Finite Group Databasebeta

← #13370313

Subgroups — #13370313

Order 1792.

1064 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90208C211yesmaximal, characteristic
2C2×#89600C211yesmaximal, characteristic, complemented
3C2×#89602C211yesmaximal, characteristic, complemented
4C7×#1798C211yesmaximal, characteristic
5#11729336C211yesmaximal, characteristic
6#11728227C211yesmaximal, characteristic, complemented
7#11728226C211yesmaximal, characteristic, complemented
8#11727663C211yesmaximal, characteristic
9#11727662C211yesmaximal, characteristic
10#11727661C211yesmaximal, characteristic
11Dic7×C22⋊C8C211yesmaximal, characteristic
12#11726374C211yesmaximal, characteristic, complemented
13#11726373C211yesmaximal, characteristic, complemented
14#11726373C211yesmaximal, characteristic, complemented
15#11726373C211yesmaximal, characteristic, complemented
16C2×C7×#117C2211yescharacteristic
17C2×#6489C2211yescharacteristic
18C22×C4×Dic7C2211yescharacteristic
19#90208—24no—
20#90208—24no—
21C2×#6453C411yescharacteristic
22C2×#6453C411yescharacteristic
23C2×#6451C411yescharacteristic
24C2×#6451C411yescharacteristic
25C2×#6441C411yescharacteristic
26C2×#6441C411yescharacteristic
27C2×#6441C411yescharacteristic
28C2×#6441C411yescharacteristic
29C2×C4×Dic14C2211yescharacteristic
30C2×C4×Dic14C2211yescharacteristic
31C2×C4×Dic14C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C2×C7×C4⋊C8C2211yescharacteristic
34C2×C7×C4⋊C8C2211yescharacteristic
35C2×C7×C22⋊C8C2211yescharacteristic
36C2×C7×C22⋊C8C2211yescharacteristic
37C2×C22⋊(C7⋊C8)C2211yescharacteristic
38C2×C22⋊(C7⋊C8)C2211yescharacteristic
39C2×#6389C2211yescharacteristic
40C2×Dic7⋊C8C2211yescharacteristic
41C2×Dic7⋊C8C2211yescharacteristic
42C2×Dic7⋊C8C2211yescharacteristic
43C2×Dic7⋊C8C2211yescharacteristic
44C2×C8×Dic7C2211yescharacteristic
45C2×C8×Dic7C2211yescharacteristic
46C2×C8×Dic7C2211yescharacteristic
47C2×#6377C2211yescharacteristic
48C2×C4×C7⋊C8C2211yescharacteristic
49#89602—24no—
50#89600—24no—
51C7×#336C2211yescharacteristic
52C7×#336C2211yescharacteristic
53#89345C2211yescharacteristic
54#89345C2211yescharacteristic
55#89345C2211yescharacteristic
56#89345C2211yescharacteristic
57#89345C2211yescharacteristic
58#89345C2211yescharacteristic
59#89345C2211yescharacteristic
60#89345C2211yescharacteristic
61#89319C2211yescharacteristic
62#89319C2211yescharacteristic
63#22509—71nomaximal, Sylow
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2×C411yescharacteristic
66C23×Dic7C2×C411yescharacteristic
67C22×Dic14C2×C411yescharacteristic
68C22×Dic14C2×C411yescharacteristic
69C22×Dic14C2×C411yescharacteristic
70C22×Dic14C2×C411yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C22×C7×C8C2311yescharacteristic
73C22×C7×C8C2311yescharacteristic
74C22×C7×C8C2311yescharacteristic
75C7×#117—22no—
76C7×#117—22no—
77C2×C7×C4⋊C4C2×C411yescharacteristic
78C2×C7×C4⋊C4C2×C411yescharacteristic
79C2×C7×C22⋊C4C2×C411yescharacteristic
80C2×C7×C22⋊C4C2×C411yescharacteristic
81C2×C42×C7C2311yescharacteristic
82C2×C42×C7C2311yescharacteristic
83C2×C22⋊Dic7C2×C411yescharacteristic
