⋊Q8—41no—
452C4×D4—22no—
453C4×D4—22no—
454#117—22no—
455#117—41no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4D4×C7311yescharacteristic
466C2×C4⋊C4C23×C7311yescharacteristic
467C2×C4⋊C4C23×C7311yescharacteristic
468C2×C4⋊C4C23×C7311yescharacteristic
469C2×C4⋊C4C23×C7311yescharacteristic
470C2×C4⋊C4C23×C7311yescharacteristic
471C2×C4⋊C4C23×C7311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4D4×C7311yescharacteristic
480C2×C22⋊C4D4×C7311yescharacteristic
481C2×C42—21no—
482C2×C42C23×C7311yescharacteristic
483#107—22no—
484#107D4×C7314yescomplemented
485#106—22no—
486#106—22no—
487#106—22no—
488C4⋊C8—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#103—41no—
494#103—41no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497#97—22no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506C24C2×D4×C7311yescharacteristic
507C24C2×D4×C7311yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
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×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4C2×D4×C7311yescharacteristic
545C22×C4C2×D4×C7311yescharacteristic
546C22×C4C2×D4×C7311yescharacteristic
547C22×C4C2×D4×C7311yescharacteristic
548C22×C4C2×D4×C7312yes—
549C22×C4#41×C7312yes—
550C22×C4C24×C7311yescharacteristic
551Q16—44no—
552M16—28no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—44no—
562C2×C8C2×D4×C7312yes—
563C2×C8C2×D4×C7312yes—
564C2×C8C2×D4×C7312yes—
565C2×C8#41×C7312yes—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—81no—
584C4⋊C4C2×D4×C7312yes—
585C4⋊C4C2×D4×C7312yes—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—81no—
595C42—21no—
596C42—21no—
597C42—42no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23#121×C7312yes—
611C23#137×C7312yes—
612C23C22×D4×C7311yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621D4—44no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—41no—
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×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4#121×C7312yes—
667C2×C4C22×D4×C7311yescharacteristic
668C2×C4C22×D4×C7311yescharacteristic
669C2×C4C2×#41×C7311yescharacteristic
670C2×C4C2×#41×C7311yescharacteristic
671C2×C4H(5,𝔽2)×C7311yescharacteristic
672C2×C42−1+4×C7311yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8#121×C7314yes—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22C2×#121×C7311yescharacteristic
692C22D42×C7311yescharacteristic
693C22#547×C7311yescharacteristic
694C22C2×#137×C7311yescharacteristic
695C22#575×C7311yescharacteristic
696C22#577×C7311yescharacteristic
697C22#578×C7311yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C2×#121×C7311yescharacteristic
711C4#537×C7311yescharacteristic
712C4#548×C7311yescharacteristic
713C4#553×C7311yescharacteristic
714C2—42no—
715C2—42no—
716C2C73×#241611yescharacteristic
717C2C73×#305611yescharacteristic
718C2C73×#306311yescharacteristic
719C2C73×#326711yescharacteristic
720C2C73×#327011yescharacteristic
721C2C73×#334411yescharacteristic
722C2C73×#334911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#470×C73C2semidirect
2. C2×#467×C73C2semidirect
4. C2×#428×C73C2semidirect
7. C73×#2068C2semidirect
8. C73×#2066C2semidirect
9. C73×#2036C2semidirect
10. C73×#2035C2semidirect
11. C73×#1971C2semidirect
12. C73×#1943C2semidirect
13. C73×#1873C2semidirect
14. C73×#1872C2semidirect
15. C73×#1807C2semidirect
122. #107×C73D4semidirect
352. #24791C73direct (N × H)
362. C2×#470C2×C73semidirect
363. C2×#467C2×C73semidirect
365. C2×#428C2×C73semidirect
368. #2068C2×C73semidirect
369. #2066C2×C73semidirect
370. #2036C2×C73semidirect
371. #2035C2×C73semidirect
372. #1971C2×C73semidirect
373. #1943C2×C73semidirect
374. #1873C2×C73semidirect
375. #1872C2×C73semidirect
376. #1807C2×C73semidirect
377. C73#24791direct (N × H)
484. #107D4×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×#467×C732
C2×#435×C732
C2×#428×C732
C73×#24172
C73×#24152
C73×#20682
C73×#20662
C73×#20362
C73×#20352
C73×#19712
C73×#19432
C73×#18732
C73×#18722
C73×#18072
#2479173