84C2×C22⋊Dic7C2×C411yescharacteristic
85#6489—22no—
86#6489—22no—
87C2×C4⋊Dic7C2×C411yescharacteristic
88C2×C4⋊Dic7C2×C411yescharacteristic
89C2×C4⋊Dic7C2×C411yescharacteristic
90C2×C4⋊Dic7C2×C411yescharacteristic
91C2×C4⋊Dic7C2×C411yescharacteristic
92C2×C4⋊Dic7C2×C411yescharacteristic
93C2×Dic7⋊C4C2×C411yescharacteristic
94C2×Dic7⋊C4C2×C411yescharacteristic
95C2×Dic7⋊C4C2×C411yescharacteristic
96C2×Dic7⋊C4C2×C411yescharacteristic
97C2×Dic7⋊C4C2×C411yescharacteristic
98C2×Dic7⋊C4C2×C411yescharacteristic
99C2×Dic7⋊C4C2×C411yescharacteristic
100C2×Dic7⋊C4C2×C411yescharacteristic
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7C2×C411yescharacteristic
104C2×C4×Dic7C2×C411yescharacteristic
105C2×C4×Dic7C2311yescharacteristic
106C2×C4×Dic7C2311yescharacteristic
107C2×C4×Dic7C2311yescharacteristic
108C2×C4×Dic7C2311yescharacteristic
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113#6453—24no—
114#6453—24no—
115#6451—24no—
116#6451—24no—
117#6441—24no—
118#6441—24no—
119#6441—24no—
120#6441—24no—
121C4×Dic14—22no—
122C4×Dic14—22no—
123C4×Dic14—22no—
124C4×Dic14—22no—
125C4×Dic14—22no—
126C4×Dic14—22no—
127C4×Dic14D414yes—
128C4×Dic14D414yes—
129C7×C4⋊C8—22no—
130C7×C4⋊C8—22no—
131C7×C22⋊C8—22no—
132C7×C22⋊C8—22no—
133C22⋊(C7⋊C8)—22no—
134C22⋊(C7⋊C8)Q814yescomplemented
135#6389—22no—
136Dic7⋊C8—22no—
137Dic7⋊C8—22no—
138Dic7⋊C8—22no—
139Dic7⋊C8—22no—
140C8×Dic7—22no—
141C8×Dic7—22no—
142C8×Dic7—22no—
143#6377—22no—
144C4×C7⋊C8—22no—
145C2×#533—71no—
146C2×#446—71no—
147C2×C8×Q8—71no—
148#1985—71no—
149#1985—71no—
150#1984—71no—
151#1984—71no—
152#1984—71no—
153#1984—71no—
154#1798—71no—
155#1798D711yescharacteristic
156#1797—71no—
157#1750—71no—
158#1750—71no—
159C4×C22⋊C8—71no—
160C24×C7C22×C411yescharacteristic
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7C22×C411yescharacteristic
166C22×C4×C7C22×C411yescharacteristic
167C22×C4×C7C22×C411yescharacteristic
168C22×C4×C7C22×C411yescharacteristic
169C22×C4×C7C22×C411yescharacteristic
170C22×C4×C7C2×Q812yes—
171C22×C4×C7#4112yes—
172C22×C4×C7C2411yescharacteristic
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—41no—
179C22×Dic7C22×C411yescharacteristic
180C22×Dic7C22×C411yescharacteristic
181C22×Dic7C22×C411yescharacteristic
182C22×Dic7C22×C411yescharacteristic
183C22×Dic7C22×C411yescharacteristic
184C22×Dic7C22×C411yescharacteristic
185C22×Dic7C22×C411yescharacteristic
186C22×Dic7C22×C411yescharacteristic
187C2×Dic14—22no—
188C2×Dic14—22no—
189C2×Dic14—22no—
190C2×Dic14—22no—
191C2×Dic14—22no—
192C2×Dic14—22no—
193C2×Dic14—22no—
194C2×Dic14—22no—
195C2×Dic14—22no—
196C2×Dic14—41no—
197C2×Dic14—41no—
198C2×Dic14C22⋊C414yes—
199C2×C7×C8—21no—
200C2×C7×C8—21no—
201C2×C7×C8—21no—
202C2×C7×C8—21no—
203C2×C7×C8—21no—
204C2×C7×C8—21no—
205C2×C7×C8—21no—
206C2×C7×C8—21no—
207C2×C7×C8—21no—
208C2×C7×C8—21no—
209C2×C7×C8—21no—
210C2×C7×C8—21no—
211C7×C4⋊C4—22no—
212C7×C4⋊C4—22no—
213C7×C22⋊C4—22no—
214C7×C22⋊C4—22no—
215C42×C7—21no—
216C42×C7—21no—
217C42×C7C2×D412yes—
218C42×C7C2×D412yes—
219C22⋊Dic7—22no—
220C22⋊Dic7—22no—
221C4⋊Dic7—22no—
222C4⋊Dic7—22no—
223C4⋊Dic7—22no—
224C4⋊Dic7—22no—
225C4⋊Dic7—22no—
226C4⋊Dic7C22⋊C414yes—
227Dic7⋊C4—22no—
228Dic7⋊C4—22no—
229Dic7⋊C4—22no—
230Dic7⋊C4—22no—
231Dic7⋊C4—22no—
232Dic7⋊C4—22no—
233Dic7⋊C4C22⋊C414yes—
234Dic7⋊C4C22⋊C414yes—
235C4×Dic7—21no—
236C4×Dic7—21no—
237C4×Dic7—21no—
238C4×Dic7—21no—
239C4×Dic7—22no—
240C4×Dic7—22no—
241C4×Dic7C2×D412yes—
242C4×Dic7C2×D412yes—
243C4×Dic7C2×D412yes—
244C4×Dic7C2×D412yes—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8C2×Q812yes—
256C2×C7⋊C8C2×Q812yes—
257#533—144no—
258#533—144no—
259C2×C4⋊Q8—71no—
260C2×C4⋊Q8—71no—
261C2×#125—71no—
262C2×#125—71no—
263C2×C22⋊Q8—71no—
264C2×C22⋊Q8—71no—
265C2×C22⋊Q8—71no—
266C2×C22⋊Q8—71no—
267C2×C4×Q8—71no—
268C2×C4×Q8—71no—
269C2×C4×Q8—71no—
270C2×C4×Q8—71no—
271C2×#117—71no—
272C2×#117C2×D711yescharacteristic
273C22×C42—71no—
274#446—144no—
275C8×Q8—144no—
276C2×C4⋊C8—71no—
277C2×C4⋊C8—71no—
278C2×C4⋊C8—71no—
279C2×C4⋊C8—71no—
280C2×C4⋊C8C2×D711yescharacteristic
281C2×C4⋊C8C2×D711yescharacteristic
282C2×C22⋊C8—71no—
283C2×C22⋊C8—71no—
284C2×C22⋊C8C2×D711yescharacteristic
285C2×C22⋊C8C2×D711yescharacteristic
286C2×#97—71no—
287C2×#97—71no—
288C2×C4×C8—71no—
289C2×C4×C8—71no—
290C2×C4×C8—71no—
291C2×C4×C8—71no—
292#336—71no—
293#336—71no—
294#336—71no—
295#336—71no—
296#336—71no—
297#336—71no—
298#336—71no—
299#336—71no—
300#336—71no—
301#336—71no—
302#336C2×D711yescharacteristic
303#336C2×D711yescharacteristic
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7C4×Q812yes—
311C23×C7C23×C411yescharacteristic
312C2×C4×C7—21no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—21no—
316C2×C4×C7—21no—
317C2×C4×C7—21no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—21no—
323C2×C4×C7—21no—
324C2×C4×C7—21no—
325C2×C4×C7—21no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7C2×C22⋊C412yes—
329C2×C4×C7C2×C22⋊C412yes—
330C2×C4×C7C4×Q812yes—
331C2×C4×C7C22×D411yescharacteristic
332C2×C4×C7C22×D411yescharacteristic
333C2×C4×C7C22×Q811yescharacteristic
334C2×C4×C7C2×#4111yescharacteristic
335C2×C4×C72−1+411yescharacteristic
336C2×C4×C72−1+411yescharacteristic
337C2×Dic7—21no—
338C2×Dic7—21no—
339C2×Dic7—21no—
340C2×Dic7—21no—
341C2×Dic7—21no—
342C2×Dic7—21no—
343C2×Dic7—21no—
344C2×Dic7—21no—
345C2×Dic7—21no—
346C2×Dic7—21no—
347C2×Dic7—21no—
348C2×Dic7—21no—
349C2×Dic7—21no—
350C2×Dic7—21no—
351C2×Dic7—21no—
352C2×Dic7—21no—
353C2×Dic7—21no—
354C2×Dic7—44no—
355C2×Dic7—44no—
356C2×Dic7C2×C22⋊C412yes—
357C2×Dic7C2×C22⋊C412yes—
358C2×Dic7C2×C22⋊C412yes—
359C2×Dic7C2×C22⋊C412yes—
360C2×Dic7#13112yes—
361C2×Dic7#13112yes—
362C2×Dic7#13112yes—
363Dic14—28no—
364Dic14—44no—
365Dic14—44no—
366Dic14—44no—
367C7×C8—41no—
368C7×C8—41no—
369C7×C8—41no—
370C7×C8—41no—
371C7⋊C8—22no—
372C7⋊C8—22no—
373C7⋊C8—41no—
374C7⋊C8—41no—
375C22×Q8—71no—
376C22×Q8—71no—
377C22×Q8—71no—
378C22×Q8—71no—
379C23×C4—71no—
380C23×C4—71no—
381C23×C4C22×D711yescharacteristic
382C22×C8—71no—
383C22×C8—71no—
384C22×C8—71no—
385C22×C8—71no—
386C22×C8C22×D711yescharacteristic
387C22×C8C22×D711yescharacteristic
388C22×C8C22×D711yescharacteristic
389C22×C8C22×D711yescharacteristic
390C4⋊Q8—144no—
391C4⋊Q8—144no—
392#125—144no—
393#125—144no—
394C22⋊Q8—144no—
395C22⋊Q8—144no—
396C22⋊Q8—144no—
397C22⋊Q8—144no—
398C4×Q8—74no—
399C4×Q8—74no—
400C4×Q8—142no—
401C4×Q8—142no—
402C4×Q8—142no—
403C4×Q8—142no—
404C4×Q8—142no—
405C4×Q8—142no—
406#117—22no—
407#117—22no—
408#117—142no—
409#117—142no—
410C2×C4⋊C4—71no—
411C2×C4⋊C4—71no—
412C2×C4⋊C4—71no—
413C2×C4⋊C4—71no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—71no—
418C2×C4⋊C4—71no—
419C2×C4⋊C4—71no—
420C2×C4⋊C4—71no—
421C2×C4⋊C4—71no—
422C2×C4⋊C4—71no—
423C2×C4⋊C4—71no—
424C2×C4⋊C4C4×D711yescharacteristic
425C2×C4⋊C4C4×D711yescharacteristic
426C2×C22⋊C4—71no—
427C2×C22⋊C4—71no—
428C2×C22⋊C4C4×D711yescharacteristic
429C2×C22⋊C4C4×D711yescharacteristic
430C2×C42—71no—
431C2×C42—71no—
432C2×C42—71no—
433C2×C42—71no—
434C2×C42—71no—
435C2×C42—71no—
436C2×C42—142no—
437C2×C42—142no—
438C2×C42C22×D711yescharacteristic
439C2×C42C22×D711yescharacteristic
440C4⋊C8—22no—
441C4⋊C8—22no—
442C4⋊C8—142no—
443C4⋊C8—142no—
444C4⋊C8—142no—
445C4⋊C8—142no—
446C22⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—74no—
449C22⋊C8—142no—
450#97—142no—
451#97—142no—
452C4×C8—142no—
453C4×C8—142no—
454C4×C8—142no—
455C4×C8—142no—
456C22×C7—22no—
457C22×C7—22no—
458C22×C7—22no—
459C22×C7—41no—
460C22×C7—41no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7C22×C22⋊C411yescharacteristic
464C22×C7C2×C4×Q811yescharacteristic
465C22×C7#51911yescharacteristic
466C22×C7C2×#13111yescharacteristic
467C22×C7C2×#13111yescharacteristic
468C22×C7C2×#13111yescharacteristic
469C22×C7#56811yescharacteristic
470C4×C7—22no—
471C4×C7—22no—
472C4×C7—22no—
473C4×C7—41no—
474C4×C7—41no—
475C4×C7#54811yescharacteristic
476C4×C7#54811yescharacteristic
477C4×C7D4×Q811yescharacteristic
478C4×C7D4×Q811yescharacteristic
479Dic7—22no—
480Dic7—22no—
481Dic7—22no—
482Dic7—22no—
483Dic7—41no—
484Dic7—41no—
485Dic7—41no—
486Dic7#40814yes—
487C24C2×C4×D711yescharacteristic
488C2×Q8—74no—
489C2×Q8—142no—
490C2×Q8—142no—
491C2×Q8—142no—
492C2×Q8—142no—
493C2×Q8—142no—
494C2×Q8—142no—
495C2×Q8—142no—
496C2×Q8—142no—
497C2×Q8—142no—
498C2×Q8—281no—
499C2×Q8—281no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—71no—
505C22×C4—71no—
506C22×C4—71no—
507C22×C4—71no—
508C22×C4—71no—
509C22×C4—71no—
510C22×C4—71no—
511C22×C4—71no—
512C22×C4—142no—
513C22×C4—142no—
514C22×C4—142no—
515C22×C4—142no—
516C22×C4—142no—
517C22×C4—281no—
518C22×C4C2×C4×D711yescharacteristic
519C22×C4C2×C4×D711yescharacteristic
520C22×C4C2×C4×D711yescharacteristic
521C22×C4C2×C4×D711yescharacteristic
522C22×C4C2×C4×D711yescharacteristic
523C22×C4#115912yes—
524C22×C4Q8×D712yes—
525C22×C4C23×D711yescharacteristic
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—72no—
539C2×C8—72no—
540C2×C8—141no—
541C2×C8—141no—
542C2×C8—141no—
543C2×C8—141no—
544C2×C8—141no—
545C2×C8—141no—
546C2×C8—141no—
547C2×C8—141no—
548C2×C8—141no—
549C2×C8—141no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—74no—
553C4⋊C4—74no—
554C4⋊C4—74no—
555C4⋊C4—142no—
556C4⋊C4—142no—
557C4⋊C4—142no—
558C4⋊C4—142no—
559C4⋊C4—142no—
560C4⋊C4—142no—
561C4⋊C4—142no—
562C4⋊C4—142no—
563C4⋊C4—142no—
564C4⋊C4—142no—
565C4⋊C4—142no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—142no—
569C22⋊C4—142no—
570C42—21no—
571C42—21no—
572C42—72no—
573C42—72no—
574C42—72no—
575C42—72no—
576C42—142no—
577C42—142no—
578C42—141no—
579C42—141no—
580C42—141no—
581C42—141no—
582C42D4×D712yes—
583C42D4×D712yes—
584C2×C7—42no—
585C2×C7Q8×C22⋊C411yescharacteristic
586C2×C7C2×#40811yescharacteristic
587C2×C7#288011yescharacteristic
588C2×C7#296011yescharacteristic
589C2×C7#296211yescharacteristic
590C2×C7#298511yescharacteristic
591C2×C7#298611yescharacteristic
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23#645012yes—
599C23C22×C4×D711yescharacteristic
600Q8—148no—
601Q8—284no—
602Q8—284no—
603Q8—284no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—72no—
621C2×C4—72no—
622C2×C4—72no—
623C2×C4—72no—
624C2×C4—72no—
625C2×C4—72no—
626C2×C4—72no—
627C2×C4—141no—
628C2×C4—141no—
629C2×C4—141no—
630C2×C4—141no—
631C2×C4—141no—
632C2×C4—141no—
633C2×C4—141no—
634C2×C4—141no—
635C2×C4—141no—
636C2×C4—141no—
637C2×C4—141no—
638C2×C4—141no—
639C2×C4—141no—
640C2×C4—141no—
641C2×C4—141no—
642C2×C4—141no—
643C2×C4—141no—
644C2×C4—284no—
645C2×C4—284no—
646C2×C4D7×C22⋊C412yes—
647C2×C4D7×C22⋊C412yes—
648C2×C4#645012yes—
649C2×C4C2×D4×D711yescharacteristic
650C2×C4C2×D4×D711yescharacteristic
651C2×C4C2×#115911yescharacteristic
652C2×C4C2×Q8×D711yescharacteristic
653C2×C4#655411yescharacteristic
654C2×C4#655411yescharacteristic
655C8—41no—
656C8—41no—
657C8—41no—
658C8—41no—
659C8—142no—
660C8—142no—
661C8—281no—
662C8—281no—
663C7#2250911yescharacteristic, complemented, Sylow
664C22—22no—
665C22—22no—
666C22—22no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22C2×D7×C22⋊C411yescharacteristic
672C22C2×#645011yescharacteristic
673C22#9020711yescharacteristic
674C22D7×#13111yescharacteristic
675C22D7×#13111yescharacteristic
676C22D7×#13111yescharacteristic
677C22#9044111yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—41no—
682C4—41no—
683C4—74no—
684C4—142no—
685C4—142no—
686C4—142no—
687C4—142no—
688C4—281no—
689C4—281no—
690C4—281no—
691C4#9028911yescharacteristic
692C4#9028911yescharacteristic
693C4#9032311yescharacteristic
694C4#9032311yescharacteristic
695C2—42no—
696C2#1173132111yescharacteristic
697C2D7×#40811yescharacteristic
698C2#1173610811yescharacteristic
699C2#1173652111yescharacteristic
700C2#1173652311yescharacteristic
701C2#1173680411yescharacteristic
702C2#1173680511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC7×#1798C2
prime radicalC24×C7C22×C4
cosocleC22×C4×C7C24
hypercenter#1798D7
hypocenterC7#22509
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#89600C2semidirect
3. C2×#89602C2semidirect
6. #11728227C2semidirect
7. #11728226C2semidirect
12. #11726374C2semidirect
13. #11726373C2semidirect
14. #11726373C2semidirect
15. #11726373C2semidirect
134. C22⋊(C7⋊C8)Q8semidirect
663. C7#22509semidirect

Maximal subgroups

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

subgroupindex
C2×#902082
C2×#896002
C2×#896022
C7×#17982
#117293362
#117282272
#117282262
#117276632
#117276622
#117276612
Dic7×C22⋊C82
#117263742
#117263732
#225097